GNSS Navigation in Difficult Environments - PANG - Parthenope

UNIVERSITA’ DEGLI STUDI DI NAPOLI ”PARTHENOPE” SCUOLA DI DOTTORATO Dottorato in Scienze Geodetiche e Topografiche XXVI Ciclo

Tesi di Dottorato

GNSS Navigation in Difficult Environments: Hybridization and Reliability

Ciro Gioia

Tutore Prof. Salvatore Gaglione

Coordinatore del corso di dottorato Prof. Lorenzo Turturici

Supervisore Aziendale PhD. Daniele Borio

Aprile 2014

Contents 1 Introduction 1.1 Background . . . . . . . . . . . 1.2 Previous Work and Limitations 1.3 Objectives . . . . . . . . . . . . 1.4 Thesis Outline . . . . . . . . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

2 Principles of Satellite Navigation 2.1 GNSS Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 GNSS Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 GNSS Observables . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 GNSS Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Navigation Solution Estimation . . . . . . . . . . . . . . . . . . . . . 2.2.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Least Squares Method . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Position Computation using Pseudorange . . . . . . . . . . . . 2.2.4 Velocity Computation using Doppler measurements . . . . . . 2.2.5 PVT Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Geometrical Aspects . . . . . . . . . . . . . . . . . . . . . . . 2.3 Reliability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Traditional RAIM . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Reliability Testing (Global Test, Local Test) . . . . . . . . . . 2.3.3 Statistical Reliability (Internal Reliability, External Reliability) 2.4 Fault Detection and Exclusion . . . . . . . . . . . . . . . . . . . . . 2.4.1 Geometry and Correlation check . . . . . . . . . . . . . . . . . 2.4.2 Observation Subset Testing . . . . . . . . . . . . . . . . . . . 2.4.3 Forward-Backward . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 The Danish Method . . . . . . . . . . . . . . . . . . . . . . . 2.5 Multi-constellation navigation and GNSS extension . . . . . . . . . . 2.5.1 Multi-constellation navigation (GLONASS and Galileo) . . . . 2.5.2 GNSS Augmentation . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Local GNSS augmentation: pseudolites . . . . . . . . . . . . ii

3 3 9 11 13 17 17 18 21 23 28 28 30 31 34 36 40 41 44 47 49 50 51 54 56 57 59 61 64 65

3 GNSS Navigation: the multi-constellation opportunity 3.1 GPS Galileo multi-constellation . . . . . . . . . . . . . . . . . . . . 3.1.1 Galielo measurements analysis . . . . . . . . . . . . . . . . . 3.1.2 Galileo only positioning performance first PVT . . . . . . . 3.1.3 GPS/Galileo multi-constellation opportunity . . . . . . . . . 3.1.4 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Urban Navigation multi-constellation opportunity GPS/GLONASS 3.2.1 GPS/GLONASS multi-constellation . . . . . . . . . . . . . 3.2.2 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

4 Pseudolite Positioning 4.1 Synchronous pseudolite navigation . 4.1.1 Double Differences Approach 4.1.2 Simulated Approach . . . . . 4.2 Asynchronous RSSI Positioning . . .

103 . 103 . 106 . 110 . 115

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

5 Results - Testing and Analysis 5.1 Urban Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Static Campaign . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Kinematic Test . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 High Sensitivity solution . . . . . . . . . . . . . . . . . . . . 5.1.4 Main results for the urban scenarios . . . . . . . . . . . . . . 5.2 Indoor Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Indoor High Sensitivity solution . . . . . . . . . . . . . . . . 5.2.2 Indoor navigation asynchronous pseudolite solution, control point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Calibration Stage for the corridor test . . . . . . . . . . . . . 5.2.4 Corridor test: results . . . . . . . . . . . . . . . . . . . . . 5.2.5 Indoor navigation using asynchronous pseudolite system, repeatability test . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6 Calibration Stage for repeatability test . . . . . . . . . . . . 5.2.7 Repeatability test results analysis . . . . . . . . . . . . . . .

69 69 70 80 89 92 93 96 102

119 . 119 . 120 . 135 . 142 . 145 . 146 . 146 . 149 . 152 . 154 . 157 . 158 . 161

6 Conclusions and future work 169 6.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Bibliography

175

iii

List of Figures 1.1

Flow chart of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1 2.2 2.3 2.4

GPS Ground Control Segment (GCS), available at gps.gov . . . . . Orbital error component . . . . . . . . . . . . . . . . . . . . . . . . GNSS Error Sources . . . . . . . . . . . . . . . . . . . . . . . . . . ENU frame, the origin is arbitrarily fixed to a point on the Earth surface; the X-axis points toward the East; the Y-axis points toward the North; the Z-axis points upward along the ellipsoid normal . . . Position Algorithm Flow Chart . . . . . . . . . . . . . . . . . . . . Velocity algorithm work flaw . . . . . . . . . . . . . . . . . . . . . . Type I Error α and Type II Error β in an One Tailed Test . . . . . Horizontal and Vertical Protection Level . . . . . . . . . . . . . . . Non-Central Chi-Square Density Functions in Global Testing . . . . Density Function of the normalized residual in the Local Test . . . Slope geometric interpretation . . . . . . . . . . . . . . . . . . . . . ARP geometric interpretation . . . . . . . . . . . . . . . . . . . . . Subset Testing workflow . . . . . . . . . . . . . . . . . . . . . . . . Forward Backward workflow . . . . . . . . . . . . . . . . . . . . . . Danish method workflow . . . . . . . . . . . . . . . . . . . . . . . . The navigation gap from [1] . . . . . . . . . . . . . . . . . . . . . . Schematic representation of the proximity principle adopted by the IMES navigation system. The receiver estimates its position as the position of the closest transmitter. From [2] . . . . . . . . . . . . .

2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17

3.1

3.2

. 18 . 26 . 28

. . . . . . . . . . . . .

32 37 40 43 45 47 49 53 54 55 57 59 66

. 68

Equipment used to collect GPS and Galileo observables, Septentrio PolarRxS receiver [3] and Javad RingAnt-G3T [4] placed on the rooftop of the European Microwave Signature Laboratory (EMSL) in the Joint Research Centre (JRC) premises in Ispra. . . . . . . . . . . 71 Schematic representation of the algorithm developed for determining PR and PR-rate residual errors . . . . . . . . . . . . . . . . . . . . . 72 iv

3.3

3.4

3.5 3.6

3.7

3.8

3.9

3.10 3.11

3.12

3.13

3.14

Mean and the standard deviation of Galileo PR errors as a function of satellite elevation and of Carrier-to-Noise power spectral density ratio (C/N0 ). The error decreases when satellite elevation and C/N0 increase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean and the standard deviation of Galileo PR-rate errors as a function of satellite elevation and of C/N0 . The error decreases when satellite elevation and C/N0 increase. . . . . . . . . . . . . . . . . . Galileo E1 SD error as a function of C/N 0 . . . . . . . . . . . . . . Mean and the standard deviation of Galileo (E1BC) and GPS (L1) PR errors as a function of satellite elevation and of C/N0 . Galileo error parameters are almost halved with respect to GPS. . . . . . . Mean and the standard deviation of Galileo (E1BC) and GPS (L1) PR-rate errors as a function of satellite elevation and of C/N0 . The two systems has similar performance, Galileo improvements in term of PR-rate are less evident than in PR case. . . . . . . . . . . . . . Mean and Standard Deviation of Galileo (E1BC) and (E5a) PR errors as a function of satellite elevation and of C/N0 . A performance degradation is observed in the Galileo E5a measurements, this degradation was not expected but a similar phenomenon was observed for GIOVE measurements. . . . . . . . . . . . . . . . . . . . . . . . . . Mean and the standard deviation of Galileo (E1BC) and (E5a) PR errors as a function of satellite elevation and of C/N0 . The PR-rate errors obtained from the two frequencies are characterized by similar performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galileo PR error distribution, the measurements have Gaussian distribution centered araund zero. . . . . . . . . . . . . . . . . . . . . Horizontal position errors of the Galileo only positioning, using E1 and E5a measurements. The clouds are very similar: slight improvements can be noted when Galileo E1BC measurements are used confirming the results obtained in the measurement domain. . . . . . . Vertical position error of the Galileo only positioning, using E1 and E5a measurements, as a function of time. The two lines are very close, only slight differences can be noted confirming the results obtained in the horizontal plane. . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal position error of the Galileo only and and GPS (with a limited DOP). The Galileo cloud is significantly reduced with respect to the GPS one. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galileo (E1bc) and GPS (with a limited DOP) horizontal position error (upper box), HDOP values (middle box) and HDOP differences (lower box) as a function of the time epoch. . . . . . . . . . . . . . v

. 74

. 75 . 76

. 77

. 77

. 78

. 79 . 80

. 81

. 85

. 86

. 86

3.15 Horizontal position errors for Galileo Iono-free combination. The solutions are centered around the true position and a linear trend is observed due to the poor geometry as in the single frequency cases . . 87 3.16 Horizontal position error as a function of the time epoch for Galileo E1BC, E5a and Iono-free configuration (upper box). Horizontal position error as a function of the time epoch for Galileo E1BC, E5a and Iono-free configuration (lower box) . . . . . . . . . . . . . . . . . . . 87 3.17 Galileo (E1BC) and GPS horizontal velocity error as a funciton of the time epoch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.18 Vertical velocity errors as a function of the time epoch, for GPS Galileo E1BC and Galileo E5a configurations. . . . . . . . . . . . . . 88 3.19 Schematic representation of the algorithm developed for determining position and velocity errors using multi-constellation GPS/Galileo measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.20 GPS and GPS/Galileo horizontal position error as a function of the time epoch (upper box). GPS and GPS/Galileo vertical position error as a function of the time epoch (middle box). Number of visible GPS/Galileo satellites (lower box). . . . . . . . . . . . . . . . . . . . 91 3.21 GPS and GPS/Galileo horizontal velocity error as a function of the time epoch (upper box). GPS and GPS/Galileo vertical velocity error as a function of the time epoch (lower box) . . . . . . . . . . . . . . . 92 3.22 GPS/GLONASS multi-constellation PVT algorithm flaw chart . . . . 94 3.23 Reference trajectory followed by the user during the urban test. A topographical approach is used for generating a reference solution, the trajectory considered has a polygonal shape, whose vertexes are surveyed by a total station. . . . . . . . . . . . . . . . . . . . . . . . 95 3.24 Reference Solution obtained trrough a topographic survey. . . . . . . 96 3.25 Equipment: NovAtel FlexPak-G2 single frequency receiver and Antcom Active L1/L2 antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.26 Pedestrian test carried out in Centro Direzionale of Naples typical example of urban canyon. The total duration of the test is about 30 minutes the total distance travelled is about 2.5 km. . . . . . . . . . . 98 3.27 Solution availability as a function of time for GPS only and GPS/GLONASS multi-constellation solutions. . . . . . . . . . . . . . . . . . . . . . . . 99 3.28 GPS and GPS/GLONASS multi-constellation horizontal position errors as function of time (upper box). GPS and GPS/GLONASS multi-constellation vertical position errors as function of time (lower box). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 vi

3.29 Horizontal (upper box) and vertical (lower box) errors as a function time. Comparison between configurations adopting altitude aiding and base-line configurations. The vertical component of the solution mainly takes advantage of aiding, because the equation adopted properly represents the slow altitude variations. . . . . . . . . . . . . 101 3.30 Horizontal (upper box) and vertical (lower box) errors as a function of time. Comparison between GPS/GLONASS base-line configuration and configuration adopting altitude aiding and configuration adopting both aiding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.1 4.2 4.3

4.4 4.5 4.6 4.7

4.8

4.9

5.1 5.2 5.3

Schematic representation of the architecture of the pseudolite system. View of the rover Fasttrax receiver which is able to jointly process GPS and pseudolite signals. . . . . . . . . . . . . . . . . . . . . . . . Experiment conducted in a large (7 m × 10 m) meeting room. Four pseudolites were placed at the corners while the antenna of the reference receiver was installed approximately in the centre of the room. . Local reference frame established for the tests conducted in the large meeting room. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation scenario adopted to investigate the properties of the PR double differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated PR double differences when considering the simulation scenario in Figure 4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Double differences of the PR collected from the four pseudolites using two u-blox receivers. Meeting room, first data collection campaign, repeatability test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Double differences of the PR collected from four pseudolites using two u-blox receivers. Meeting room, second data collection campaign, repeatability test. During the first 60 seconds, reference and rover receivers were kept in a zero-base line configuration. . . . . . . . . . . Position solution obtained using corrected PR measurements where initial synchronization biases were removed exploiting the zero-base line configuration adopted during the first 60 seconds of the test. When the user start moving, synchronization corrections were no longer valid and the position solution diverged. . . . . . . . . . . . . .

104 106

107 108 111 112

113

114

115

Antenna placed on the roof of the PANG (PArthenope Navigation Group) laboratory building, at Centro Direzionale of Naples (Italy) . 121 Horizontal scatter of the base-line configuration compared with that of the Danish method. . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Horizontal scatter of the base-line configuration compared with that of the Subset test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 vii

5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18

5.19 5.20

5.21

5.22 5.23

Horizontal scatter of the base-line configuration compared with that of the Forward-Backward scheme. . . . . . . . . . . . . . . . . . . . . 125 Horizontal solutions provided by the configuration using the different Receiver Autonomous Integrity Monitoring (RAIM) schemes. . . . . . 126 Detailed view of the horizontal error pertaining to the three best configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Danish and base-line vertical errors as a function of the local time. . . 128 Subset and base-line vertical errors as a function of the local time. . . 128 Forward-Backward and base-line vertical errors as a function of the local time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Vertical error pertaining to the six configurations using the three different RAIM schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Danish method horizontal and vertical velocity error as a function of local time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Subset test horizontal and vertical velocity error as a function of local time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Forward-Backward horizontal and vertical velocity error as a function of local time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Horizontal and vertical velocity errors for the trhee RAIM schemes . . 133 Number of the PRs excluded by the three RAIM algorithms plotted as a function time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Number of the PR rate measurements excluded by the three RAIM algorithms considered. . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Pedestrian test carried out on 21st June 2012 around 10:00 am in Centro Direzionale of Naples (Italy), a typical example of urban canyon.135 Sky plot pertaining an epoch where only three GPS satellites were available and the solution was obtained exploiting aiding information. Geometrically, the pseudo-measurement can be interpreted as a satellite at the zenith. . . . . . . . . . . . . . . . . . . . . . . . . . 138 Horizontal and vertical positition error of the configurations considered without RAIM application. . . . . . . . . . . . . . . . . . . . . . 139 Horizontal and vertical errors for base-line configurations with and without RAIM, considering only reliable epochs and using the NovAtel OEM615 receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Horizontal and vertical errors for the configurations with RAIM each configuration is analyzed in the relative reliable epochs and using Novatel OEM615 receiver. . . . . . . . . . . . . . . . . . . . . . . . . 141 Horizontal (upper box) and vertical (lower box) errors as a functin of time using u-blox receiver without RAIM application. . . . . . . . . . 143 Horizontal (upper box) and vertical (lower box) errors as a function of time using the u-blox receiver with RAIM application. . . . . . . . 144 viii

5.24 Horizontal (upper box) and vertical (lower box) errors as a function of time using the u-blox receiver. Performance conparison between configuration with and without RAIM shows the advantages of the use of the quality checks and of aiding. . . . . . . . . . . . . . . . . . 145 5.25 Equipment used for indoor positioning: a u-blox LEA-6T single frequency High-Sensitivity (HS) Global Positioning System (GPS) receiver and a GPS antenna. The test was carried out in the corridor of the first floor of a large office building in the JRC premises (Ispra, Italy) on July 2013. Several control points were placed in the corridor for performance evaluation. . . . . . . . . . . . . . . . . . . . . . . . 147 5.26 Indoor GNSS navigation solution. Position fixes obtained using the measurements from a HS Global Navigation Satellite System (GNSS) receiver. Although the measurements were taken indoors, position fixes are only occasionally inside the building seleceted. . . . . . . . . 148 5.27 Universal Software Radio Platform (USRP) pseudolites. Two configurations used for signal transmission. A passive GNSS antenna was initially used for signal transmission as indicated in a). To limit the transmit power, a second configuration, with the transmit antenna removed was adopted b) . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.28 Location of the control points and of the three USRP pseudolites . . . 151 5.29 Control point distances from the different pseudolites . . . . . . . . . 152 5.30 Estimated C/N0 values as a function of the control point location. . . 153 5.31 Calibration results interpolating C/N0 values as a function of distance.153 5.32 Estimated C/N0 values as a function of time. The measurements presented were used for demonstrating Received Signal Strength Indicator (RSSI) positioning. . . . . . . . . . . . . . . . . . . . . . . . . 155 5.33 Horizontal position estimates obtained using an RSSI based algorithm.156 5.34 North coordinate evolution as a function of time. The red dotted line indicates the position of the control points. . . . . . . . . . . . . . . . 157 5.35 Calibration results interpolating C/N0 values as a function of distance considering different power parameters, Ki . Meeting room tests. . . . 159 5.36 Calibration results interpolating C/N0 values as a function of distance considering a single power parameter, K. Meeting room tests. . . . . 160 5.37 Estimated C/N0 values as a function of time. The measurements were used for Received Signal Strength (RSS) positioning. . . . . . . 161 5.38 Position estimates obtained using the RSS algorithm and processing raw C/N0 measurements. . . . . . . . . . . . . . . . . . . . . . . . . . 162 5.39 Estimated C/N0 values as a function of time. Filtered C/N0 measurements using a Butterworth filter of order 13. . . . . . . . . . . . . 163 ix

5.40 Power Spectral Densitys (PSDs) of the C/N0 measurements and transfer function of the Butterworth filter used to pre-process raw observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.41 Position estimates obtained using filtered C/N0 measurements. . . . . 5.42 Position estimates obtained using filtered C/N0 measurements, each lap is analyzed separately. Lap 3 is considered separately in Figure 5.43 in order to better investigate the impact of loss of lock. . . . . . 5.43 Effect of the loss of lock of one pseudolite signal in the position estimates obtained using filtered C/N0 measurements. Third lap. . . . . 5.44 Position solution in the WGS84 absolute coordinate system. Meeting room, repeatability test. . . . . . . . . . . . . . . . . . . . . . . . . .

x

164 164

165 166 167

List of Tables 1.1

Average signal attenuation for different material. . . . . . . . . . . . .

2.1

Four outcomes for making a decision. The decision can be either correct (correctly reject or retain null) or wrong (incorrectly reject or retain null). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 GPS Galileo and GLONASS Differences . . . . . . . . . . . . . . . . 61

2.2 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 4.1

8

Coordinates of the antenna placed on the rooftop of the EMSL in the JRC premises in Ispra . . . . . . . . . . . . . . . . . . . . . . . . . . 70 IOV E1BC PR error parameters . . . . . . . . . . . . . . . . . . . . . 74 GPS (L1) and Galileo (E1BC) PR errors statistics . . . . . . . . . . . 75 IOV E1BC PR-rate error parameters . . . . . . . . . . . . . . . . . . 76 GPS (L1) and Galileo (E1BC) PR-rate error statistics . . . . . . . . . 78 E1bc and E5a PR error statistics . . . . . . . . . . . . . . . . . . . . 79 E1BC and E5A PR Rate error statistics . . . . . . . . . . . . . . . . 79 E1BC and E5a Galileo Only position error statistics . . . . . . . . . . 82 GPS Limited DOP and Galileo horizontal position error parameters. . 83 Galileo Iono-free position error statistics . . . . . . . . . . . . . . . . 84 Horizontal velocity error statistics for GPS Limited DOP, Galileo E1bc and Galileo E5a configurations. . . . . . . . . . . . . . . . . . . 84 Vertical velocity error statistics for GPS, Galileo E1BC and Galileo E5a configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Horizontal and vertical position error statistics for GPS and GPS/GALILEO multi-constellation positioning. . . . . . . . . . . . . . . . . . . . . . 91 Horizontal and vertical velocity error statistics for GPS and GPS/Galileo multi-constellation velocity solution. . . . . . . . . . . . . . . . . . . . 92 Solution availability values of the configurations considered. . . . . . 98 Horizontal and vertical error statistics for GPS and GPS/GLONASS multi-constellation solutions. . . . . . . . . . . . . . . . . . . . . . . . 99 Location of the four pseudolites and Master Control Statio (MCS) used for the meeting room tests. . . . . . . . . . . . . . . . . . . . . . 107 xi

4.2 4.3

Location of the control points placed in the meeting room. . . . . . . 109 Location of the Master Pseudolite (MPL) for the second data collection campaign performed in the meeting room. . . . . . . . . . . . . . 113

5.1 5.2 5.3 5.4

Coordinates of the antenna placed on the roof of the PANG laboratory120 Solution Availability and Reliable Availability of the position. . . . . 122 Solution Availability and Reliable Avaliability of the velocity solution. 123 Statistical position error parameters: Root Mean Square (RMS) and maximum errors for both horizontal and vertical components. . . . . 126 Statistical position error parameters: RMS and maximum errors for both horizontal and vertical components. . . . . . . . . . . . . . . . . 131 Solution Availability and Reliable Availability of the position using Novatel OEM625 receiver . . . . . . . . . . . . . . . . . . . . . . . . . 136 Statistic parameters of the errors for the base-line configurations without RAIM application. . . . . . . . . . . . . . . . . . . . . . . . . . . 138 GNSS performance in the kinematic test with RAIM, using Novatel OEM615 receiver and considering only reliable epochs . . . . . . . . . 140 Statistical parameters of horizontal and vertical errors for the configurations with RAIM using NovAtel OEM615 receiver and considering only reliable epochs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Solution Availability and Reliable Availability of the position using the u-blox receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Statistical parameters of the horizontal and vertical errors for the configurations without RAIM using the u-blox receiver. . . . . . . . . 143 Statistical parameters of horizontal and vertical errors for the configurations with RAIM using u-blox receiver, considering only reliable solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Statistical parameters of horizontal and vertical errors for the aided configurations using u-blox receiver, considering only reliable solutions 145 Coordinates of control points placed on the corridor of the first floor of the building selected for the data collection. . . . . . . . . . . . . . 148 Pseudolite coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Parameters for RSSI positioning obtained through calibration. . . . . 154 Power parameters and path loss exponent for the meeting room experiments considering different received power levels. . . . . . . . . . 158 Power parameter and path loss exponent for the meeting room experiments considering a single, K. . . . . . . . . . . . . . . . . . . . . 159

5.5 5.6 5.7 5.8 5.9

5.10 5.11 5.12

5.13 5.14 5.15 5.16 5.17 5.18

xii

List of Acronyms AAIM Aircraft Autonomous Integrity Monitoring AGC Automatic Gain Control ARP Approximate Radial-error Protected BOC Binary Offset Carrier BPSK-R Binary Phase Shift Keying with Rectangular spreading symbols bps bits per second C/A Coarse/Acquisition CDMA Code Division Multiple Access C/N0 Carrier-to-Noise power spectral density ratio COTS Commercial Off-the-Shelf DGPS Differential GPS DIA Detection Identification and model Adaptation DVB-T Digital Video Broadcasting - Terrestrial DNS Decca Navigation System DoD Department of Defense DOP Dilution Of Precision DSSS Direct Sequence Spread Spectrum ECEF Earth Centered Earth Fixed EDOP East DOP EGNOS European Geostationary Navigation Overlay Service EMSL European Microwave Signature Laboratory ENU East North Up ESA European Space Agency xiii

FD Fault Detection FDE Fault Detection and Exclusion FDI Fault Detection and Identification GAGAN GPS Aided Geo Augmented Navigation GBAS Ground Based Augmentation System GCS Ground Control Segment GGSP Galileo Geodetic Service Provider GGTO Galileo to GPS Time offset GIM Global Ionosferic Map GIOVE Galileo In-Orbit Validation Element GLONASS GLObal NAvigation Satellite System GMS Galileo Mission System GNSS Global Navigation Satellite System GPS Global Positioning System GST Galileo System Time GT Global Test GTRF Galileo Terrestrial Reference Frame HDOP Horizontal DOP HIL Horizontal Integrity Limit HPL Horizontal Protection Limit HPS High Precision navigation Signals HS High-Sensitivity ICAO International Civil Aviation Organization IMES Indoor MEssaging System IOV In Orbit Validation xiv

JAXA Japan Aerospace Exploration Agency JRC Joint Research Centre LBS Location Based Service LORAN LOng RAnge Navigation LOS Line Of Sight LS Least Squares LT Local Test MCS Master Control Statio MDB Minimum Detectable Blunder MEO Medium Earth Orbit MPL Master Pseudolite MSAS Multi-functional Satellite Augmentation System MSE Mean Squared Error NNSS Navy Navigation Satellite System NDOP North DOP P Precision PDOP Position DOP PPL Position Protection Level PPP Precise Point Positioning PPS Precise Positioning Service PRN Pseudo Random Noise PSD Power Spectral Density PVT Position Velocity Time PZ90.02 Parametrop Zemp 1990 version 2 QZSS Quasi-Zenith Satellite System xv

RAIM Receiver Autonomous Integrity Monitoring RF Radio-Frequency RMS Root Mean Square RSS Received Signal Strength RSSI Received Signal Strength Indicator SA Selective Availability SBAS Satellite-based Augmentation System SD Single Difference SDCM System of Differential Correction and Monitoring SIS Signal in Space SNAS Satellite Navigation Augmentation System SNR Signal-to-Noise Ratio SoL Safety of Life SPS Standard Positioning Service SS Space Segment SSF Space System Finland STD STandard Deviation TAI Temps Atomique International TGD Time Group Delay TTA Time To Alarm URA User Range Accuracy US User Segment USRP Universal Software Radio Platform UTC Universal Coordinate Time VDOP Vertical DOP xvi

VPL Vertical Protection Level VHF Very High Frequency WAAS Wide Area Augmentation System WARP Weighted ARP WGS84 World Geodetic System 1984 WLS Weighted LS WMSE Weighted MSE WRAIM Weighted RAIM

xvii

Acknowledgements The author would like to thank the STA Unit (Security and Technology Assessment) of the JRC (Joint Research Centre) for the valuable support and for providing the test equipment.

2

Chapter 1 Introduction In this chapter a summary of the background material used in this thesis is provided: the importance and the limitations of satellite navigation are analyzed, highlighting the difficulties of navigation in degraded scenarios such as urban canyons, dense vegetation or indoor environments. Then an overview of previous work and its limitations are introduced; the main objective of this research, i.e. the investigation of the performance of Receiver Autonomous Integrity Monitoring (RAIM) algorithms in different scenarios, is discussed. Their performance is evaluated in urban scenarios using Global Navigation Satellite System (GNSS) alone and in indoor environments using a hybrid system composed by GNSS and pseudolites .

1.1

Background

Navigation is the answer to the human needs of exploring, traveling and finding the way home. Navigation is defined as the science of determining position and direction on and near the Earth surface. The bases of such discipline are rooted on different sciences such as astronomy and mathematics and it was initially developed by sailors as a primary way to guide themselves safely to their final destinations. The devices mainly used were based on the observation of the stars such as the sextant. The development of new technologies introduced the use of different methods and source of measurements. In the first middle of XIX century Radio-Frequency (RF) signals were used to determine position and a new branch of navigation, denoted as radionavigation, was introduced. The first idea of using radio beams for navigation goes back as far as at the beginning of 1900, when Scheller proposed: “marking of ship lanes with the use of two beams, one from each of two 3

1 – Introduction

radio transmitter, which crossed each other”. The first application of this concept was in the 1925 with the “four-course-navigationsystem” used until 1978. After this milestone, several radio-navigation systems were developed such as: Decca Navigation System (DNS), able to provide radio positioning for mariners and aviators. Users were able to estimate their positions measuring time differences between the received and transmitted signals. DNS system was shut down in the spring 2000; The LOng RAnge Navigation (LORAN) system the user was able to compute its position measuring the time difference between the receipt of signals from a pair of radio transmitters. This time difference can be represented by a hyperbolic line of position, which can be plotted on LORAN time delay chart. The intersection between hyperbolic lines relative to a two piars of stations provide the user position; TRANSIT system, formally known as Navy Navigation Satellite System (NNSS), was based on the use of the Doppler frequency shift to determine the user position. TRANSIT was the first satellite navigation system and it was able to provide continuous navigation satellite service from 1964 to 1996.

With the TRANSIT development started the satellite navigation era. Since then an user equipped with a receiver has been able to determine his position using signals transmitted by a constellation of satellites. Satellite navigation has been traditionally carried out in “open sky” environments (without obstructions); these scenarios are characterized by relatively good lineof-sight signal reception conditions and a high number of visible satellites. There is however a growing need to use GNSS for a large number of problems arising in signal degraded environments such as urban canyons and indoors. The use of satellite navigation in ‘hostile’ environments promotes the development of suitable navigation techniques in order to provide seamless outdoor and indoor availability which could enable a large number of applications such as personal digital assistant location, vehicular navigation and emergency services. Navigation system performance can be analyzed in terms of: Availability defined as the percentage of time that the services of the system is usable [5]; Accuracy defined as the degree of conformance1 of an estimated or measured position with respect to the true position [5]; 1

Conformance is how well something is compliant with certain accepted standards or norms

4

1.1 – Background

Coverage defined as the surface area or space volume in which the signals are adequate to determine position within a specified level of accuracy [5]; Integrity defined as the measure of trust that can be placed in the correctness of the information supplied by a system [5].

A single GNSS operating in a degraded scenario may not satisfy one or more requirements on the aforesaid parameters; a possible approach to enhance GNSS performance in these environments is the use of a multi-constellation system, i.e. using together measurements provided by different GNSS, such as Global Positioning System (GPS), GLObal NAvigation Satellite System (GLONASS) and Galileo. GPS and GLONASS are the only two systems fully operational while Galileo is in its development phase. The algorithms and the advantages of the multi-constellation approach are detailed in the Section 2.5. Multi-constellation system provides improvements with respect to a single GNSS in signal degraded scenarios [6], so its use brings a key added value to the solution availability, especially in urban environments. Despite this advantages, it is usually not sufficient for indoor scenarios where a different approach is required. Applications performed in difficult signal conditions, where the signals are blocked or strongly attenuated, push the use of special High-Sensitivity (HS) GNSS receivers, able to track weak GNSS signals that a traditional receiver would otherwise be unable to process. HS receivers are characterized by massive parallel correlation, in this case the processing gain can be as much as 30 dB (1000 times) higher than in a standard GNSS receiver [7]. This allows the HS receiver to acquire signals and work in many places where GNSS positioning was not previously possible, even indoors and where the line-of-sight between the receiver and the satellites is obstructed [8]. HS GNSS receivers usually maintain track of weak GNSS signals extending the integration time; this technique is the key to increase sensitivity, but even if signals are weak, the receiver still needs to get a fix in a reasonable amount of time (a few seconds), so the code/frequency search space has to be reduced. This reduction could be achieved using different techniques, i.e. coarse-time assistance and finetime assistance [7]. HS receivers guarantee a more continuous solution with respect to traditional devices improving the availability of the solution. However they do not necessarily guarantee an improvement in terms of position accuracy. Due to low Signal-to-Noise Ratio (SNR) values and multipath effects, the navigation accuracy is degraded and increased measurement noise prevents high-sensitivity receivers from achieving the level of accuracy performance typical for example of high accuracy, geodetic GNSS devices [9]. As above mentioned, one of the critical parameters for navigation systems is integrity which refers to the ability of the system to provide timely warnings to users 5

1 – Introduction

when the system should not be used. In several applications, information about the reliability of the GNSS solution has great importance. For example, in integrated navigation when inertial sensors are used along with GNSS measurements, the biases of the low cost inertial sensors have to be estimated using information provided by GNSS. If the navigation solution obtained using GNSS is unreliable an erroneous calibration of the inertial sensors is performed degrading the final performance of the whole system. GNSS provide integrity information to the user via the navigation message, but this may not be timely enough for some applications. The most common anomaly sources reported during GNSS operations are related to satellite clocks Since the ground control segments of legacy GNSS do not have full time satellite visibility, an anomaly in one of the satellites could take up to a few hours to be identified and disseminated. Therefore, additional means of providing integrity are necessary. Different techniques are available to provide integrity information: Aircraft Autonomous Integrity Monitoring (AAIM) integrates the measurements obtained from GNSS receivers with information from independent on board sensors to improve integrity and availability; Ground Based Augmentation System (GBAS) is designed to improve accuracy and integrity and, hence, availability for precision approach operations according to International Civil Aviation Organization (ICAO) requirements. This technique uses local-area ground stations to monitor the satellite system status and calculate correction terms which are broadcast to the users through a Very High Frequency (VHF) communication channel; Satellite-based Augmentation System (SBAS) is a wide-area differential augmentation system, composed by a network of ground stations at known positions to monitor the ranging signals of the satellite constellation. The SBAS collects and process all the input data provided by the station network in order to compute and provide corrections with respect to the original navigation information determined using the primary constellation. In addition to this, it provides integrity bounds over a certain region. These pieces of information are broadcast to the users using geostationary satellites. Currently, three SBAS systems are fully operational, Wide Area Augmentation System (WAAS) in the U.S., European Geostationary Navigation Overlay Service (EGNOS) in Europe, and Multi-functional Satellite Augmentation System (MSAS) in Japan. Other systems such as System of Differential Correction and Monitoring (SDCM) in Russia, GPS Aided Geo Augmented Navigation (GAGAN) in India and Satellite Navigation Augmentation System (SNAS) in China are under development. Their role is to augment the performance of GNSS improving their service integrity and accuracy;

6

1.1 – Background

RAIM uses the redundancy of simultaneous measurements to check whether they are consistent or if there are erroneous observations; in the case of five received satellite signals, simple redundancy allows the receiver to detect if a satellite is transmitting inaccurate information. A minimum of six satellites is required to identify which satellite is faulty.

The first technique involves the use of additional sensors to obtain the integrity information and is usually adopted in the avionic application, GBAS and SBAS involve the use of a network of ground stations, so additional infrastructures are required. These techniques are however not able to detect local errors. For the aforesaid reasons, in this thesis the RAIM technique is adopted. It is a user level technique and is able to detect user level errors such as multipath or local interference sources. Several schemes have been proposed in order to perform a reliability analysis and quality monitoring to identify, and eventually reject, the erroneous measurements. Traditionally, interest in the position solution integrity and reliability has focused on safety-critical navigation applications such as in aviation. So, initially, RAIM was considered as a part of air navigation; hence the algorithms developed assume that navigation is performed in an open sky and only one satellite at a time transmits an erroneous signal. Most RAIM algorithms, that are currently used, were developed when only GPS was fully operating and the main application was the use of GPS as a supplementary navigation system for the en-route phase of the flight. Some important characteristics of the initial operation environment for RAIM are: only GPS was involved and no system interoperability issues were considered; the accuracy of GPS was at least an order of magnitude better than was required for the application, despite the presence of Selective Availability (SA); under nominal conditions SA was the dominant error source, which allowed an easy and simple (same for all satellites) characterization of the ranging errors and their time-correlation properties; the ranging errors from different satellites could be considered to be essentially uncorrelated.

In signal degraded environments, the hypothesis of one blunder is not sufficient; often two or more measurements are affected by gross errors. Hence the classical RAIM algorithms need to be modified to take in to account the presence of multiple blunders. However in personal applications, typically carried out in hostile environments, the usage of RAIM could be limited due to the absence of sufficient redundancy to perform statistical testing required by RAIM. Pseudo measures and 7

1 – Introduction

additional measurement sources, could be used to increase the availability of a navigation solution as well as the reliability assessment: these approaches are detailed respectively in Section 3.2 and in Section 5.1.2. In order to overcome GNSS limitations in indoor navigation, additional ranging signals transmitted from ground-based pseudolite are considered. In these scenarios, satellite signals are severely attenuated depending on the type of building materials as shown in Table 1.1 [10]. The concepts of pseudolites was proposed even before the launch of the first GPS satellites: pseudolites broadcasting GPS like signals were originally developed to test GPS receivers. Since them, several pseudolite solutions have been developed for a variety of positioning and navigation applications. Currently, a pseudolite system can be used as a local augmentation tool for GNSS positioning systems. Pseudolite systems can be divided in two main categories depending on the principle adopted for positioning. Positioning can be performed using a trilateration technique if pseudolites are synchronized and able to provide range measurements, or using the proximity principle or other techniques if asynchronous pseudolites are adopted. When the proximity principle is adopted, the user position is determined as that of transmitter associated to the strongest received pseudolite signal. Pseudolites can be considered as a technology complementary to GNSS with the potential of bringing Location Based Service (LBS) indoors. In some cases, their development is encouraged by government organizations as part of their GNSS. For example, in the latest version of the Quasi-Zenith Satellite System (QZSS) Interface Control Document the signal structure for a ground based pseudolite system called Indoor MEssaging System (IMES) is detailed. Although IMES is not a ranging systems, it is based on the proximity principle and it could be considered as a component of a hybrid system together with GNSS. Such hybrid system improves the performance

Table 1.1.

Average signal attenuation for different material.

Building Material Wood Brick Double Brick Concrete Reinforced Concrete Glass Tinted Glass Double Brick Around Concrete Sand Tiles 8

Attenuation [dB] 2.4 5.19 10.38 9.57 16.70 2.43 24.44 19.95 2 5.19

1.2 – Previous Work and Limitations

with respect to GNSS in terms of: Solution availability directly related to measurements availability; Accuracy because of positioning solutions geometry is significantly strengthened; Integrity, the increased measurements availability and so the enhanced redundancy of the system improves the detection of gross errors.

1.2

Previous Work and Limitations

Most of the RAIM research has been targeted at avionic applications requiring high levels of integrity. This topic is properly investigated in [11], where the availability of the RAIM-Fault Detection and Exclusion (FDE) function based on [12] are analyzed. In addition RAIM is evaluated and compared with conventional snapshot based techniques using measurements from a single epoch. In the literature this approach is opposed to sequential algorithms that process not only the present measurements but also the past ones. Details on how to implement Weighted RAIM (WRAIM) and how to use geometry selection to guarantee a certain level of protection are provided in [13] and the introduction of different weights for the measurements is presented. Different approaches could be adopted for quality monitoring, i.e. analyzing least squares residuals or parity vectors. In [14] a review of range-comparison, least squares residuals and parity RAIM methods is performed in order to demonstrate the equivalence of the three techniques. One of the main goals of RAIM techniques is the computation of Horizontal Integrity Limit (HIL) or Horizontal Protection Limit (HPL), which is a metric representing the radius of a circle centered on the GNSS position solution and is guaranteed to contain the user position within the specifications of the RAIM scheme considered. The HPL is calculated as a function of the RAIM threshold and the satellite geometry at the time of the measurements. Although RAIM researches mainly focused on the horizontal component, several work has been targeted at the development of algorithms for vertical guidance as in [15] and in [16]. The focus of [15] was the use of modernized GPS and new satellite navigation systems to aid air navigation in approach and landing phases. In [16], the concept of Vertical Protection Level (VPL) was investigated with specific emphasis on which VPL could be achieved with RAIM using GPS and Galileo. All the above mentioned researches were developed for open sky applications, considering only one fault on a single satellite; these approaches can not be used in signal degraded environments where the hypothesis of one blunder is not realistic: often two or more measurements are affected by gross errors and hence the approaches 9

1 – Introduction

presented in [15, 16] need to be modified. One of the most common approach to enhance RAIM performance is the introduction of additional measurements provided by other GNSS; hence the development of new GNSS, such as the European system Galileo and the Chinese Beidou and modernization of the Russian GLONASS promote the development of suitable RAIM algorithms for multi-constellation configurations as proposed in [17]. Although a solution for integrated GPS/GLONASS was proposed by [17], the analysis was carried out only simulating the performance of the two considered constellations. The multi-constellation approach promotes the investigation of different measurement weighting for RAIM purposes. In [18] the need to adapt Fault Detection (FD) and FDE algorithms are considered to take into account the characteristics of the post SA range errors and the presence of different types of satellites with different failure characteristics. The benefits of GLONASS measurements are evaluated in [19] where the main target was to test RAIM algorithms in GPS/GLONASS configurations and verify the advantages of the GLONASS inclusion with respect to the GPS only case. The performance of RAIM algorithms has been investigated also for high-precision applications with a good line of sight condition and the adoption of RAIM algorithms using carrier phase measurements has been analyzed. In [20], a new RAIM algorithm for outlier identification and rejection has been developed for aircraft precision approach and landing using carrier phase measurements. In [21] a simple but effective RAIM and fault isolation technique is presented using carrier-phase measurements with an effective floating ambiguity technique along with real-time orbit and clock corrections generated at ground network processing hubs. As mentioned before, the RAIM research has mainly focused on aircraft applications but some research activities are carried out also for marine navigation. For instance in [22] a combination of RAIM and a marine Differential GPS (DGPS) systems has been presented whereas in [23] RAIM algorithm performance is investigated using a selection of typical marine-grade GPS receivers. There is a growing need to use satellite navigation for an array of navigation problems in degraded signal environments, such as urban canyons and indoors, hence RAIM techniques have to be enhanced and, in some cases, redesigned in order to be adopted in these scenarios. Several approaches are proposed in [7], where the author assessed reliability testing and quality control procedures at the user level in poor signal conditions using HS GPS receivers. In [24] classical reliability testing was also extended by including an assessment of the redundancy and the geometry of the obtained user position solution. In [25] performance evaluation of RAIM algorithm has been carried out and the benefit of the inclusion of pseudo-measurements has been assessed.

10

1.3 – Objectives

1.3

Objectives

Erroneous measurements, that frequently occurs encountered in degraded signal environments, need to be identified and eventually rejected with appropriate reliability monitoring techniques such as RAIM. Although RAIM adds complexity to the navigation process, reliability and quality monitoring improve the accuracy of the navigation solution identifying outliers or at least providing an alarm if the solution is not reliable. So the use of a suitable technique for checking the quality of the measurements is essential. The design of a reliability test scheme is a challenging task in “hostile” environments due to: lack of measurements; presence of a multiple blunders and their large magnitudes.

RAIM techniques are essentially based on statistical tests which could be properly performed only if the assumptions about the error distributions are sufficiently valid; so the following parameters have to be carefully selected: appropriate variance model for the observables to enhance the solution estimation and reliability assessment; value of probability of false alarm used to compute the statistical test threshold in order to avoid erroneous warning; proper satellite geometry quality value involved in the detection phase.

The detection capability of RAIM algorithms has to be validated at first in the case of a single blunder and then the identification and rejection of the erroneous measurements have to be performed subsequently. Sometimes, reliability monitoring is unavailable due to insufficient redundancy. In order to increase the number of measurements different approaches are introduced in this thesis: multi-constellation system combining different GNSS as detailed in Section 2.5; pseudo-measurements introduction considering the system state dynamics as described in Section 2.5.2; use of pseudolite technologies for indoor navigation as presented in Section 5.2.

The first approach involves the use of GLONASS and Galileo along with GPS: multi-constellation improves the geometry of the system [6]. The combined use of GPS, GLONASS and Galileo provides a near two-thirds increase in the number of 11

1 – Introduction

available measurements. In hostile environments, improvements in accuracy and availability becomes more evident [25] with respect to the open sky conditions, so multi-constellation could be a suitable approach to enhance navigation performance in signal degraded environments [6]. GLONASS and Galileo are therefore used in this research as an augmentation to GPS. In the second approach, information related to the dynamics of the system are used as additional equations in the measurement model enhancing the redundancy of the system. For example in multi-constellation configurations, an equation representing the behavior of the inter-system bias could be used; i.e. in a multiconstellation approach a further unknown, representing the offset between the systems time scales, has to be included in the navigation solution. This offset could be considered constant during a brief period of time [26], so this information can be translated in an equation representing the dynamics of the unknown as detailed in Section 2.5.2. The benefits of the pseudo-measurement introduction has been demonstrated in [27]. With respect to indoor navigation, two different approaches have been considered. In the first approach, an asynchronous system based on the proximity principle and on Received Signal Strength Indicator (RSSI) positioning has been considered whereas the second technique considers a synchronized pseudolite system providing range measurements. The performance of the two configurations has been analyzed and the benefits of the combined use of GNSS and pseudolite has been evaluated with specific focus on the performance of RAIM algorithms. Due to the limitations of the literature mentioned in the previous section, the main goals of this thesis are: modify classical navigation RAIM approaches to consider the presence of multiple blunders and discuss position and velocity reliability monitoring under this condition; modification of classical parameters, such as the Approximate Radial-error Protected (ARP), to p enhance the failure detection process trough satellite geometry; the modifications suggested should weight differently measurements of different quality; development of a RAIM technique suitable for indoor navigation using high sensitivity receivers; evaluation of hybrid systems combining GNSS and pseudolite measurements; investigation of the benefit of FDE algorithms for navigation in signal degraded environments;

12

1.4 – Thesis Outline

performance assessment of the FDE algorithms for indoor navigation using a combined system composed by multi-constellation and asynchronous pseudolites ; evaluation of the enhancement provided by the inclusion of the synchronized pseudolite system in indoor navigation.

1.4

Thesis Outline

The thesis is organized in six main chapters. The remaining five chapters are briefly described below. The principles of satellite navigation are presented in Chapter 2. The main features in terms of Space, Ground and User Segments of the three GNSS considered in this thesis are illustrated along with a description of GNSS observables and their relative errors. Mathematical details of the estimation techniques used are provided. The concept and interpretation of residuals is introduced in order to clarify their use in reliability theory. Navigation algorithms are presented and a complete description of the reliability theory is provided. Classical RAIM techniques are analyzed and finally the multiconstellation approach and GNSS augmentation systems are described. In Chapter 3, the opportunity provided by the use of the multi-constellation , typically combing GPS and GLONASS or GPS and Galileo, in urban navigation is illustrated. The benefits of combined GPS/GLONASS and GPS/Galileo measurements in urban environments are discussed. Moreover, a thorough analysis of the measurements obtained from the first four Galileo In Orbit Validations (IOVs) satellites is provided. Finally, the potential of combining GPS and Galileo is discussed. In Chapter 4, a complete description of the pseudolite technology adopted for this thesis is provided. The principles of asynchronous and synchronous systems are discussed. In addition, the solution suggested for the hybrid system combining GNSS and pseudolites is presented. Finally FDE techniques are modified and applied to the hybrid system. The experimental results obtained in different scenarios are described in Chapter 5. In particular, the tests conducted can be divided in three main categories. At first, tests have been conducted in good signal conditions considering both pedestrian and vehicular dynamics to evaluate the basic performance of RAIM algorithms. The analysis has been then extended to difficult scenario

13

1 – Introduction

where HS GNSS receivers have been used along with reliability testing. Finally, indoor navigation in heavily degraded signal conditions has been carried out using pseudolites . The role of RAIM in such conditions has also been investigated. The results are analyzed in terms of accuracy, continuity and integrity. In Chapter 6, several conclusions are provided highlighting the advantages of quality control and FDE techniques in signal degraded environments. The improvements of multi-constellation approach in urban navigation are evaluated and finally the benefits of the use of a hybrid system GNSS/pseudolite are illustrated.

A flow chart highlighting the main topics of the thesis and their connections is provided in Figure 1.1 along with the relationships among the different chapters.

14

1.4 – Thesis Outline

Figure 1.1.

Flow chart of the thesis

15

16

Chapter 2 Principles of Satellite Navigation In this chapter an overview on Global Navigation Satellite System (GNSS) is provided, highlighting the importance and the principles of the satellite navigation. The architecture of the considered GNSSs is described and the operation principles of the satellite navigation are introduced. Then navigation solution is described, the estimation technique used and the Position Velocity Time (PVT) algorithms developed are analyzed. Then reliability theory is introduced, Receiver Autonomous Integrity Monitoring (RAIM) and different Fault Detection and Exclusion (FDE) techniques are discussed. The multi-constellation approach is detailed, analyzing advantages and limitations of this technique. Finally the pseudolite concept and the relative positioning methodologies are introduced.

2.1

GNSS Overview

GNSS were conceived as ranging systems from known positions of satellites, in space, to unknown positions on land and sea, as well as in air and space [28]. Hence a GNSS involves a constellation of satellites orbiting at about twenty thousand kilometers altitude over the Earth surface. The satellites continuously transmit signals that enable users to determine their three-dimensional position velocity and time synchronization with respect to Universal Coordinate Time (UTC) [28]. GNSS services, such as positioning and time synchronization, are provided with global coverage and in all weather conditions. Currently, only two systems are fully operational: the system created and realized by the U.S. Department of Defense (DoD), Global Positioning System (GPS), and system developed by the Russian Aerospace Defence Forces, GLObal NAvigation Satellite System (GLONASS). Other systems such as the European Galileo or the Chinese Beidou are in the development phase, e.g. Galielo currently (January 2014) 17

2 – Principles of Satellite Navigation

has only 4 satellites. In this research only GPS, GLONASS and Galileo are considered. All GNSS are characterized by a similar structure but with several meaningful differences. The GNSS structure and the main differences between the considered systems are analyzed in Section 2.1.1.

2.1.1

GNSS Structure

A GNSS is usually divided into three major segments: the Ground Control Segment (GCS), the Space Segment (SS) and the User Segment (US). The GCS is composed by a network of monitoring stations that store and process the signals received by the satellites. One of the main goals of the GCS is to estimate the orbit parameters, referred to as ephemerides, the satellite clock error and other parameters such as ionospheric correction. Finally the navigation messages are generated and uploaded to the satellites through ground antennas. The GCS is responsible for maintaining the satellites and their proper functioning, this includes maintaining the satellites in their proper orbital positions (this operation is referred as station-keeping) and monitoring satellite subsystem health and status. Furthermore, the GCS activates spare satellites (if available) to maintain system availability. Each system has its own control segment whose stations are strategically placed. Additional details about this topic are available in [28] and [29]. The displacement of the station composing the GPS GCS is shown in Figure 2.1. The SS consists of a constellation of artificial satellites and its functions are to transmit radio-navigation signals with a specific signal structure, and to store and

Figure 2.1.

GPS GCS, available at gps.gov

18

2.1 – GNSS Overview

re-transmit the navigation message sent by the GCS. These transmissions are controlled by highly stable atomic clocks on board the satellites. Each GNSS constellation is different and a brief description of the three constellations used in this work is provided in the following. A complete description of the SS is available on [28] and [29]. GPS constellation is defined as an Expandable 24-Slot constellation [30]. A slot is defined as the location containing at least one operational satellite. 24 slots are placed on six orbital planes, with four slots per plane. Three slots are expandable, i.e. can be occupied by two satellites in backward and forward positions with respect to the pre-defined slot location. Satellites without a predefined slot are considered surplus [30]. The right ascensions of the adjacent ascending nodes are spaced 60 degrees, the orbits are almost circular with an inclination of about 55 degrees and an average altitude of 20200 km. The orbital period is half a sidereal day1 so that the ground traces repeat each sidereal day. Currently GPS constellation is composed by 31 Medium Earth Orbit (MEO) satellites (http://www.navcen.uscg.gov). GLONASS constellation is nominally composed by 24 artificial satellites placed in three orbital planes whose ascending nodes are 120 degrees apart. There are 8 satellites per plane, separated by 45 degrees in argument of latitude. The difference in the argument of latitude of satellites in equivalent slots in two different orbital planes is 15 degrees. Each satellite is identified by its slot number, which defines the orbital plane and its location within the plane. The orbits are planned to be circular with an inclination of 64.8 degrees and an average altitude of 19100 km, corresponding to an orbital period of 11 h 15m the ground tracks repeating every 17 orbital periods [31]. Currently GLONASS constellation is composed by 29 satellites as reported on the official web site of the system http://new.glonass-iac.ru. Galileo SS will comprise 27 operational satellites, and 3 active spares, in a Walker constellation 2 . The space vehicles are displaced on three orbital planes, with a nominal inclination of 56 degrees and an average altitude of 23222 km. The satellites will be spread evenly around each plane and will take about 14 hours to orbit around the Earth, so the constellation has a repeat

1

Sidereal day is defined as the length of time which passes between a given fixed star crossing a given projected meridian. The sidereal day for the Earth is 23 h 56 m 4.1 s 2

Walker constellation is characterized by circular inclined orbits of equal altitude and inclination, the orbital planes are equally spaced around the equatorial plane and satellites are equally spaced within orbital planes

19


cycle of 10 orbits in 17 days. Currently Galileo constellation is in development phase and is composed by only 4 In Orbit Validation (IOV) satellites (http://www.satellite-navigation.eu/). The US consists of all GNSS receivers including space, air, ground and marine. Early receivers were designed for military operations, they were bulky, heavy and large compared to recent devices. A typical GNSS user device consists of mainly five components: antenna, receiver, processor, input/output, and power supply [32]. Receiver’s cost and dimensions change rapidly according to the intended application. For example, a receiver may be embedded in a cell phone like an integrated chip or it can be placed in an aircraft as a big box. The main function of the GNSS receiver is to receive and process GNSS signals, in order to determine GNSS observables and to solve the navigation equations obtaining the PVT solution. GNSS satellites broadcast signals in the L band, the signals are similar but with several meaningful differences and a brief description of the signals used by the three systems considered is provided in the following. A more extensive treatment could be find in [29] and [32]. Each GPS satellite transmits data on three frequencies: L1 1575.42 MHz, L2 1227.60 MHz and L5 1176.45 MHz. Carrier frequencies are generated by multiplying the fundamental frequency 10.23 MHz by 154, 120 and 115, respectively. All satellites broadcast different spreading sequences on a common carrier frequency using Code Division Multiple Access (CDMA) technique [33]. GPS satellite transmits signals, for civilian users on three frequencies: L1 L2C and L5, but only the L1 frequency contains the civilian Coarse/Acquisition (C/A) code. GPS satellites generate a navigation message based upon data periodically uploaded from the GCS and adds the message to a 1.023 MHz Pseudo Random Noise (PRN) C/A code, referred to as Standard Positioning Service (SPS). Each code is unique, and provides the mechanism to identify satellite in the constellation. GPS satellites broadcast also the Precision (P) code, sometimes called the Precise Positioning Service (PPS). GLONASS satellites transmit coded signals in two frequencies located on two frequency bands, 16021615.5 MHz and 12461256.5 MHz, with a frequency interval of 0.5625 MHz and 0.4375 MHz, respectively. Antipodal satellites, which are on the same orbit plane separated by 180 degrees in argument of latitude, transmit on the same frequency. Each carrier frequency is modulated by the modulo-2 summation of either a 511 kHz or 5.11 MHz PRN ranging code sequence and a 50 bits per second (bps) data signal. This 50 bps data signal contains the navigation message. Each GLONASS satellite is allocated a pair of carrier frequencies, referred to as L1 and L2, according to the following

20


equation [31]: f=

K 178.0 + 16

∗Z

(M Hz)

(2.1)

where: – K is an integer value between −7 and +12; – Z is 9 for L1 and 7 for L2. GLONASS has two levels of services the SPS and the High Precision navigation Signals (HPS). Six independent signals, in the frequency E1 (1.5591.592 MHz), E5 (1.1641.215 MHz) and E6 (1.2601.300 MHz), are transmitted by all Galileo satellites. The signals transmitted are denoted: L1F, E5a, E5b, E6C, L1P, E6P. The first four signals are open-access, while the last two are restricted-access signal encrypted using a governmental encryption algorithm. The signals are modulated using Binary Offset Carrier (BOC) techniques or Binary Phase Shift Keying with Rectangular spreading symbols (BPSK-R) the same technique used to modulate GPS and GLONASS signals. All satellites use the same carrier frequencies with different ranging codes through CDMA transmission [34].

2.1.2

GNSS Observables

GNSS receivers are able to provide three types of measurements: pseudoranges (PR), Doppler frequencies (PR-rate) and carrier phases (phase). In this research only PR and PR-rate measurements are used, thus they will be described in detail in this section. A PR represents the apparent distance between the satellite and the receiver antenna. These measurements are derived from the PRN codes, by measuring the time shift required to align the PRN code replica generated by the receiver and the one received from the satellite [28]. The aforesaid time shift scaled by the speed of light provides the PR measurement, containing the clock receiver bias (GNSS receivers are not synchronized to GNSS time) so the measurement is referred to as PR and not range. The equation of an ideal PR, ρtrue , i.e. in error-free condition, is: ρtrue = d + cdts − cdtr where d is the distance between satellite and receiver; cdtr is the receiver clock error (m);

21

(2.2)


cdts is the satellite clock error (m); c is the speed of light3 .

The measured PR is affected by various propagation and system specific errors, a brief overview of these error sources is provided in the next section. A complete treatment of each error source can be found in [29, 32, 28]. In this research, single point positioning is used and all the error terms are either modeled or neglected thus leaving four unknowns which are the three receiver coordinates, included in the d term, the clock bias the cdtr . Thus, independent GNSS navigation requires signals from at least four satellites for computation of a complete PVT, solving the system of equations Eq. (2.2). The position accuracy obtainable in single point is about 10 meters [32], if a more accurate position is required a different observable has to be used, such as phase whose equation is: λ · Φ = d + cdts − cdtr + λ · N + eorbital − dIono + dT ropo +

(2.3)

where λ is the wavelength of the carrier; Φ is the phase measurement; eorbital are the orbital error; dIono is the ionospheric error (m); dT ropo is the tropospheric error (m); contains the errors due to multipath, receiver noise and residual errors (m); N is the number of cycles in the satellite/receiver distance.

The phase measurement is more precise than PR with more than two orders of magnitude less noise [32], but implies the estimation of unknown number of carrier cycles between the satellite and the receiver, N . This cannot be determined in single point positioning [29]. The Doppler measurement is defined as the derivative of the carrier phase and represents the frequency shift due to the relative receiver-satellite motion [32]. Doppler observables scaled by λ, represent the derivative of the satellite-receiver range and can be used to compute the user velocity (considering known the satellite motion) 3

The value for c, 299792.458 m/s, was determined during the World Geodetic System 1984 (WGS84) which is the nominal source for all constants used throughout this research.

22


with a cm/s order accuracy as detailed in Section 2.2.4. The Doppler measurement equation is obtained by taking the derivative of Eq. (2.3) and can be expressed as: ˙ s − cdt ˙ r + e˙ orbital + d˙Iono + d˙T ropo + ρ˙ ρ˙ = d˙ + cdt

(2.4)

where ρ˙ is the measured range derivative, from Doppler measurements (m/s) d˙ is the range rate between the satellite and the receiver (m/s), e˙ orbital is the satellite orbital error drift(m/s); d˙Iono is the ionospheric error drift (m/s); d˙T ropo is the tropospheric error drift (m/s); ρ˙ contains the errors due to multipath error drift (m/s), receiver noise and residual errors (m/s).

2.1.3

GNSS Errors

The accuracy with which a user receiver can determine the PVT solution depends on the interaction of various factors. GNSS accuracy performance depends on the quality of the measurements as well as the broadcast navigation data. There is a number of sources of error that corrupt GNSS measurements as shown in Eq. (2.5); these error sources are briefly discussed in this section. A more comprehensive overview is found in [35], [22] and [29]. The measured PR is affected by various propagation and system specific errors, and is generally expressed by: ρ = d + cdts − cdtr + eorbital + dIono + dT ropo + ρ

(2.5)

where eorbital is the satellite orbital error (m); dIono is the ionospheric error (m); dT ropo is the tropospheric error (m); ρ contains the errors due to multipath, receiver noise and residual errors (m), as previously defined.

23


The role of the receiver and satellite clocks is very important in GNSS positioning; the receiver clock parameters have to be estimated in the navigation solution while the satellite clock errors have to be modelled and corrected. The satellite clock error is the offset between the time maintained by the atomic clocks on board the satellite and the reference system time. The GCS determines and transmits clock correction parameters to the satellites to be rebroadcast within the navigation message. These correction parameters are used by the receiver in a second-order polynomial model [33]:

cdts = af 0 + af 1 (t − toc ) + af 2 (t − toc )2 + δtr

(2.6)

where: – af 0 is the clock bias (s); – af 1 is the clock drift (s/s); – af 1 is the frequency drift (s/s2 ); – toc is the clock data reference time (s); – t is the current time epoch (s); – δtr is the correction due to relativistic effects (s). The user has to apply the relativistic correction δtr in order to account for the effects that the slight eccentricity of the satellite orbits causes. The satellite travels through different levels of gravitational potential and a change in its velocity occurs thus causing changes in the clock [32]. Due to rotation of the Earth during the time of signal transmission, a relativistic error is introduced, known as the Sagnac effect as detailed in [32] [29]. The receiver clock error is a time-varying error that affects all the range measurements in the same amount for a fixed epoch and is included as an unknown in the navigation solution in single point positioning. Its drift affects all the Doppler measurements in the same way [32] hence it is included as an unknown in velocity estimation. GNSS signals are affected by the medium through which they travel from the satellites to the receiver antenna, the signals travel through Ionosphere and Troposphere. The first one is defined as the layer extending from a height of about 50 km to about 1000 km and consists of ionized air (free electrons and ions) [28]. The presence of free electrons affects the refractive indices of the various layers of

24


the ionosphere, and thus the GNSS signals do not travel at the speed of light in the vacuum; the change in velocities ultimately results in phase advance and code delay [32]. The ionosphere effect could be reduced with different techniques, the single frequency receivers have to apply an ionospheric correction model, such as Klobuchar Ionospheric Model [36] and NeQuick Ionospheric Model [37], to remove as much as possible this effect. A complete description and comparison between the aforesaid models is provided in [37]. Multi-frequency receivers can remove the ionospheric effect using a Iono-free measurement combination as shown in Section 2.1.2 because the ionosphere is a dispersive4 medium. Using a linear combination of the observables is it possible to remove the ionospheric effect. The expression of the new observable is: PI = c1 P 1 − c2 P2

(2.7)

where P1 and P2 are the PR related to L1 and L2 frequencies, and c1 and c2 are determined to eliminate the ionospheric effect. Their expression is [28]: f12 f12 − f22 f2 c2 = 2 2 2 f1 − f2 c1 =

(2.8)

The troposphere is the atmospheric layer placed between Earth’s surface and an altitude of about 60 kilometers. The effect of the troposphere on the GNSS signals appears as an extra delay in time of flight of the signal. This delay depends on the temperature, pressure, humidity as well as the transmitter and receiver antenna locations [29]. The tropospheric error is typically divided in two components: a dry component, including about 90% of the error and highly predictable, and a wet component, including about 10% of the error and more difficult to predict. In single point positioning, tropospheric delay is usually computed using model such as the Hopfield [28] or Saastamoinen model [38]. In this research the first of the above mentioned models is used, a complete description of the models could be find in [28]. The satellite orbital errors are the difference between the true satellite positions and the computed values. Satellites ephemerides are computed and 4

In a dispersive medium the wave propagation speed and the refractive index depends on the frequency of the transmitted signal

25


up-linked by the GCS to the satellites which rebroadcast them to the user. As for the satellite clock corrections, ephemeris parameters are predicted using a curve fit by the control segment. The orbital error has three components expressed in the satellite coordinate system5 [39]: along-track, cross-track and radial as shown in Figure 2.1.3.

^

K

Cross-track ^

W

v ^

S Along-track

^

^

I

J

Figure 2.2.

^

R

Radial

Orbital error component

The range error is essentially related to the radial component, the magnitude of the ephemeris prediction error is, however, realized when the total error vector is projected onto the user Line Of Sight (LOS) unit vector. The multipath error is caused by the arrival at the receiver of the signal via multiple paths due to reflections during the signal propagation [29]. Multipath errors vary significantly in magnitude depending on the environment, satellite elevation angle, receiver signal processing, antenna gain pattern, and signal characteristics. Multipath generally causes a systematic error in the measurements and can cause the measured range to be larger or smaller with 5

Satellite Coordinate Systems, RSW moves with the satellite. The R axis points from the Earth center along the radius vector toward the satellite as it moves through the orbit. the W axis is normal to the orbital plane (usually is not aligned with the K axis), and the S axis is normal to the position vector and positive in the direction of the velocity vector. The S axis is aligned with the velocity vector only for circular orbits [39].

26


respect to the true range, depending on the phase of the reflected signal or signals [32]. Code, carrier phase and Doppler measurements can be affected by multipath phenomenon, though in different ways. In the code measurements case, multipath can vary from few meters to over one hundred meters [29] and can be much greater in situations where only the echoes are received [40]. For phase measurements, multipath is generally much smaller, it is of centimeter order. Doppler measurements are also affected by the multipath problem, Doppler measurements are the derivative of carrier phase so they are affected by the derivative of the multipath present in the phase measurements, which is usually of centimeter order; hence the multipath effect on the velocity estimation is very small [41]. The multipath error can be the dominant error in some scenarios like urban environments, this error can be mitigated by proper antenna site selection, receiver design, and error detection techniques such as RAIM and FDE. Shadowing is the excess attenuation of the direct path signal, due to the propagation through foliage or other structures. Receiver error includes the contributions from the thermal noise error and the effects of dynamic stress on the tracking loops. The magnitude of this error is dependent on the technology incorporated in a particular receiver [42]. In high quality receivers, these errors are negligible for carrier phase and a few decimeters for code phase.

The GNSS errors are schematically represented in Figure 2.3.

27


Figure 2.3.

2.2

GNSS Error Sources

Navigation Solution Estimation

GNSS positioning is based on the one-way ranging technique: the time of travel of a signal, transmitted by a satellite, is measured and scaled by the speed of light to obtain the PR whose equation is Eq. (2.2). Three-dimensional user coordinates and receiver clock offset are computed using trilateration technique and PR measurements, details on the position estimation are provided in Section 2.2.3. Doppler measurements are used to compute user velocity and clock drift of the receiver, a complete description of the algorithm used for the velocity estimation is provided in 2.2.4. In order to compute user coordinates and velocity at least four measurements from four satellites are necessary, due to the presence of bias and drift of the receiver clock as unknowns. Usually more than four measurements are available so an optimization criterion has to be adopted for the PVT estimation; details on the estimation technique adopted are discussed in Section 2.2.1

2.2.1

Estimation

Estimation is the process of obtaining a set of unknowns from a set of uncertain measurements, according to a definite optimization criterion [43]. The estimation 28

2.2 – Navigation Solution Estimation

process can be divided in two main phases represented by measurements and process model. The measurement model, also referred to as observation model, is defined as a functional relationship between the measurements and the states of the system, it is used in order to estimate the unknowns. The implicit form of the model is: f (x, z) = 0

(2.9)

where f () is the mathematical model, it is defined as a theoretical system by which one describes a set of events [44]; x is the state vector, containing the m unknowns; z is the vector containing the n observations;

From Eq. (2.9) it is possible to obtain the condition and parametric form of the measurements model: f (z) = 0 z = f (x)

(2.10)

The measurement model could be solved for the unknowns if (m >= n), if the measurements are redundant (i.e. m > n), the solution can be estimated in some optimal sense, finally if m = n the solution is unique and there is no space for optimization. The adjustment is in general meaningful only in those cases in which redundant observations are available. In a statistical sense, adjustment is a method of deriving estimates for stochastic variables and their distribution parameters from observations [44]. Least Squares (LS) is by far the most common adjustment method, it will be described in Section 2.2.2. Additional equations could be considered in order to estimate the set of unknowns even in case of measurement lack as in the Kalman filter. This estimation technique extends the concept of LS including knowledge of how the state vector evolves in time [45]. These additional equations, referred to as process model or system model, are used to predict the value of the state vector along with its covariance matrix. The process model is: ˙ x(t) = F (t)x(t) where: x˙ is the time derivative of the state vector; t is time;

29

(2.11)


F is the dynamics matrix.

A complete description of the process model and its key rule in the Kalman filter can be find in [45]. In this thesis, the equations representing the system state dynamics, are included in the measurement model as shown in Section 2.5.2. The benefits of the inclusion of these additional equations are evaluated in Section 2.5.2.

2.2.2

Least Squares Method

The most common adjustment method used in geomatic is LS, its introduction is attributed to C.F. Gauss and its first application was on an astronomical problem [44]. LS adjustment could be divided into two groups of adjustment techniques the first one is the LS adjustment with conditions only, presented in Section 2.2.2, and the second one is the LS adjustment with conditions and constraints detailed in Section 2.5.2. The optimization criterion adopted by the LS method is the minimization of the residuals defined as: r=z−H ·x ˆ (2.12) where: H is the design matrix or geometry matrix, containing the geometry of the observations with respect to the state vector, it is used to project measurements into the vector state space; x ˆ is the estimated state.

A cost function could be introduced: J = rT W r

(2.13)

where W is the weighting matrix representing the different accuracy of the measurements. Assuming uncorrelated measurements with standard deviation σn , W is a diagonal matrix expressed by:   1/σ12 0 ... 0  0 1/σ22 . . . 0    W =  .. (2.14)  .. . .  . . . 0  0 0 . . . 1/σn2 Replacing Eq. (2.12) in the expression of the cost function 2.13, you can obtain: J = (z − H · x ˆ)T W (z − H · x ˆ) 30

(2.15)


To obtain an optimal estimate of the states, the cost function expressed in Eq. (2.15) has to be minimized: dJ =0 dˆ x d (z − H · x ˆ)T W (z − H · x ˆ) =0 dˆ x d(zT W z − zT W Hˆ x − HT x ˆT W z + x ˆT H T W Hˆ x) =0 dˆ x

(2.16)

Using matrix calculus rules, the following derivative can be computed: d zT W z =0 dˆ x d −zT W Hˆ x = −zT W H dˆ x d −H T x ˆW z = −H T W z = −zT W H dˆ x d x ˆT H T W Hˆ x = 2ˆ xT H T W H dˆ x

(2.17)

replacing the previous expression in Eq. (2.16): − 2zT W H + 2ˆ xT H T W H = 0 −1 T x = HT W H H Wz

(2.18)

The second equation in Eq. (2.18) is the LS solution; its variance/covariance matrix Cxˆ can be easily obtained, applying the variance law propagation to Eq. (2.18): Cxˆ = H T W H

−1

H T W Cz W H H T W H

−1

(2.19)

where Cz is the variance/covariance matrix of the measurements.

2.2.3

Position Computation using Pseudorange

In this section, the algorithm employed to compute receiver position using PRs is described. The algorithm is developed in East North Up (ENU)6 frame which is illustrated in 31


Figure 2.4. ENU frame, the origin is arbitrarily fixed to a point on the Earth surface; the X-axis points toward the East; the Y-axis points toward the North; the Z-axis points upward along the ellipsoid normal

Figure 2.4. As shown in Eq. (2.2), PRs are affected by several errors as detailed in Section 2.1.3, applying all the corrections described and including all the residual errors in the term ρ the PR equation becomes: ρ = d + cdtr + ρ where d is the satellite receiver distance which expression is: p d = (ES − ER )2 + (NS − NR )2 + (US − UR )2 6

(2.20)

(2.21)

ENU is a coordinate frame fixed to the Earth surface, based on the WGS84. ENU origin and axes are defined as the following: the origin is arbitrarily fixed to a point on the Earth surface; the X-axis points toward the East; the Y-axis points toward the North; the Z-axis points upward along the ellipsoid normal.

32


where ES , NS , NS are the satellite coordinates expressed in the ENU frame, computed using ephemeris as detailed in [32]; ER , NR , NR are the receiver coordinates expressed in the ENU frame.

Measurement equation Eq. (2.20) is not linear in the unknowns, hence it has to be linearized about a nominal value, which is the current best estimate [29]. In order to linearize 2.20, it has to be expanded in Taylor series about the nominal b = [E0 , N0 , U0 , cdt0 ] truncating the expansion at the first order obtaining: position x ρ = ρ0 +

∂P R ∂P R ∂P R ∂P R |xb (E − E0 ) + |xb (N − N0 ) + |xb (U − U0 ) + |xb (cdt − cdt0 ) ∂E ∂N ∂U ∂cdt (2.22)

where ρ0 is the is the predicted PR, i.e. the PR evaluated in the approximate point x0 ; R is the the partial derivative of the PR with respect to x, evaluated in ∂P ∂x x b b. the approximate point, x

After same manipulations Eq. (2.22) can be written as: δρ = a∆x + b∆y + c∆z + ∆(cdt)

(2.23)

where s s s , b = N0d−N , c = U0d−U are the cosine directors of the vector form a = E0d−E 0 0 0 the receiver position to the satellite;

δρ = (ρ − ρ0 ) is the difference between the measured and predicted PR.

As there are k satellites, a system of k 2.23 can be written in matrix notation:      δρ1 a1 b1 c1 1 ∆E δρ2  a2 b2 c2 1      ∆N   + ρ δρ =  ..  =  .. .. .. ..    .   . . . .   ∆U  (2.24) ∆(cdt) δρk ak bk ck 1 obtaining the compact expression δρ = Hρ ∆x + ρ where 33

(2.25)


∆x is the vector containing the unknowns (∆E, ∆N, ∆U, ∆(cdt)), which has to be estimated using an estimation technique such as LS; Hρ is the geometry matrix which contains the cosine directors; ρ is the vector containing the residual errors.

Finally the receiver coordinates and the receiver clock bias can be computed as: b + ∆x x=x

(2.26)

To obtain the latitude, the longitude and the altitude of the receiver the following expression can be used [46]: ∆N RM + h ∆E λ = λ0 + (RN + h) cos ϕ h = h0 + ∆U

ϕ = ϕ0 +

(2.27)

where: ϕ0 , λ0 , h0 are the geographic coordinates of the approximate receiver position; RN is the prime vertical radius of curvature; RM is the meridian radius of curvature.

2.2.4

Velocity Computation using Doppler measurements

GNSS receivers are able to provide the Doppler measurements representing the frequency shift produced by the satellite receiver relative motion [32]. Using Doppler observables, GNSS receivers are able to compute the three-dimensional user velocity, the algorithm adopted for velocity estimation is developed in ENU frame as for the position computation. The received frequency, fR , is related to the transmitted one, fT , by the classical Doppler equation [32]: (vS − vR ) · a (2.28) fR = fT 1 − c where: vS and vR are the vectors containing respectively the satellite and receiver velocity, both referenced to a common ENU frame;

34


a is the unit vector pointing along the line of sight from the user to the satellite.

The dot product (vS − vR ) · a is the projection of the relative velocity vector along the receiver satellite direction, i.e. the range rate. The Doppler shift produced by the relative motion can be easily obtained: ∆f = fr − ft = ft

(vS − vR ) · a c

(2.29)

Scaling the previous equation by the wavelength, λ, the expression of the range rate is obtained: d˙ = −λ∆f (2.30) The measured range rate, P˙R, is affected by the receiver clock drift, so the measurement is called PR rate expressed by the following formula: P˙R = −λ fˆR − fˆT (2.31) where: fˆR is the received frequency related to the ideal received frequency by the relation: fˆR = fR + ∆fR . ∆fR is related to the drift of the user clock, and represents the rate at which the users clock is running faster or slower relative to the system time; fˆT is the actual transmitted frequency which is related to the nominal frequency by the relation:fˆT = fT + ∆fR . ∆fT is the correction determined by the GCS and broadcast within the navigation message update.

Eq. (2.31) can be rewritten considering the relation between the nominal values and the actual values of the frequencies, and considering cδt˙S = λ∆fS and cδt˙R = λ∆fR : P˙R = d˙ + cδt˙S + cδt˙R

(2.32)

Different approaches can be adopted to compute the user velocity using PR rate measurements. In this research, the approach which considers known the receiver position is adopted. This approach is immediate, P˙R is correct for the satellite clock drift, then replacing d˙ with the dot product (vS − vR ) · a yelds: P˙R = (vS − vR ) · a + cδt˙R P˙R − vS · a = −vR · a + cδt˙R

(2.33)

Introducing δ ρ˙ = P˙R − vS · a, which is the difference between the measured and the predicted psudorange rate, the previous equation becomes: δ ρ˙ = −vR · a + cδt˙R 35

(2.34)


Expanding the dot product in Eq. (2.34) yelds: δ ρ˙ = vRE a1 − vRN a2 − vRU a3 + cδt˙R

(2.35)

where: E vR , vRN , vRU are the East North and Up components of the receiver velocity;

a1 , a2 , a3 are the three components of the unit vector pointing along the line of sight from the user to the satellite.

Considering k equations, the matrix form of    δ ρ˙1 a11 δ ρ˙2  a1    2 δ ρ˙ =  ..  =  ..  .  . ak2 δ ρ˙k

Eq. (2.35) is obtained:  a12 a13 1 a22 a32 1  .. .. ..  v . . . ak2 ak2 1

(2.36)

The compact expression is: δ ρ˙ = Hρ˙ v + ρ˙

(2.37)

Finally, the user velocity and receiver clock drift can be estimated: v = HT H

2.2.5

−1

H T δ ρ˙

(2.38)

PVT Algorithms

In this section, the PVT algorithm developed considering a single satellite system is explained. The algorithm could be divided in two main blocks. The first yields position computation, the relative flow chart is shown in Figure 2.5; the second block is used for the velocity computation and the flow chart is shown in Figure 2.6. The PVT algorithms were developed in Matlab environment [27] and used to process GNSS data in a single point mode. The main inputs of the algorithm used to compute the receiver position are GNSS observables and GNSS ephemerides. The ephemerides are used to compute satellite position and velocity; different orbital propagators are implemented for the various GNSS considered, since the ephemerides are differently parameterized; additional details on this topic will be provided in Section 2.5. The GPS orbital propagator is extensively treated in [33] and [47], for GLONASS the main reference is [31] and for Galileo details are available in [34]. Raw PRs are corrected for the satellite clock error which is computed starting from ephemerides using the orbital propagator. The model adopted is shown in Eq. (2.6). 36


Figure 2.5.

Position Algorithm Flow Chart

In case of single point positioning using L1 frequency the clock error has also to be corrected for the Time Group Delay (TGD) using the following relation: cdtL1 s = cdts − tgd

(2.39)

TGD correction is broadcast within the navigation message and it is related to the E1/L1 frequency but it can be easily adapted for the other frequencies using the following formula: f 12 (2.40) tgdf 2 = 2 tgd f2 This correction term has to be applied only by single frequency users and it is due to the estimation of the satellite clock offset parameters, which are based on the effective PRN code phase as apparent with two frequency ionospheric corrections [33]. As shown in Eq. (2.6), the term cdts contains also the relativistic correction ∆trel which is computed using the expression: √ ∆trel = F · ecc a sin E (2.41) 37


where F = −4.44280763310−10 (s/m1/2 ); ecc is the orbit eccentricity; a is the orbital semi major axis; E is the eccentric anomaly of the satellites orbit.

Due to the Earth rotation during the time of signal travel, a relativistic error is introduced, known as the Sagnac effect. It can be compensated rotating satellite position according to:  corr     cos(ω ∗ Tof ) sin(ω ∗ Tof ) 0 Xs Xs  Yscorr  = − sin(ω ∗ Tof ) cos(ω ∗ Tof ) 0  Ys  (2.42) corr Zs 0 0 0 Zs where Xs , Ys , Zs are the satellite coordinate expressed in the Earth Centered Earth Fixed (ECEF)7 frame; ω is the Earth angular velocity; Tof is the time of flight, it is the difference between the reception and transmission time.

PRs are then corrected for the atmospheric effects. In this research, the model adopted for the ionosferic delay computation is the Klobuchar model. This model is implemented using 8 parameters broadcast within the GP S navigation message. Details on the Klobuchar model are available in [36] [37]. The tropospheric delay is computed using the Hophield model, a complete description of which can be found in [48]. Finally corrected PRs are used to estimate the user position; the estimation technique adopted in this thesis is a Weighted LS (WLS), and the weighting matrix is related to the satellite elevation. Accuracy of the measurements is computed using the following formula [49]: 2 2 σρ2 = σU2 RA + σIono + σT2 ropo + σM ultipath

(2.43)

where: 7

ECEF frame is centered in the center of mass of the Earth, the positive Z axis goes out the north pole. The X-Y plane will be the equatorial plane. The X axis along the prime meridian, the Y axis then set to make the system right handed.

38


σU2 RA is the User Range Accuracy (URA) related to the satellite ephemeris and clock, broadcast in the navigation message [32]; 2 σIono is the accuracy related to ionospheric delay after applying the corrections obtained using the Klobouchar model [49];

σT2 ropo is the accuracy related to tropospheric error after applying the Hopfield model corrections [49]; 2 σM ultipath is the accuracy related to the multipath error [49].

The second block of the algorithm is used to estimate user velocity as shown in Figure 2.6. The main inputs are the GNSS PR rates and GNSS ephemerides used to compute position and velocity of the satellite in the ECEF frame. The orbital propagator provides also the correction for the satellite clock drift which is obtained using the following formula derived from Eq. (2.6): cδt˙S = af 1 + 2af 2 (t − toc )

(2.44)

The raw PR rate measurements are corrected for the satellite clock error, then, as in the previous, case satellites position and velocity has to be corrected for the Sagnac effect. The PR rate is defined as the time derivative of carrier phase observable, so the main error terms affecting it (orbital, atmospheric, multipath) can be neglected because they are the derivative of the errors effecting the phase measurements. Hence no further corrections has to be applied. Finally, PR rates are used to computed receiver velocity and receiver clock drift, using a weighted LS method, in this case, the PR rate accuracy is simply assumed to be inversely proportional to sin(el), where el is the satellite elevation. The work flow of the PR rate algorithm is shown in Figure 2.6.

39


Figure 2.6.

2.2.6

Velocity algorithm work flaw

Geometrical Aspects

PVT errors depend on the measurement accuracy and on the geometry of the satellites. Considering an a priori measurement accuracy σ0 and assuming all the measurements uncorrelated and with the same accuracy, the state vector variance covariance matrix can be expressed as: P = σ02 (H T H)−1

(2.45)

The matrix (H T H)−1 is related only to the satellite position, hence it represents the geometry of the system. Since the value of such matrix is generally greater than one, the accuracy is diluted so the matrix is usually defined as Dilution Of Precision (DOP) matrix. Hence, besides measurement signal quality, positioning accuracy depends on how possible measurement errors affect the error in the position estimate. This is determined by the satellite geometry and is quantified by the DOP. A measure of the overall quality of the LS solution, σsol , can be obtained by taking the square root of the sum of the parameter estimate variances:

σsol

v u P u X 2 = tσ02 DOPk,k k=1

40

(2.46)

2.3 – Reliability Theory

where P indicates the dimension of the DOP matrix. Hence every elements of the state vector has a corresponding DOP value. In this thesis, the PVT algorithms are developed in the ENU frame and the meaningful DOP parameters are listed below: q 2 EDOP = σ02 DOP1,1 q 2 N DOP = σ02 DOP2,2 q 2 V DOP = σ02 DOP3,3 √ HDOP = EDOP 2 + N DOP 2 √ P DOP = EDOP 2 + N DOP 2 + V DOP 2

(2.47)

where East DOP (EDOP) North DOP (NDOP) and Vertical DOP (VDOP) are the Dilution Of Precision value relative to the East North Up components, respectively.

2.3

Reliability Theory

In this section basics of statistical inference and hypothesis testing are reviewed, then FDE methods for positioning are presented. Reliability can be defined in several ways: applicability of a system to its purpose as a function of time; ability of a system to guarantee the operational performance requirements under given conditions during a period of time; probability that a system carries out the operational requirements for a period of time; robustness of a device or system.

In satellite navigation, reliability is related to the probability of correct operation of the system and it is quantified using the failure probabilities of the components as a function of time [32]. Statistical tests are widely applied in different applications, they are used to compare results with a given standard. In testing, one seeks a judgment as to whether some estimator function is consistent with the assumption that the sample was drawn from a population with specified parameter values, such as Normal distribution with a given standard deviation. In order to answer to this question, hypothesis8 testing 8

A hypothesis is a statement about the probability distribution of a random variable.

41


approach could be adopted Hypothesis testing is used to make a decision between a null hypothesis9 H0 , assumed as true, and one or several alternative hypothesis10 , H1 ; this method is adopted to test a claim or hypothesis about a parameter in a population, using data measured in a sample. The four steps of hypothesis testing are: state the null hypothesis related to the value for specific parameters characterizing a population in a null hypothesis. This hypothesis is assumed true; set the criteria for a decision: this is the level of significance 11 and it is denoted by α; compute the test statistic, using a mathematical formula that allows the determination of the likelihood of obtaining sample outcomes if the null hypothesis were true; make a decision, the values of the test statistic are used to make a decision about the null hypothesis. The null hypothesis can be accepted or rejected.

Two types of potential errors are involved in a statistical test and are identified as type I and type II errors [7] [50]. A type I error is defined as the error of rejecting the null hypothesis when it is true, while a type II error is defined as the error of accepting H0 when it is actually false, and the probability of committing this type of error is denoted by β. Two alternative decisions about null hypothesis can be made with four possible outcomes. The possible outcomes of the test are summarized in Table 2.1. If the probability of both types I and II error have to be reduced. Graphical interpretation of the abovementioned parameters is provided in Figure 2.7 In Figure 2.7 the bleu area, α, represents the false alarm rate, i.e., the significance level of the test. Whereas the area β shows the probability accepting of the null hypothesis when the alternative hypothesis is and represents the probability of a missed detection. It is not possible to make both α and β arbitrarily small, i.e. decreasing the probability for a type I error increases the probability for a type II 9 The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true 10

An alternative hypothesis is a statement that directly contradicts the null hypothesis by stating that the actual value of a population parameter is less than, greater than, or not equal to the value stated in the null hypothesis. 11

Level of significance refers to a criterion of judgment upon which a decision is made regarding the value stated in a null hypothesis. The criterion is based on the probability of obtaining a statistic measured in a sample if the value stated in the null hypothesis were true.

42


Table 2.1. Four outcomes for making a decision. The decision can be either correct (correctly reject or retain null) or wrong (incorrectly reject or retain null).

Hypothesis

H0 is true

Decision Retain the null Reject the null Correct decision Con- Error Type I Signififidence level 1 − α cance level α

H0 is false

Error Type II Probability β

Correct Power of 1−β

Null Hypothesis

δ

Alternative Hypothesis

α

β

Null Hypotesis

Figure 2.7.

decision the test

Altenative Hypotesis

Type I Error α and Type II Error β in an One Tailed Test

error and vice versa. Balancing type I versus type II errors depends on the purpose of the test .

43


2.3.1

Traditional RAIM

The integrity problem is fundamental for many GNSS applications and becomes crucial for aviation, where anomalies can be caused by either the satellites or the GCS, resulting in unpredictable range errors above the operational tolerance. Hence a method to provide integrity information is needed: these reasons promoted the development of the classical RAIM algorithms. There are four main sources of integrity anomalies: system-allocated Signal in Space (SIS) aberrations, space segment allocated SIS aberrations, control segment allocated SIS aberrations, and user segment SIS aberrations [32]. Theoretical investigation of signal integrity monitoring for Safety of Life (SoL) applications has started since the first GNSS constellation become operational. In addition to provide PVT solution, GNSS has to provide timely warnings to the users when the system should not be used; this capability is referred to as the integrity of the system. Integrity is a measure of the trust that can be placed in the correctness of the solution. GNSS broadcast integrity information to the users within the navigation message, but unfortunately, this information is only available after a delay hence it is not timely enough for real time applications. The use of faulty signals may have disastrous results, for example in aviation applications. Due to inherent latency of GNSS integrity information, methods to verify integrity of the signals inside the receiver have been developed and are usually referred to as RAIM is within the receiver hence the term autonomous monitoring. The task of satisfying integrity requirements using RAIM algorithms must be functionally equivalent to independent external integrity monitors, such as Aircraft Autonomous Integrity Monitoring (AAIM), Ground Based Augmentation System (GBAS) and Satellite-based Augmentation System (SBAS). All these techniques use additional infrastructure or the information provided by external sensors [51]. RAIM algorithms are implemented within the receiver, hence are the only techniques useful to identify user level errors, such as multipath and local interference sources. For these reasons, the use of RAIM technique is investigated in this thesis. In the classical RAIM approach, measurement errors are assumed Normally distributed, such assumption is not true in degraded signal environments. If only a single blunder is present within the measurement set, methods for outlier identification work properly. However, it is more difficult to detect outliers when there are two or more of them [52]. In this thesis, positioning reliability is considered from the point of view of statistical reliability which is referred to as the capability of an estimation method to detect gross errors. The inputs to RAIM algorithm are: accuracy of the measurements; measurement geometry;

44


probabilities of false alarm and missed detection.

The outputs of the algorithm are the protection levels Horizontal Protection Limit (HPL) and Vertical Protection Level (VPL) [32]. HPL is the radius of a circle in the horizontal plane, centered at the aircraft position that is assured to contain the indicated horizontal position with the given probability of false alarm and missed detection. It is a function of the satellite geometry and the expected error characteristics, i.e., it is not affected by actual measurements. VPL is half the length of a segment on the vertical axis with center at the true position, which describes the region that is assured to contain the indicated vertical position [49]. HPL and VPL concepts of are graphically represented in Figure 2.8. RAIM goal is to protect against excessive horizontal position error which is defined

Figure 2.8.

Horizontal and Vertical Protection Level

45


as the difference between the estimated position xˆ and the true position x: ˆ−x e=x e = HT H

−1

e = HT H

−1

HT z − x

H T (Hx + ) − x −1 T −1 T e = HT H H Hx + H T H H −x −1 T T e= H H H

(2.48)

As the absolute error, which cannot be observed directly, residuals are an estimation of measurement error. Hence the residual vector r defined in Eq. (2.49) can be used for quality check of the solution. r = z − zˆ

(2.49)

where zˆ is the vector of the predicted measurements whose expression is: ˆ zˆ = H x

(2.50)

Replacing Eq. (2.50) and the expression of the LS solution Eq. (2.18) in Eq. (2.49), an expression of the residuals connected to the measurements error is obtained: ˆ r = z − Hx −1 T r = z − H HT H H z −1 T T r= I −H H H H z −1 T r = I − H HT H H (Hx + ) −1 T r = I − H HT H H

(2.51)

Two different types of RAIM methods have been developed: sequential and snapshot algorithms. The fundamental idea of sequential algorithms is the use of a history of consecutive measurements which would allow comparing navigation solutions over time in order to detect faults; the drawback of these algorithms is related to the fact that, in practice, there is a short Time To Alarm (TTA) requirement for all detected integrity faults, while actual GNSS measurement errors exhibit a high degree of correlation over longer periods (tens of seconds) [32]. Confidence bounds are formed around the position estimate based upon different subsets of the measurements and specified performance parameters. GNSS receivers 46


containing FDE algorithms, extension of RAIM, can not only detect the faulty satellite, but are able to reject it from the navigation solution, increasing the continuity of the system. These methods use a minimum of six visible satellites to identify and reject erroneous measurements, they are essentially based on statistical tests which are detailed in Section 2.3.2.

2.3.2

Reliability Testing (Global Test, Local Test)

To detect a blunder within the measurements, the residuals could be statistically tested; this procedure is performed using two different tests. The first one is carried out to verify the measurement set consistency and is called Global Test (GT), if such test fails, i.e. the measurement set is declared inconsistent, a test to identify the outlier, so called Local Test (LT), has to be performed. In a GT, the null-hypothesis assumes that the adjustment model is correct and the distributional assumptions meet reality; in the blunder-free case, the errors are assumed to be Gaussian with zero mean. The alternative hypothesis assumes that the adjustment model is not correct. In the GT, the statistical variable, D, used to test the null hypothesis, is the quadratic form of the residual, r defined in Eq. (2.12) , weighted by the weighting matrix W Eq. (2.14). D = rT W r (2.52) D follows a central chi-square distribution with m − n degrees of freedom if the observation errors are Normally distributed as N (0, Σ) as shown in Figure 2.9. The

Figure 2.9.

Non-Central Chi-Square Density Functions in Global Testing

47


parameter m − n is the redundancy of the system defined as the difference between the measurements number m and the number of the unknowns n. D is compared with a threshold, TG , which is usually related to the probability of false alarm and to the redundancy as shown below: TG = χ21−α,(m−m)

(2.53)

where the notation χ21−α,(m−m) indicates the abscissa corresponding to a probability value 1 − α of a χ2 distribution of (m − n) order. A common procedure consists of fixing α according to the application requirements and letting the threshold vary with the redundancy; a typical value for the probability of false alarm is 0.1% [53, 19]. In the GT, the decision is taken as follows: H0 : D ≤ TG H1 : D > TG

No failure Failure

(2.54)

If H0 is rejected and H1 accepted, an inconsistency in the measurement set is assumed, and the blunder should be identified and mitigated. The GT is applied to the whole set of measurements, while to identify outlier an individual measurement test has to be carried out. In this case, the test performed is the LT. In the LT, the decision variable w adopted is the vector containing the standardized residual of the ith satellite, defined as: r i i = 1, . . . , m (2.55) wi = p (Cr )ii where (Cr )ii is the ith diagonal element of the residual covariance matrix Cr . The standardized residuals are assumed to be Normally distributed Figure 2.10 and are compared with a local threshold, TL , defined as: TL = N(1−PF A /2)

(2.56)

TL is defined as the abscissa corresponding to the probability value (1 − PF A/2) of a normal distribution; the largest standardized residual exceeding the threshold is regarded as a blunder. For the LT, the decision is taken as follows: H0 : D ≤ TL H1 : D > TL

The ith measurements in not an outlier The ith measurements in an outlier

(2.57)

If H0 is rejected and H1 accepted, the measurement is flagged as blunder and could be rejected or de-weighted. The assumption of a single blunder within the measurement set is not realistic in degraded signal conditions; however, it was found that data snooping can also work with multiple blunders if it is performed iteratively [53, 25, 7]. The rejection of an observation can be repeated for that epoch until no additional outliers are identified, or until the solution is declared impossible to check. 48


Figure 2.10.

2.3.3

Density Function of the normalized residual in the Local Test

Statistical Reliability (Internal Reliability, External Reliability)

The reliability measure is used to evaluate the capability to detect outliers and assess the impact of undetectable outliers on the solution. Reliability comprises the ability of the system to detect outliers, referred to as internal reliability, and to quantify the effect of undetectable outliers on the estimated parameters, referred to as external reliability [54]. The smallest bias of the measurement, which can be detected by statistical testing is called Minimum Detectable Blunder (MDB), it is used as a measure of internal reliability [54]. Selecting non-centrality parameter based on some predefined values for α and β, the magnitude of the blunder capable of being detected can be computed as: δ (2.58) M DBi = q (Cr )i,i where δ is the non centrality parameter which depends on the given false alarm rate α and the detectability β. The MDB represents the theoretical error limit which can be detected and isolated on the ith measurement. External reliability indicates the effect of the smallest detectable bias on the estimated parameters. Assuming a bias with magnitude on the ith measurement, and that no errors are present in the 49


other measurements the external reliability e is defined as: ei = − H T W H

−1

H T W M DBi

(2.59)

H Eq. (2.25) and W Eq. (2.14) are respectively defined in Section 2.2.3 and in Section 2.2.2. External reliability tells how large the estimation errors the testing can be protect against by a test. It is also called Position Protection Level (PPL) [53]. Assuming that the first three elements of the state vector are the position coordinates; the protection level can be computed using the following formula: q P P L = e21 + e22 + e23 (2.60) In a similar way, the HPL is computed considering only the first two components of the state vector. Protection levels are not equal for different measurements, so protection levels for all measurements are computed and the largest one is selected.

2.4

Fault Detection and Exclusion

RAIM provides a method to provide integrity information, but there are more general techniques used to identify integrity monitoring techniques such as Fault Detection (FD), Fault Detection and Identification (FDI), and FDE. FD indicates that there is a violation of integrity, while FDI and FDE are processes used to identify and exclude a faulty satellite. Although FDE add complexity to the navigation algorithm, it is an essential part of navigation integrity monitoring and reliability assurance. In this research, FDE techniques are considered: they are an extension of RAIM. FDE techniques use a minimum of six visible satellites and are able to exclude outliers from the navigation solution so that operations can continue without interruption. Reliability monitoring can be performed using all type of observables: in this research only PRs and PR rates are monitored in order to reduce the error in the PVT solution in signal degraded environments. There are several approaches to providing integrity assurance of the navigation system. In this work, the main focus is on snapshot schemes using LS estimation techniques. Integrity monitoring can be easily extended when information about the dynamics of the unknowns are available as in the case of the Kalman filter. Details on the application of FDE using Kalman filter and dynamic information are available in [55] and [56]. Kalman filter could provide improvements with respect to LS techniques if the state and observation model assumptions are correct; if the equations contained within 50

2.4 – Fault Detection and Exclusion

the process model do not properly represent the dynamics of the state, a degradation of the navigation solution could be observed [27]. Erroneous assumptions about the system state dynamics could cause inconsistency between the measurements, in this case the outlier is not present in the measurement model but is due to the process model information. Therefore, reliability monitoring is essential, even in filtering adopting Detection Identification and model Adaptation (DIA) techniques as shown in [57] and [58]. User dynamics for pedestrian and vehicular navigation in urban environments, considered in this thesis, are difficult to represent due to the continuous variations of the motion, hence LS approach is preferred. This reduces the effect of an erroneous process model. The snapshot approaches to be discussed are, however, extendable for the filtering application. Before introducing the various FDE techniques developed, details about the additional checks introduced such as geometry and correlation checks are provided in Section 2.4.1. These additional tests are adopted to modify, the classical FDE techniques and to optimize their behavior for navigation in signal degraded environments.

2.4.1

Geometry and Correlation check

RAIM algorithms are based on the statistical testing procedures detailed in Section 2.3.2. The reliability of detecting outliers is highly dependent on the redundancy and the geometry in the navigation solution. RAIM is available when there is a minimum of five satellites visible with sufficiently strong geometry: redundancy is essential to permit measurement consistency checks. With only five satellites available, one outlier can be detected but it is impossible to identify which measurement is the outlier. It is also noted that more redundant measurements and stronger geometry will increase the capability of quality monitoring procedures in both detecting and identifying the outliers. RAIM performance could be evaluated in terms of reliability and separability. Reliability is the capability to detect the outliers, while separability assesses the capability to correctly identify the outlier from the measurements processed. Separability is of the upmost importance and represents the risk of incorrectly flagging a good measurement as an outlier. In cases of poor satellite geometry, the DOP could be very large and the navigation accuracy degrades; the performance of the integrity monitoring algorithms is degraded and large errors can occur before that the outliers are detected; hence before integrity monitoring application, a check is performed to screen out bad geometries, which could imply erroneous detections. In [49], the integrity requirements are demanded, both required detection probability and false alarm rate have to be met for any location and time [29]. If the satellite geometry does not guarantee 51


both specifications the solution has to be flagged as impossible to check. It should be noted that these poor detection geometry, might yield good navigation solution; however in these conditions, FDE and RAIM algorithms do not have appropriate redundancy to properly monitor the measurements, so the observations have to be screen out carefully. The first parameter adopted to evaluate the geometry detection was δHmax defined as [29]: 1 (2.61) δHmax = max HDOPi2 − HDOP 2 2 i

HDOPi2

where are the squared of the DOP associated with the n subset solution, n is the number of satellites, HDOP 2 is the HDOP computed with all satellite. A threshold is set for δHmax in accordance to the integrity specifications, if the computed value passes the threshold, the solution is declared impossible to check. A more intuitive method, equivalent to the δHmax method was proposed in [59, 29]; it is based on Approximate Radial-error Protected (ARP) defined as: ARP = SLOP Emax × TG

(2.62)

where SLOPE parameter is the ratio between the position error (horizontal or vertical) and the test statistic when a deterministic error is considered on a single measurement and stochastic perturbations are omitted [59]. Slope can be calculated from the satellite geometry and it is different for each satellite, as shown in Figure 2.11 the expression of the SLOPE for the ith satellite is [60]: q A21,i + A22,i (2.63) SLOP Ei = Si,i where A = HT H

−1

and S = I − H HT H

HT

−1

(2.64) HT

(2.65)

The satellite whose bias error causes the largest position error is the most difficult to detect and it is associated to the SLOP Emax . A geometric interpretation of the ARP parameter is provided in Figure 2.12. The classical parameter, ARP, considers all measurements with the same accuracy, in order to consider different weights for each satellite, a generalization of the ARP is considered: it is called Weighted ARP (WARP) and its expression is: W ARP = W Slopemax × TG

(2.66)

where WSlope is the weighted version of the slope parameter. A large blunder, within the measurement set, could cause abnormal residual in other 52


Figure 2.11.

Slope geometric interpretation

measurements, therefore an erroneous measurement rejection. In order to avoid erroneous rejections, a technique based on the separability concept is adopted. A parameter properly representing the separability is the correlation coefficient, γij , of the normalized residual wi Eq. (2.55) [61]: (Cr )ij γij = p (Cr )ij

(2.67)

where j ∈ {1, . . . , m} − (i) i ∈ {1, . . . , m} &

& wj > TL wj = max w

(2.68)

If there is at least one coefficient larger than a threshold, the measurement flagged by the LT is not rejected and the solution is considered unreliable. If each correlation coefficients are less then threshold, the measurement is rejected. Several FDE technique could be obtained combining GT LT geometry and separability check. In the following section the three techniques developed in this thesis will be detailed. 53


Figure 2.12.

2.4.2

ARP geometric interpretation

Observation Subset Testing

Subset testing is an FDE technique based only on GT [29, 7, 19]; it can be adopted to localize gross errors by assessing the LS residuals. However, this estimation technique may spread multiple gross errors across the whole measurement set. Hence localization of the blunders based on statistical rejection of residuals could be very difficult. A possible solution is to perform several LS adjustments using a subset of the measurements in order to find a subset from which the supposed blunders are excluded. If a measurements set is declared inconsistent, all the possible combinations of measurements are checked, i.e all the possible subsets including n + 1 to m − 1 measurements, where m is the number of measurements and the n is the number of unknowns. Only the subset that passes the GT is declared consistent and is used to compute the navigation solution; if more subsets pass the GT, the set with the minimum statistic variable and the largest number of measurements is chosen. In this technique the separability check is not performed, because standardized residuals are not analyzed. A complete scheme of the algorithm implemented 54


Figure 2.13.

Subset Testing workflow

is shown in Figure 2.13. This method is computationally heavy because all the combinations have to be checked, e.g. in case of 20 available satellite signals from three GNSS systems and 6 unknowns, it would be necessary to assess up to 988115 subsets in one epoch. 55


2.4.3

Forward-Backward

Forward-Backward is an FDE technique that involves the use of both GT and LT to identify and exclude the outlier. This method consists of two different steps [7, 19]. The first algorithm section, called Forward, is carried out to identify and exclude erroneous measurements. In the Forward phase, preliminary checks, GT, LT and separability check are used. This part of the algorithm contemplates the following steps: 1. the measurement set is preliminary tested for the integrity geometry to screen out bad geometries which could imply erroneous detections; 2. if the system has strong geometry, the GT is carried out in order to verify measurements consistency; 3. in case of GT failure, the LT is performed to identify erroneous measurements; 4. in case of failure of the LT, the separability check is carried out to avoid erroneous rejection of a good observation due to the mutual influence of the observations, if no outliers are identified the solution is declared unreliable due to contradictory results between GT and LT; 5. the measurement flagged, in the LT, as possible blunder is excluded only if it is not correlated with other measures. The forward process is performed recursively until no more erroneous measurements are found and the solution is declared reliable or unreliable. If the solution is declared reliable and k measurements are excluded (with k ≥ 2), the Backward scheme is applied to reintroduce observations wrongly excluded. The Backward procedure use only the GT. Rejected measurements are iteratively reintroduced and the GT is performed to verify the consistency of the measurement set; the observation set which passes the GT is used to compute the navigation solution in order to ensure that the order of the excluded measurements does not cause an unnecessary exclusion and to minimize the number of unnecessary exclusions. A complete scheme of the Forward-Backward technique is shown in Figure 2.14

56


Figure 2.14.

2.4.4

Forward Backward workflow

The Danish Method

An estimation technique is robust if it only marginally influenced by the presence of gross errors in the data. In this context, gross errors are defined as observations, which do not fit the stochastic model assumed for parameter estimation. The LS adjustment, as described in Section 2.2.2, is very susceptible to gross errors due to the fact that erroneous observations can lead to completely wrong results and may even prevent convergence of the adjustment. Several sophisticated statistical methods have been applied to identify gross errors in the LS adjustments. The idea of only using residuals combined with an iteration process in an automatic procedure for gross error elimination has been used by the Geodetic Institute in Denmark since long time. Such procedure was proposed by the geodesist T. Krarup around 1968 [62] and it is denoted as Danish method. It showed to be a very efficient and cheap method for blunder detection. The method is an iterative de-weighting of erroneous measurements, it is defined as an iteratively reweighted LS algorithm, used to achieve consistency between the measurements by modifying the a priori weights. 57


In this thesis, the Danish method is used for signal degraded environments in order to minimize the effect of blunders on the LS adjustment. This technique involves the use of the GT, to verify the consistency of the measurements, and the LT to identify and de-weight the outliers. As any robust estimator, it can be successful applied only if there are more good observations than outlying ones. The Danish algorithm contemplates the following steps: 1. a measurement set is checked for the geometry, as in the previous FDE techniques, in order to screen out bad geometries which could limit detection; 2. if the system has strong geometry for the detection purpose, the GT is performed to verify measurements consistency; 3. in case of GT failure, the LT is performed to identify erroneous measurements; 4. in case of failure of the LT, the separability check is carried out, to verify the correlation among the measurements and to avoid the rejection of blunder-free measurement; 5. the measurement flagged as possible blunder is de-weighted only if it is not correlated with other measurements. The variance of the suspected measurement is exponentially increased (and consequently the weight is decreased) as: 2 2 σi,j+1 = σi,0 ∗ ewi,j /TL if wi,j > TL

(2.69)

2 2 where σi,j+1 is the variance of the ith observation after j + 1 iterations, σi,0 is the a priori variance of the observation, and wi,j is the standardized residual of the ith observation after j iterations.

If the normalized residual of the ith observation does not exceed the threshold, its variance is maintained, i.e. the measurement is not de-weighted. Danish process is performed recursively until no more erroneous measurements are found and the solution is declared reliable or unreliable. The scheme of the Danish procedure is shown in Figure 2.15.

58

2.5 – Multi-constellation navigation and GNSS extension

Figure 2.15.

2.5

Danish method workflow

Multi-constellation navigation and GNSS extension

The multi-constellation approach has recently attracted increasing interest among the navigation community due to the GLONASS modernization and the development of the new systems such as Galileo and Beidou, hence the potential 102− satellites constellation offered by the combination of observations from the above mentioned systems has obtained considerable interest among the GNSS community. Significant benefits, are obtained by the navigation users from the combined use of 59


several GNSSs due to the improved reliability, availability and accuracy especially in signal degraded environments such as in urban or mountainous areas. However, the multi-constellation system raises problems that must be considered, e.g. the different time scale adopted by the systems which will be analyzed in Section 2.5.1. Several works demonstrate the potentiality of the combined use of GPS, GLONASS and Galileo measurements. In [63], the performance of the first receiver which took advantage of combined GPS GLONASS navigation was analyzed, in [64] a comprehensive study on Precise Point Positioning (PPP) using combined GPS/GLONASS dual frequency code and carrier phase observations was conducted. The major errors and reduction approaches pertaining to combined GPS/GLONASS positioning are discussed in [65]. In [66], a variety of mathematical and stochastic modeling methodologies and ambiguity resolution strategies are analyzed for the multi-constellation case. The combination of different GNSSs could be a suitable approach to improve the performance of satellite navigation in urban scenarios. Since multi-constellation system guarantees an improved satellite availability as compared to stand-alone GPS. Enhanced accuracy and continuity of the navigation solution were demonstrated in [27]. The combined use of GPS and GLONASS in a high sensitivity receiver provides an increased number of available satellites with respect to the single system case [6] and in harsher environments (C/N0 on the order of 10 dB − Hz can be processed), improvements in accuracy and availability are more apparent [9]. The benefits of the multi-constellation in terms of integrity are evaluated in [55] where a RAIM scheme along with reliability and separability measures are used to assess integrity performance levels of standalone GPS and integrated GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo systems. The improved performance of RAIM in urban environments using GPS/GLONASS combination is analyzed in [19]. In [67], the performance of the combined multi-constellation considering GPS and Galileo is evaluated in the position and velocity domain, and the first complete navigation solution using Galileo only is evaluated demonstrating the competiveness of Galileo with respect to existing GNSS systems. The benefits of the inclusion of Galileo measurements, performing a joint GPS/Galileo navigation solution are also discussed. Although the use of multi-constellation provide benefits for the users, in several situations the visible satellite number could be insufficient to obtain a position solution; because of at least five visible satellites are required to determine a position due to an offset between the time scales12 . In [26] an algorithm has been proposed to

12

In the multi-constellation case five satellite are required because the systems adopt different time scale. The difference between the time scales has to be included in the estimation process,

60


obtain a position solution with only four visible GPS/GLONASS satellites.

2.5.1

Multi-constellation navigation (GLONASS and Galileo)

GPS, GLONASS and Galileo are very similar, they are based on the same operational principle as detailed in Section 2.1, but with some meaningful differences, classifiable as: constellation, signal and reference differences as summarized in Table 2.2 Table 2.2.

Constellation

Signal

Reference

GPS Galileo and GLONASS Differences

Parameter

GPS

GLONASS

Number of SV

24 Expandable

24

6

3

3

20200 km

19100 km

23222 km

55 deg

64.8 deg

56 deg

1 Sideral Day

8 Sideral Days

1575.42 MHz, 1227.60 MHz, 1176.45 MHz

1602 + K ∗ 0.5625, 1246 + K ∗ 0.4375, TBD

10 Sideral Days 1.559-1.592 MHz, 1.559-1.592 MHz, 1.559-1.592 MHz

CDMA

FDMA

CDMA

Keplerian

ECEF

Keplerian

WGS84

PZ90.02

GTRF

GPS Time

GLONASS Time

GST

Orbital planes Orbit Altitude Orbit Inclination Ground Trak Period

Carrier Frequencies

Multiple Access Broadcast Ephemerides Reference Frame System Time

Galileo 27 Operational + 3 spares

scarifying one measurement, because no broadcast parameter can be used to align the time scales

61


GPS, GLONASS and Galileo systems adopt different coordinate frames to express the satellite and user coordinates: WGS84, Parametrop Zemp 1990 version 2 (PZ90.02) and Galileo Terrestrial Reference Frame (GTRF) whose details are in [33, 31, 34] . GPS and GLONASS reference frames are nearly coincident, but a measurement combination from both systems require a seven parameters transformation; neglecting this transformation yields a position error from a single receiver of metric order [68] the transformation between the two frame is detailed in [69]. Galileo adopted GTRF, it was developed by a consortium named the Galileo Geodetic Service Provider (GGSP) and it could be considered coincident to WGS84 the difference between the two system is in the centimeter level [34]. The most significant difference for the scope of this thesis is related to the time scale, i.e. GPS, GLONASS and Galileo adopt different reference time scales, connected with different UTC realizations: GPS time is connected withUTC maintained by the US Naval Observatory; UTC scale is connected to the astronomical definition of time by occasionally adjusting it of one second to keep the scale close to the mean solar time. GPS time scale is indeed continuous and so GPS time scale and UTC differ for an integer number of seconds (called leap seconds, currently 16). Moreover GPS time and UTC are maintained by different master clocks, producing a further difference of typically less than 100 ns; this difference is broadcast to the users in the navigation message [29] [33]. GLONASS time is based on the GLONASS Central Synchronizer time scale (analogous to the GPS master clocks) and is connected with UTC(SU). GLONASS time is adjusted by leap seconds, according to the UTC adjustments, so they do not differ for an integer number of seconds, but only for a difference of less than 1 millisecond, broadcasted in the GLONASS navigation message [31]. GPS and GLONASS time scales are connected by the following relation:

tGP S = tGLO + τr + τu + τg

(2.70)

where: – tGP S is the GPS time; – tGLO is the GLONASS time; – τr = tU T C(SU )−tGLO is broadcast within the GLONASS navigation message; – τg = tU T C(U SN O) − tGP S is broadcast within the GPS navigation message; – τu = tU T C(U SN O) − tU T C(SU ) , it is broadcast within GLONASS navigation message, but it is not an immediate parameter. 62


To perform the transformation 2.70, τu should be known, but this information is not provided in real-time. An estimation of the inter-system bias between GPS and GLONASS is broadcast as non-immediate parameter in the GLONASS almanac [31], but it does not take into account the inter-system hardware delay bias which is dependent on the specific receiver [26]. Galileo System Time (GST) is a continuous time scale maintained by the Galileo Mission System (GMS) and synchronized to the Temps Atomique International (TAI) [34]. The time difference between GPS and Galileo is broadcast within the Galileo navigation message and it is possible to align GPS and Galileo measurements with respect to a common time scale using parameters such as the Galileo to GPS Time offset (GGTO). The relationship between the two system time scales is:

GGT O = tGal − tGP S (2.71) GGT O = A0G + A1G [T OW − t0G + 604800 ((W N − W N0G ) mod64)] where: – tGal is the GST; – tGP S is the GPS system time; – A0G is the constant term of the GGTO, broadcast within the Galileo navigation message; – A1G is the rate of change of the GGTO, broadcast within the Galileo navigation message; – t0G is the reference time for GGTO; – W N is the Week Number; – TOW is the time of the week; – W N0G Week Number of the GGTO reference. Therefore, when GPS, and GLONASS or GPS and Galileo measurements are used together, the inter-system bias is included in the estimation process as unknown. The design matrix in the multi-constellation configuration could be divided in two blocks: the first block is related to the GPS measurements, as detailed in Section 2.2.5 but with an additional column of zero. The second block of the design matrix is related to the observation of the second system considered, such as GLONASS or Galileo, in this case the 4th column is zero and the 5th contains one, so the completed 63


design matrix is: 

aGP S1 aGP S2 .. .

bGP S1 bGP S2 .. .

cGP S1 cGP S2 .. .

1 1 .. .

 0 0  ..  .

  HM C =   aGLO/Gal bGLO/Gal cGLO/Gal 0 1 In the case of multi-constellation the state vector is:   ϕ  λ     x=  h   cdtR  cdtSys

(2.72)

(2.73)

where cdtR is the receiver clock offset with respect to GPS time scale, and cdtSys is the offset between the system time scales i.e. τu for GLONASS and the GGTO for Galileo.

2.5.2

GNSS Augmentation

Satellite navigation in scenarios such as urban canyons is characterized by long periods of lack of visible satellites, in order to improve the availability of positioning, additional information could be used in the estimation process. One of the methods discussed in this thesis is the conditional LS adjustment where extra conditions, representing the state dynamics, are included into the measurement model. The conditions, of course, should properly represent the behavior of the unknowns. The conditions are known with certain a priori accuracy. In this thesis two different constraint are introduced the first one is related to the altitude variation. In urban navigation, pedestrian or vehicular, the height is usually slowly varying during brief time intervals; for this reason a further equation, observing directly the altitude state, can be introduced as shown below: h i (haid − h0 ) = 0 0 1 (0)1×(n−3) (2.74) where: haid is an old estimate of the altitude, computed with low value of the corresponding state variance covariance matrix or with low VDOP; h0 is the previous altitude estimation; n is the number of the states.

64


This condition can be included in the measurement model 2.10, allowing solution with only three visible satellites for single system configuration. This aiding is also used in case of measurements sufficient to obtain the solution, to enhance the measurement model redundancy and to improve the performance of FDE techniques [70]. The second constraint introduced is related to the inter-system bias. When GPS measurements are used along with GLONASS and Galileo observables, the difference between the system time scales must be estimated, thus limiting the full use of multi-constellation, since one observation has to be sacrificed to estimate the additional unknown. The offset between the system time scales can be considered constant in a brief interval [26], hence a pseudo-measurement, observing directly cdtSys , can be introduced: h i (cdtSysaid − cdtSys0 ) = (0)1×(n−1) 1 · ∆x (2.75) where cdtSysaid is an old estimate of the parameter, computed with a low value of the corresponding state variance/covariance matrix; cdtSys0 is the previous state element.

Eq. (2.75) can be included in the measurement model 2.25, allowing a multiconstellation solution with only 4 mixed visible satellites; this aiding is also used in case of sufficient observables to enhance the measurement model redundancy as in the altitude case [27]. If both pseudo-measurements (i.e. aiding on altitude and inter-sytem bias) are used, it is possible to compute the navigation solution with only three mixed visible satellites [70].

2.5.3

Local GNSS augmentation: pseudolites

The grooving request to navigate in all environments, such as indoors, promoted the development of augmentation systems to aid or replace GNSS. GNSS navigation has gaps in several environmental as shown in Figure 2.16. On the horizontal axis of Figure 2.16 the urban/indoor and rural/open environments are represented; the vertical axis roughly represents altitude, from ground level all the way up to space. GNSS navigation cover much of this two-dimensional trade space (indicated by the solid blue shape), but it can not cover the bottom left corner. High-Sensitivity (HS) GNSS receivers have helped to reduce the size of this gap (indicated by the striped blue shape), but there still remains a gap where availability, accuracy, or reliability of GNSS by itself is not sufficient for many applications. In order to fill this gap augmentation systems have to be adopted. One of the local augmentation system complementary to GNSS is the pseudolite [71] [2]. Pseudolites are transceivers able 65


Figure 2.16.

The navigation gap from [1]

to receive and broadcast signal in different bands and using different modulation techniques, they can be used to create a local ground-based GNSS alternative. The use of pseudolites in the L1 band is of particular concern since it can create interference problems with GPS and other GNSS. The main problems related to the pseudolite network are: interference problem near-far problem

Interference problems can arise, for example, when pseudolites signals overpower the much weaker GNSS components. Three methods could be adopted to reduce interference problem [71]: Introducing a frequency offset; Using different pseudorandom noise codes; Implementing a pulsing scheme.

These could be used alone or in combination. All of them are able to reduce interference, but each one has complications in terms of receiver design, pseudolite network design, or regulatory compliance. In order to reduce interference, the pseudolite signal adopted in this thesis has a pulsing scheme. It consists of transmitting pseudolite signals only during dedicated time slots. Although a GNSS receiver is essentially blinded during the pulse, it can still operate normally during the time slots not allocated for pseudolite transmissions. This approach was adopted by [72], 66


who suggested a pulsing scheme with a 10% duty cycle, i.e. pseudolite signals were transmitted only 10% of the time. Several pulsing schemes have been proposed in the literature and an overview of the different solutions proposed can be found in [73]. The near-far problem arises when a strong pseudolite signal biases the measurements extracted from a weaker component. GNSS and pseudolite signals use Direct Sequence Spread Spectrum (DSSS) modulation schemes and a receiver is able to separate the different received components. Independent processing of the different components is performed by exploiting the orthogonality of the codes used for spreading the different signals. When a signal is significantly stronger than another, the receiver is unable to separate the different components and biases can be introduced in the range measurements. In order to receive pseudolite signals relatively few receiver modifications are required, because pseudolite signals are similar to standard GNSS ones. An important modification that could be required for the processing of pseudolites is to account for potential time scale differences. A GNSS receiver determines the user position using trilateration, as detailed in Section 2.2.5, this is possible because all the satellites are synchronized to a common time scale. Using pseudolites , location based on trilateration and travel time measurements is possible only if the pseudolites are synchronized. Pseudolites synchronization may lead to an improvement of the system complexity and to a significant deployment of the cost. Moreover, biases in the measurements could still be present due to multipath propagation. For these reasons, a second class of pseudolites operating in an asynchronous way has been recently suggested as alternative solutions to travel time measurements. Asynchronous systems could use different principles. The first solution is based on the proximity principle [74, 75]. A network of devices is deployed and each device operates independently continuously broadcasting its position. The user determines its position as that of the closest Indoor MEssaging System (IMES) transmitter. This concept has been propose by Japan Aerospace Exploration Agency (JAXA) for the development of the IMES which is an extension of the Quasi-Zenith Satellite System (QZSS) [76]. The proximity principle is illustrated in Figure 2.17. The use of IMES has been demonstrated for applications such as patient tracking in hospitals during ION GNSS 2012. The Japanese government has authorized the use of IMES operating in the GPS L1 frequency band. The second approach used for the asynchronous pseudolite system is based on the Received Signal Strength (RSS) concept. RSS is defined as the voltage measured by a receiver’s Received Signal Strength Indicator (RSSI) circuit and corresponds to the measured power on a logarithmic scale, this approach is detailed in Section 4.2.

67


Figure 2.17. Schematic representation of the proximity principle adopted by the IMES navigation system. The receiver estimates its position as the position of the closest transmitter. From [2]

68

Chapter 3 GNSS Navigation: the multi-constellation opportunity In this chapter a performance analysis of ther Galileo observables is presented; the analysis has been carried out to characterize the quality of the Galileo observables and to use their estimated accuracy1 as weight in the WLS algorithm for the navigation solution. The analysis is also useful to verify the assumption adopted for Receiver Autonomous Integrity Monitoring (RAIM) algorithms, i.e. the measurements have zero mean Gaussian distribution. The performance in the position domain of the European Global Navigation Satellite System (GNSS) and the first Galileo only complete Position Velocity Time (PVT) are analyzed. The benefits of thei9nclusion ot the Galileo measurements in multi-constellation GPS/Galileo navigation solution are evaluated. Performance is analyzed in terms of horizontal and vertical errors in the position and velocity domain. The last part of the chapter investigates the opportunity of GPS/GLONASS multiconstellation navigation in urban environments. The performance is evaluated in terms of availability and accuracy.

3.1

GPS Galileo multi-constellation

Galileo, the European GNSS, is currently in its In Orbit Validation (IOV) phase and only four satellites are available. The availability of the Galileo satellites allows researchers to investigate the potentiality of the Galileo system extending the results based on the signals broadcast by the Galileo In-Orbit Validation Element (GIOVE) satellites. Although the two GIOVE satellites (GIOVE-A and GIOVE-B) did not 1

The estimated variance of the measurements is used as weight in the Weighted LS (WLS) as shown in Section 2.2.2

69

3 – GNSS Navigation: the multi-constellation opportunity

allow the computation of the user position, it was possible to test the performance of the new acquisition and tracking algorithms designed to fully exploit the benefits of the new Galileo signals. The ranging capabilities of the Galileo experimental satellites has been investigated in [77]. The first two IOV satellites were launched in October 2011, whereas the complete constellation of the IOV was completed in October 2012. Using the signal transmitted bythe four IOV satellites, Galileo-only positioning has been possible since March 2013 when European Space Agency (ESA) started disseminating Galileo ephemerides. On 12 March 2013, ESA has announced that the first autonomous position fix using only Galileo satellite signlas was achieved. The accuracy of the fix is in the 10-meter range, fulfilling expectations since the infrastructure required by the Galileo system is only partially deployed. Since March 2013, several research groups reported successful Galileo-only positioning [78, 67]. Despite the race for demonstrating Galileo-only positioning, limited analysis has been performed to evaluate the accuracy of the measurements broadcast from Galileo satellites. In particular, ranging capabilities of the IOV satellites can be assessed employing the precise orbits determined using the approach described in [79] and available from ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex. The accuracy analysis is useful to determine the weights to use for the Galileo measurements in the GPS/Galileo multi-constellation navigation solution.

3.1.1

Galielo measurements analysis

Galileo satellites are able to provide three types of measurements: PR, Doppler meausurements and carrier phase on three different frequencies: E1 E5 and E6. In this research only PR and Doppler measurements on E1bc and E5a are considered. In order to collect Galileo and GPS observables, a Javad RingAnt-G3T was mounted on the rooftop of the European Microwave Signature Laboratory (EMSL) in the Joint Research Centre (JRC) premises in Ispra (Italy). The EMSL is the highest building of the area, hence it was selected in order to minimize multipath effects. The position of the antenna was carefully surveyed in order to obtain an accurate position to use in the algorithm detailed below; the coordinates of the antenna are reported in Table 3.1. The antenna was connected to a Septentrio PolarRxS receiver Table 3.1. Coordinates of the antenna placed on the rooftop of the EMSL in the JRC premises in Ispra

Latitude [deg] 45.810361551

Longitude [deg] 8.629943325 70

Altitude [m] 279.0016

3.1 – GPS Galileo multi-constellation

able to simultaneously collect GPS, GLONASS, Galileo and Beidou measurements on several GNSS bands. The equipment described is shown in Figure 3.1. Galileo measurements analysis has been carried out in order to characterize the quality of Galileo observables and to use its accuracy as weight in the WLS algorithm for the navigation algorithm. Performance evaluation has been carried out on the E1bc and E5a frequencies. In order to compute Galileo PR and PR rate errors for the E1 frequency, GPS and Galileo observations are used together; raw PR and PR-rate measurements are corrected for the satellite clock related errors, relativistic effects, Sagnac effect and atmospheric delays according to: S ρc = ρ + cdtsv − cTGD − cdtu + cdtsag − dI − dT − cdtGP Gal ˙ S ˙ + cdt˙ − cdtGP ρ˙ = ρ˙ + cdt˙ − cdt c

sv

u

sag

(3.1)

Gal

where ρc and ρ˙c are the corrected PR and PR-rate respectively. All the correction terms have been defined in Section 2.2.5. The flaw chart of the algorithm used to compute the PR and PR-rate errors is detailed in Figure 3.2. The main inputs of the algorithm are: GPS and Galileo precise ephemerides used to compute the satellite position, velocity and clock errors; raw GPS and Galileo observables; Global Ionosferic Map (GIM) used to compute the ionospheric delay.

GPS and Galileo measurements can be used together to estimate the navigation solution as detailed in Section 2.5.1. Using this approach the state vector contains

Figure 3.1. Equipment used to collect GPS and Galileo observables, Septentrio PolarRxS receiver [3] and Javad RingAnt-G3T [4] placed on the rooftop of the EMSL in the JRC premises in Ispra.

71


Figure 3.2. Schematic representation of the algorithm developed for determining PR and PR-rate residual errors

position, velocity and receiver clock parameters. When the user position and velocity are known, the state vector is composed only by the clock parameters: S x = cdtu , cdtGP Gal h i ˙ GP S ˙ v = cdtu , cdtGal 72

(3.2)


In this way, all the measurements are used to estimate the clock unknowns, providing a better estimation of such parameters. Galileo measurements are used to estimate ˙ S S GP the unknowns cdtGP Gal and cdtGal Due to the lack of GPS L5 measurements, a different approach is used to compute Galileo PR and PR-rate errors for the E5a frequency. Only Galileo measurements are used in this case and the state vectors are: x = cdtGal u h i (3.3) ˙ Gal v = cdtu and cdt˙Gal are the bias and the drift between receiver time and Galileo where cdtGal u u System Time (GST). E5a raw PR and PR-rate measurements are corrected for the satellite clock errors, relativistic effects, Sagnac and atmospheric effects as for E1. After computing the corrected PRs and PR-rates their residual errors are defined as: Eρ = |ρc − d| Eρ˙ = ρ˙c − d˙

(3.4)

Several weeks of data were collected using the antenna placed on the rooftop of the EMSL in the JRC premises in Ispra (Italy). Data were collected and analyzed since December 2012; in this thesis, in order to avoid repetion of results, only the results pertaining to the GPS week 1744 are presented. One week of data, on E1 and E5a frequencies, was used for the PR and PR-rate analysis and results pertaining to the IOVs are detailed below. PR and PR-rate errors are analyzed in terms of Root Mean Square (RMS), mean, maximum and STandard Deviation (STD) values. Measurements from the E1 frequency are considered as first; a comparison of the PR errors of the four IOVs is shown in Figure 3.3, the mean and the STD of the PR errors are depicted as a function of satellite elevation and Carrier-to-Noise power spectral density ratio (C/N0 ). The colored bars represent the mean of the errors while the standard deviation is represented by the black lines. For the satellite elevation, a mask angle of ten degrees is adopted whereas for the C/N0 , values lower than 35 dB-Hz are discarded. The behavior of the PR error is similar for the four IOV: the error decreases when satellite elevation and C/N0 increase. The mean error reaches a maximum value of 0.50 m for the IOVs with Pseudo Random Noise (PRN) 19. The error statistics for the four IOVs are summarized in Table 3.2. The maximum error varies from 1.86 m for satellite 12, to 2.47 m for satellite 19; the RMS values are similar for all satellites with a difference of less than 10 cm. In order to evaluate the thermal noise contribution, it is possible to use two receivers connected to the same antenna 73


Figure 3.3. Mean and the standard deviation of Galileo PR errors as a function of satellite elevation and of C/N0 . The error decreases when satellite elevation and C/N0 increase. Table 3.2.

PRN 11 12 19 20

IOV E1BC PR error parameters

MAX [m] 2.12 1.86 2.47 2.29

RMS [m] 0.31 0.35 0.37 0.35

in a zero-baseline configuration and consider Single Differences (SDs) removing all the common systematic errors [29]. The SD is defined as: SD = ρR1 − ρR2 = cdtR1−R2 + SD

(3.5)

where cdtR1−R2 is the difference between the two receivers clock, which is estimated using all the available measurements and it is removed to analyze the residual errors SD . The RMS of the SD error for the four IOVs is plotted as a function of the C/N0 in Figure 3.5. A comparison between Galileo and GPS PR errors is performed in order to obtain a complete evaluation of Galileo performance in the E1 frequency. In this case, GPS PR errors are used as refeference. In Figure 3.6, mean and STD of the PR error of the considered systems are plotted 74


Figure 3.4. Mean and the standard deviation of Galileo PR-rate errors as a function of satellite elevation and of C/N0 . The error decreases when satellite elevation and C/N0 increase.

as a function of the satellite elevation and of C/N0 . From the results it clearly emerges that Galileo PR errors (blue bars) are smaller with respect to the GPS ones (green bars). The values relative to Galileo errors are almost halved with respect to GPS. For instance, in the GPS case, the mean error reaches a maximum value of 0.88 m (for an elevation of 15 degrees) whereas for Galileo this value is limited to 0.50 m. Error statistics pertaining to GPS and Galileo PR errors are summarized in Table 3.3. An analysis, similiar to that performed for the PR errors, has been carried out on the PR-rates. First, the PR rate errors on E1 of the four IOVs are analyzed; then the performance of the European GNSS are compared with with that of GPS. As for the PRs, the error decreases when the satellite elevation and signal C/N0 increase. The error mean reaches a maximum value of 0.0162 m/s for IOV 11 with a STD equal to 0.0125 m/s. The figures of merit of the PR-rate error of the four

Table 3.3.

GPS (L1) and Galileo (E1BC) PR errors statistics

System GPS Galileo

MAX [m] 4.49 2.47 75

RMS [m] 0.84 0.34


E1 SD Error for each IOV GAL 11 GAL 12 GAL 19 GAL 20

RMS Error [m]

0.1

0.05

0 34

36

Figure 3.5.

38

40

42 44 C/N0 [db-Hz]

46

48

50

52

Galileo E1 SD error as a function of C/N 0

IOVs are summarized in Table 3.4. The four satellites are characterized by similar performance, for instance, the maximum error varies from 0.0741 m/s, for satellite 19, to 0.0955 m/s for satellite 12. The RMS errors are very close with a difference of less than 2 mm/s. As for PR, GPS and Galileo PR-rate errors are compared as a function of the satellite elevation and C/N0 in Figure 3.7. The two systems have similar performance. The improvements brought by Galileo in term of PR-rate are less evident than in the PR case. However Galileo PR-rate errors are reduced with respect to GPS, for instance the maximum is more than halved passing from 0.2772 m/s to 0.0955 m/s. Despite this results, there is only a slight improvement in terms

Table 3.4.

PRN 11 12 19 20

IOV E1BC PR-rate error parameters

MAX [m/s] 0.0911 0.0955 0.0741 0.0946 76

RMS [m/s] 0.010 0.011 0.009 0.008


Figure 3.6. Mean and the standard deviation of Galileo (E1BC) and GPS (L1) PR errors as a function of satellite elevation and of C/N0 . Galileo error parameters are almost halved with respect to GPS.

Figure 3.7. Mean and the standard deviation of Galileo (E1BC) and GPS (L1) PR-rate errors as a function of satellite elevation and of C/N0 . The two systems has similar performance, Galileo improvements in term of PR-rate are less evident than in PR case.

77


Figure 3.8. Mean and Standard Deviation of Galileo (E1BC) and (E5a) PR errors as a function of satellite elevation and of C/N0 . A performance degradation is observed in the Galileo E5a measurements, this degradation was not expected but a similar phenomenon was observed for GIOVE measurements.

of RMS errors with a difference lower than millimeter per second as detailed in Table 3.5. PR and PR rate errors on E5 are evaluated and compared with respect to the E1 case in order to have a complete analysis of the Galileo performance. The PR error mean and STD of the considered frequencies, are plotted as a function of the satellite elevation and C/N0 in Figure 3.8. Galileo E1bc and Galileo E5a PR-rate error staitstic are detailed in Table 3.6. A performance degradation is observed in the Galileo E5a measurements, the mean error passes from 0.48 m on E1bc to 0.83 m on E5a for the weakest signal conditions. This degradation was not expected but a similar phenomenon was observed by [80] and [81] for GIOVE-A measurements. The cause of this slight degradation could be the presence of residual ionospheric errors which are 1.8 times bigger on E5a than on E1 [82]. Despite the theoretical

Table 3.5.

GPS (L1) and Galileo (E1BC) PR-rate error statistics

System GPS Galileo

MAX [m] 4.49 2.47 78

RMS [m] 0.84 0.34


Table 3.6.

E1bc and E5a PR error statistics

Frequency E1 E5a

MAX [m] 2.47 3.80

RMS [m] 0.34 0.49

Figure 3.9. Mean and the standard deviation of Galileo (E1BC) and (E5a) PR errors as a function of satellite elevation and of C/N0 . The PR-rate errors obtained from the two frequencies are characterized by similar performance.

superiority of the E5a signal, performance similar to that of the E1BC signal was observed, the maximum PR error is reduced of more than one meter when moving from E5a to E1BC; also The RMS error is reduced of 15 cm. The PR-rate error mean and STD, of the considered frequencies, are plotted as a function of the satellite elevation and C/N0 in Figure 3.9.The PR-rate errors obtained from the two frequencies are characterized by similar performance, as summarized by the PR-rate error statistics detailed in Table 3.7. In order to verify the assumption, adopted for

Table 3.7.

E1BC and E5A PR Rate error statistics

Frequency E1 E5a

MAX [m/s] 0.0955 0.1097 79

RMS [m/s] 0.010 0.011


6

x 10

PR Error Distribution for E1 Frequency

4

5

Bins

4

3

2

1

0 -2.5

-2

-1.5

-1

-0.5 0 PR Error [m]

0.5

1

1.5

2

Figure 3.10. Galileo PR error distribution, the measurements have Gaussian distribution centered araund zero.

the RAIM algorithms, i.e. the measurements have zero mean Gaussian distribution, the distribution of Galileo PR errors are analyzed. PR error distribution is depicted in Figure 3.10. In order to remove the un-modeled residual systematic errors the analysis is carried out using two identical receiver connected to the same antenna performing zero base-line configuration and building the single difference observables. Figure 3.10 shows that the measurements have Gaussian distribution centered to zero, validating the assumption considered above.

3.1.2

Galileo only positioning performance first PVT

On 12th March 2013, Galileo ephemerides were broadcast for the first time allowing the analysis of Galileo only positioning. Two different PVT analyses are performed: for the first one, broadcast ephemerides are adopted and a single frequency solution is computed, using E1 and E5a separately. In order to evaluate Galileo positioning performance, Galileo only solution is compared with respect to the GPS only solution. In the second case, broadcast ephemerides are used to analyze the performance of Galileo only positioning using Iono-free combination. One week of data are used for the PVT analysis. Data were collected with a 1 Hz rate using the configuration described in Section 3.1.1. Position and velocity performance is analyzed in terms of RMS and maximum error for horizontal and vertical components. The horizontal position errors of the Galileo only positioning, using E1 and E5a measurements, are shown in Figure 3.11. The clouds are very similar: slight improvements are observed when Galileo E1 measurements are used confirming the 80


Figure 3.11. Horizontal position errors of the Galileo only positioning, using E1 and E5a measurements. The clouds are very similar: slight improvements can be noted when Galileo E1BC measurements are used confirming the results obtained in the measurement domain.

results obtained in the measurement domain; the position error statistics are summarized in Table 3.8 which shows that the RMS values of Galileo E1 horizontal and vertical errors are reduced by 25 cm with respect to the E5a case, while the maximum horizontal and vertical error are reduced of 2 m when E5a PRs are used. The vertical position errors of the Galileo only positioning, using E1 and E5a measurements, are shown in Figure 3.12. The configurations considered guarantee similar performance; the blue line representing the E1BC vertical position error and the 81


red line representing the E5a vertical position error are very close. Only slight differences can be noted confirming the results obtained in the horizontal plane. The error in the first part of the section is due to the geometry of the satellite as shown in the middle box of Figure 3.13. This error is also present in the horizontal plane, in Figure 3.11 can be noted the blue brush stroke away form the center, which corresponds to the same initial epochs. From Figure 3.12, a jump in the vertical error can be noted; this is due to the change of ephemerides set. Galileo control segment is only partially development, hence Galileo satellites can not be continuosly monitored so the ephenerides parameters in the first part of the test were degraded, when a new set of parameters were available an imporvement in the navigation solution can be noted in both horizontal and vertical channel as shown in Figure 3.13 and Figure 3.12. In order to have a complete evaluation of Galileo position performance a comparison with respect to GPS is carried out. Galileo currently has only four satellites so its position performance is strongly affected by geometry limitations; hence in order to perform a fair comparison between GPS and Galileo, similar geometry conditions are considered and the GPS satellite geometry is artificially degraded. In particular, the following approach is adopted: The Galileo only solution and its satellite geometry is computed; GPS satellites are then progressively excluded such that a geometry value similar to that of Galileo is obtained; GPS only solution is computed using the selected GPS satellites.

This process is repeated for each epoch analyzed; the two solutions are compared in the same epochs, i.e. during those epochs when the four IOVs are available. The parameter selected to quantify the geometry is the Horizontal DOP (HDOP); hence a fair comparison between the two systems is possible only for the horizontal component. Horizontal position errors for Galileo E1 and GPS (with a limited DOP) are shown in Figure 3.13. The spread of the clouds provides an immediate representation of the magnitude of the error and allows a simple comparison between GPS and Galileo performance. The Galileo cloud (blue dots) is significantly reduced with respect to the GPS one (red dots). In order to further investigate the Table 3.8.

E1BC and E5a Galileo Only position error statistics

Frequency E1 E5a

RMS[m] Horizontal Vertical 8.45 11.11 8.70 11.41 82

Max [m] Horizontal Vertical 51.71 59.74 49.57 57.37


performance of the aforesaid configurations, horizontal position errors (upper box), HDOP values (middle box) and difference between HDOP using Galileo and HDOP using GPS (lower box) are plotted as a function of time in Figure 3.14. Figure 3.14 shows that the Galileo horizontal position error (blue line) is higher than the GPS one (red line) only during the initial phase when the HDOP is higher than 3. This error corresponds to the linear trend observed in Figure 3.14 where the Galileo estimated position is far away from the central cloud corresponding to the correct position. Horizontal error parameters, such as maximum and mean, are summarized in Table 3.9, from which it emerges that in average Galileo provides a significant reduction in the position error confirming the results obtained in the measurement analysis. In particular, the mean position error is reduced by 2 meters passing from 6 m to 4 m. Galileo maximum position error exceeds the corresponding GPS value, this is due to a poor geometry and occurs in correspondence of the linear trend discussed above. In order to fully exploit the potentiality of the European GNSS, a Iono-free solution using E1 and E5a measurements combination is evaluated. Horizontal position errors for Galileo Iono-free combination is shown in Figure 3.15. The Iono-free observable is obtained in accordance with Eq. (2.7). The cloud obtained using Iono-free observables is very similar to the clouds shown in Figure 3.11, the solutions are centered around the true position and a linear trend is observed due to the poor geometry as in the single frequency cases. In order to further investigate Iono-free performance, a comparison between single frequency and Iono-free solutions is performed in Figure 3.16. In the upper box the performance is compared in the horizontal plane while the error for the vertical channel is shown in the lower box. From Figure 3.16, it emerges that the three considered configurations provide similar performance in the position domain for both horizontal and vertical components. Iono-free combination is characterized by the lowest RMS horizontal error (8.40 m) but its maximum error is also the biggest, since the removal of the first order component of the ionospheric delay is paid by the amplification of the other measurement errors which are combined [83]. For example, multipath can be amplified by a factor 3 with respect to single frequency measurements [29]. The same behavior is observed for the vertical component. Statistics relative to the horizontal and vertical components for the configuration considered are summarized in Table 3.10. In order to have a complete analysis of the Galileo PVT solution, velocity estimated using only Galileo measurements is computed and compared with respect to

Table 3.9.

GPS Limited DOP and Galileo horizontal position error parameters.

Configuration GPS Limited DOP Galileo E1

Mean[m] 6.03 3.99 83

Max [m] 38.57 51.71


Table 3.10.

Iono-Free

Galileo Iono-free position error statistics

RMS[m] Horizontal Vertical 8.40 11.06

Max [m] Horizontal Vertical 57.87 64.76

the GPS limited DOP velocity solution. Horizontal velocity error of the considered configurations, i.e. Galileo E1BC, Galileo E5a and GPS limited DOP are depicted in Figure 3.17. Galileo E1 and E5a solutions are nearly coincident, the solution provided is in the dm/s order, as expected by the literature. In the velocity domain, GPS provides the best solution, the light blue line is ever lower than the others but the difference between the two systems is of cm/s order. Statistics relative to the velocity horizontal error for the configurations considered are summarized in Table 3.11. The vertical velocity error of the considered configurations, i.e. Galileo E1bc, Galileo E5 and GPS are depicted in Figure 3.18. As in the horizontal plane also in the vertical component, GPS provides a more accurate solution with respect to the Galileo configurations. The differences in terms of RMS values between GPS and Galileo are of cm/s order as in the previous case. More evident is the degradation for the maximum value which pass form 10 cm/s for the GPS case to 50 cm/s for the Galileo ones, this is due to the poor Galileo geometry. Galileo configurations are characterized by similar performance and the differences are of mm/s in term of RMS error and cm/s order for the maximum error. Statistics of the vertical velocity error for the configurations considered are summarized in Table 3.12.

Table 3.11. Horizontal velocity error statistics for GPS Limited DOP, Galileo E1bc and Galileo E5a configurations.

Configuration GPS Limited DOP E1 E5a

RMS[m/s] 0.0271 0.0614 0.0652 84

Max [m/s] 0.3049 0.4288 0.5263


Table 3.12. Vertical velocity error statistics for GPS, Galileo E1BC and Galileo E5a configurations.

Configuration GPS E1 E5a

RMS[m/s] 0.0145 0.0834 0.0863

Max [m/s] 0.0975 0.4998 0.5620

Galileo Vertical Position Error 60 Galielo E1 Galielo E5a 50

Vertical Error [m]

40

30

20

10

0 0

0.5

1

1.5 Epoch [s]

2

2.5 4

x 10

Figure 3.12. Vertical position error of the Galileo only positioning, using E1 and E5a measurements, as a function of time. The two lines are very close, only slight differences can be noted confirming the results obtained in the horizontal plane.

85


Horizontal Error [m]

Figure 3.13. Horizontal position error of the Galileo only and and GPS (with a limited DOP). The Galileo cloud is significantly reduced with respect to the GPS one. 60 Galileo L1 GPS L1 DOP Limited

40 20 0 0

0.5

1

1.5

2

2.5 4

Horizontal DOP

x 10 15

5 0 0

Horizontal DOP Differences

Galileo L1 GPS L1 DOP Limited

10

0.5

1

1.5

2

2.5 4

x 10 0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5 4

x 10

Figure 3.14. Galileo (E1bc) and GPS (with a limited DOP) horizontal position error (upper box), HDOP values (middle box) and HDOP differences (lower box) as a function of the time epoch.

86


Figure 3.15. Horizontal position errors for Galileo Iono-free combination. The solutions are centered around the true position and a linear trend is observed due to the poor geometry as in the single frequency cases


60 Galileo E1 Galileo E5 Galileo Iono-free

50 40 30 20 10 0 0

0.5

1

1.5

2

2.5 4 x 10

Vertical Error [m]

80 Galileo E1 Galileo E5 Galileo Iono-free

60 40 20 0 0

0.5

1

1.5

2

2.5 4 x 10

Figure 3.16. Horizontal position error as a function of the time epoch for Galileo E1BC, E5a and Iono-free configuration (upper box). Horizontal position error as a function of the time epoch for Galileo E1BC, E5a and Iono-free configuration (lower box)

87


Horizontal Velocity Error 0.6 Galileo E1 Galileo E5 GPS L1 DOP Limited 0.5

Error [m\s]

0.4

0.3

0.2

0.1

0 0

0.5

1

1.5 Epoch [s]

2

2.5 4

x 10

Figure 3.17. Galileo (E1BC) and GPS horizontal velocity error as a funciton of the time epoch. Vertical Velocity Error 0.6 Galileo E1 Galileo E5 GPS L1 DOP Limited 0.4

Error [m\s]

0.2

0

-0.2

-0.4

-0.6

-0.8 0

0.5

1

1.5 Epoch [s]

2

2.5 4

x 10

Figure 3.18. Vertical velocity errors as a function of the time epoch, for GPS Galileo E1BC and Galileo E5a configurations.

88


3.1.3

GPS/Galileo multi-constellation opportunity

Galileo performance analysis demonstrated the potentiality of the European GNSS, which could become a valid alternative to GPS. Considering the high compatibility between Galileo and GPS, the European GNSS can also be adopted as aiding to the existing GNSSs. The benefits of the inclusion of Galileo measurements are evaluated computing a combined solution using GPS and Galileo together. The flaw chart of the algorithm developed for such multi-constellation navigation solution is described in Figure 3.19. One week of data are used for PVT analysis; data were collected with a 1 Hz rate using the configuration described in Section 3.1.1. Position and velocity performance is analyzed in terms of RMS and maximum error for horizontal and vertical components. The main inputs of the algorithm are the raw GNSS observables, i.e. PR and Doppler measurements, and the broadcast ephemerides used to compute satellites position, velocity and clock related errors. Raw measurements are corrected for satellite clock and atmospheric errors, specifically the Klobuchar and Hopfield models are adopted to reduce ionosphere and troposphere delays, respectively. The estimation technique used is a WLS as detailed in Section 2.2.2, the measurement models are shown in Eq. (2.25) and Eq. (2.37) respectively for PR and PR rate. The state vectors are: S S x = [∆P∆cdtGP ∆cdtGP R GAL ] ˙ S cdtGP ˙ S] v = [VcdtGP R

(3.6)

GAL

S S where x contains the receiver position ∆P and receiver clock bias ∆cdtGP ; ∆cdtGP R GAL is the difference between GPS and Galileo time scales which has to be estimate, since the Galileo to GPS Time offset (GGTO) is currently transmitted in a discontinuous ˙ S , and the drift way. v contains the receiver velocity, ∆V, receiver clock drift, cdtGP R ˙ S between GPS and Galileo time scales cdtGP GAL . The horizontal and vertical position errors of the GPS alone and GPS/Galileo joint positioning are shown separately in Figure 3.20; the joint solution is computed considering GPS/Galileo time offset as additional unknown as mentioned above. In order to present a fair comparison, the two solutions are analyzed only in the common epochs, i.e. during those epochs when at least one Galileo satellite is available. If only one Galileo satellite is available its measurements are used to estimate the GGTO parameters, hence in this case no advantages can be noted with respect ot the GPS only case. The horizontal error is depicted in the upper box of Figure 3.20, the lines representing the error behavior of the configuration considered are very close and only a slight difference can be noted. The inclusion of Galileo measurements provides a slight improvement in the horizontal solution; a slight reduction of the RMS value can be observed and a reduction of 3 meters of the maximum error is achieved. The vertical error is depicted in the central box of

89


Figure 3.19. Schematic representation of the algorithm developed for determining position and velocity errors using multi-constellation GPS/Galileo measurements.

Figure 3.20, as for the horizontal case also for the vertical component the inclusion of the Galileo observables provides only a slight improvements. The number of visible GPS/Galileo satellites varies between 7 and 15 (with a mean of 10) as shown in the lower box of Figure 3.20 for open-sky conditions. Position error statistics, for GPS 90



15 GPS/Galileo GPS

10 5 0 0

0.5

1

1.5

2

2.5

3

Vertical Error [m]

Epoch 15

GPS/Galileo GPS

10 5 0 0

0.5

1

1.5

2

2.5

3

Epoch SV Used in the Nav Sol

3.5 5 x 10

15

3.5 5 x 10 Number of IOV Number of GPS

10 5 0 0

0.5

1

1.5

2 Epoch

2.5

3

3.5 5 x 10

Figure 3.20. GPS and GPS/Galileo horizontal position error as a function of the time epoch (upper box). GPS and GPS/Galileo vertical position error as a function of the time epoch (middle box). Number of visible GPS/Galileo satellites (lower box).

and GPS/Galileo multi-constellation solution, are summarized in Table 3.13. The horizontal and vertical velocity errors for GPS and GPS/Galileo configurations are plotted in Figure 3.21. In the velocity domain the benefits of Galileo are less evident than in the position domain. This is probably due to the increased variance of the Galileo PR rate measurements highlighted in Section 3.1.1. The inclusion of Galileo measurements provides a reduction of 1 mm/s for both horizontal and vertical RMS errors and a reduction of 2 cm/s for the maximum error values as detailed in Table 3.14.

Table 3.13. Horizontal and vertical position error statistics for GPS and GPS/GALILEO multi-constellation positioning.

Frequency GPS Only GPS/Galileo

RMS[m] Horizontal Vertical 3.34 4.37 3.21 4.32 91


Horizontal Velocity Error [m/s]


0.12 GPS GPS/Galileo

0.1 0.08 0.06 0.04 0.02 0 0

0.5

1

1.5

2

2.5

3

Epoch

3.5 5 x 10

Vertical Velocity Error [m/s]

0.12 GPS GPS/Galileo

0.1 0.08 0.06 0.04 0.02 0 0

0.5

1

1.5

2 Epoch

2.5

3

3.5 5 x 10

Figure 3.21. GPS and GPS/Galileo horizontal velocity error as a function of the time epoch (upper box). GPS and GPS/Galileo vertical velocity error as a function of the time epoch (lower box) Table 3.14. Horizontal and vertical velocity error statistics for GPS and GPS/Galileo multi-constellation velocity solution.

Frequency GPS Only GPS/Galileo

3.1.4

RMS[m/s] Horizontal Vertical 0.010 0.014 0.009 0.013

Max [m/s] Horizontal Vertical 0.105 0.171 0.085 0.151

Main results

PR analysis demonstrates that IOV measurements are characterized by similar accuracies, error is of metric order. E5a signal has performance similar to that of the E1BC signal. PR-rates analysis demonstrates that the four Galileo satellites provide similar measurement accuracies and differences are of mm/s order. Galileo PR errors is halved with respect to Global Positioning System (GPS). In both position and velocity domains the comparison between Galileo and GPS demonstrates Galileo potentiality. In the velocity domain the configurations considered are characterized by similar performance with differences

92

3.2 – Urban Navigation multi-constellation opportunity GPS/GLONASS

lower than 2 cm/s. The use of multi-constellation GSP/Galileo shown only a slight reduction of maximum positioning error with respect to the GPS-only case. Galileo Iono-free combination is characterized by the lowest RMS horizontal error (8.40 m) but its maximum error is also the biggest.

3.2

Urban Navigation multi-constellation opportunity GPS/GLONASS

In signal-degraded environments such as urban canyons or mountainous areas, GNSS signals are blocked or strongly degraded by natural or artificial obstacles. The multi-constellation approach, using GPS and Galileo together as proposed in Section 3.1.3, is not useful in these scenarios because of the limited Galileo availability. Galileo has only four satellites hence the improvements provided by GPS/Galileo multi-constellation is very limited in urban scenarios. As aiding to GPS, GLObal NAvigation Satellite System (GLONASS) is currently the main candidate in a multiconstellation configuration: it is fully operational and its inclusion provids an improvement of the satellite availability. In this section the PVT algorithm developed for GPS/GLONASS multi-constellation will be introduced. The algorithm is implemented in Matlab and processes GPS and GLONASS data in single point mode. The flaw chart of the algorithm is shown in Figure 3.22. Main inputs of the algorithm are the GPS and GLONASS raw measurements, i.e. PR and Doppler shift, and the GNSS ephemerides, used to compute satellite position and velocity and clock related errors. Two different orbital propagators are implemented for the considered GNSS because the ephemerides are differently parameterized as described in Section 2.5.1. Raw measurements are corrected for satellite clock and atmospheric errors, Klobuchar and Hopfield models are adopted to reduce ionosphere and troposphere delays respectively. For GLONASS ionospheric corrections, a modified Klobuchar model is developed in order to consider the different frequencies used. The estimation technique used is the WLS detailed in Section 2.2.2; the measurement models are shown in Eq. (2.25) and Eq. (2.37) respectively for PRs and PR-rates. The state vectors are: S S x = [∆P∆cdtGP ∆cdtGP R GLO ] ˙ S] v = [VcdtGP

(3.7)

R

S where x contains the receiver position, ∆P, and receiver clock bias, ∆cdtGP . R GP S ∆cdtGLO is the difference between GPS and GLONASS time scales which has to be estimate even if a parameter to align the two time scales is broadcast within

93


Figure 3.22.

GPS/GLONASS multi-constellation PVT algorithm flaw chart

the GLONASS navigation message. The use of the broadcast parameter is not suitable for GPS/GLONASS multi-constellation navigation because the broadcast parameter does not take into account the delay introduced by the receiver on the measurements, i.e. GPS and GLONASS signal are processed using different chain within the receiver front-end, so a different delay is introduced. In order to consider S such hardware delay, ∆cdtGP GLO has to be estimated as additional unknown in the navigation solution. v contains the receiver velocity, ∆V, and receiver clock drift 94


Figure 3.23. Reference trajectory followed by the user during the urban test. A topographical approach is used for generating a reference solution, the trajectory considered has a polygonal shape, whose vertexes are surveyed by a total station.

˙ S .2 cdtGP R In order to demonstrate the opportunity offered by combining GPS and GLONASS for urban navigation, several test has been performed. The tests were carried out in Centro Direzionale of Naples (Italy), typical example of urban canyon; many GNSS signals are blocked by skyscrapers or are strongly degraded by multipath problems. The test scenario and the trajectory adopted for tests are shown in Figure 3.23. In order to verify the performance of the configuration considered a reference trajectory is adopted. A topographical approach is used for generating a reference solution, specifically the considered trajectory to travel is a polygonal, whose vertexes are surveyed by a total station (consisting of an electronic theodolite among with a distance meter). In Figure 3.24 the yellow markers are the vertexes surveyed and the total station is pointed in green (the distance between the station and the farthest vertex is about 120 m). Using range and angular measurements the vertex positions relative to the total station are computed; to frame the coordinates in an absolute reference system, two GPS geodetic receivers are placed in the area, indicated as Base 1 and 2 in Figure 3.24. Base 1 is coo located with total station, the direction Base1-Base 2 is assumed as reference for the angular measurements. To associate an epoch to each surveyed vertex, the rover receiver is equipped with an external device (a button) used to mark the transit on the vertexes. Finally the points among adjacent vertexes are obtained by linear interpolation assuming constant velocity in each segment. The position accuracy of the surveyed vertexes is of centimeter order.

2

The drift between GPS and GLONASS time scales is not included in the navigation solution, because it is neglictable due to the high stability of the time scales.

95


Figure 3.24.

3.2.1

Reference Solution obtained trrough a topographic survey.

GPS/GLONASS multi-constellation

In this section, the GPS/GLONASS multi-constellation opportunity is demonstrated in the above mentioned environment. Several GNSS configurations are considered and analyzed, differing each other for the satellite system used and for adoption of aiding. The base-line configurations are: GPS only; multi-constellation GPS/GLONASS.

In order to enhance the performance of the considered configurations, equations representing the dynamic of the unknowns are introduced. This process is called aiding. The aided configurations could include pseudo-measurements on the altitude (denoted with H at the end of the corresponding baseline name), on the intersystem time offset (indicated with T) or both (indicated with HT) hence the aided considered configurations are: GPS considering altitude aiding (GPS H); GPS/GLONASS multi-constellation considering altitude aiding (GG H);

96


GPS/GLONASS multi-constellation considering inter system bias aiding (GG T); GPS/GLONASS multi-constellation considering both aiding (GG HT).

The comparison is carried out in terms of solution availability, defined as the percentage of time mission when solution is available, and position accuracy; for a fair comparison, accuracy analysis is performed considering only the solution common to all configurations (i.e. if GPS fix is available) with good geometry Position DOP (PDOP) less than 10. The equipment used for the test is a NovAtel FlexPak-G2 single frequency receiver able to track GPS and GLONASS; to the receiver was connected an Antcom Active L1/L2 antenna. The used devices are showed in Figure 3.25. The data collection is a pedestrian test Figure 3.26 and was carried out in the scenario described in Section 3.2 typical example of urban canyon. The total duration of the test is about 30 minutes the total distance travelled is about 2.5 km. First of all, a comparison in term of solution availability is performed; the comparison between the base-line configurations shown that the GLONASS measurement inclusion provides an enhancement of about 5% with respect to GPS only case. A graphical representation of the solution availability is provided in Figure 3.27; the enhancements due to the inclusion of GLONASS measurements are highlithed in the circled areas. Several fix are obtained where GPS only does not guarantee a solution. In order to further improve the solution availability, additional equations are introduced in the measurement model; the use of pseudo-measurements affects the solution availability, allowing a GPS fix with only 3 visible satellites or a GPS/GLONASS fix with only 4 (aiding on altitude or on inter system bias) or 3 mixed visible satellites (both types of aiding). The use of aiding provide enhancements in terms of solution availability which reaches the maximum value of 89% for the GG HT configuration. The values of the solution availability of the configurations considered are summarized in Table

Figure 3.25. Equipment: NovAtel FlexPak-G2 single frequency receiver and Antcom Active L1/L2 antenna.

97


Figure 3.26. Pedestrian test carried out in Centro Direzionale of Naples typical example of urban canyon. The total duration of the test is about 30 minutes the total distance travelled is about 2.5 km.

3.15.

The accuracy analysis is carried out in terms of RMS and maximum errors Table 3.15.

Solution availability values of the configurations considered.

GPS 79

Solution Availability [%] GPS H GG GG H GG T GG HT 86 84 88 86 89

for horizontal and vertical components. First of all, the benefits of the inclusion of GLONASS measurements are evaluated considering the base line configurations. The horizontal and vertical errors are plotted as a function of time in Figure 3.28. GPS/GLONASS multi-constellation solution demonstrates improved performance with respect to GPS only for all the parameters considered. The RMS values are reduced of one meter for both horizontal and vertical components. More evident is the improvement in the maximum error which is reduced of 8 meters in horizontal plane. Errors statistics for the base-line configurations are summarized in Table 3.16. The use of the altitude aiding improves significantly the performance in terms of both RMS and maximum position errors for both horizontal and vertical components. Such enhancements are clear for both GPS only and GPS/GLONASS cases. Horizontal and vertical errors of the configurations adopting altitude aiding are shown in Figure 3.29. As expected the vertical component of the solution mainly takes advantage of the aiding, because the equation adopted properly represents the slow variations of altitude, typical of land navigation. The RMS values, of the aided configurations, are reduced of 2 meters with respect to the base-line configurations, 98


Figure 3.27. Solution availability as a function of time for GPS only and GPS/GLONASS multi-constellation solutions.

Table 3.16. Horizontal and vertical error statistics for GPS and GPS/GLONASS multi-constellation solutions.

Configuration GPS Only GPS/GLONASS GPS H GG H GG T GG HT

RMS[m] Horizontal Vertical 7.7 5.7 6.8 4.7 5.3 3.4 5.6 3.2 6.8 4.7 5.6 3.2

Max [m] Horizontal Vertical 47.2 32.2 39.0 29.5 30.7 7.1 31.0 6.8 39.0 29.5 31.0 6.8

for both horizontal and vertical components. The improvements are more evident when the maximum errors values are considered. The vertical errors are reduced by a factor 4 passing from 32.2 m to 7.1 m for the GPS and from 29.5 m to 6.8 m for the 99


Figure 3.28. GPS and GPS/GLONASS multi-constellation horizontal position errors as function of time (upper box). GPS and GPS/GLONASS multi-constellation vertical position errors as function of time (lower box).

GPS/GLONASS case. The benefits on the horizontal component can be explained considering that the pseudo-measurement observes directly the altitude, practically constraining it and allowing the actual measurements to estimate mainly the other states; on the other hand if a blunder is present, it will strongly affect the horizontal estimation. Statistics of the horizontal and vertical errors for the configuration adopting aid on altitude are summarized the 3rd and 4th raws of Table 3.16. The use of multi-constellation implies the ”sacrifice” of one measurements to estimate the additional unknown as detailed in Section 2.5.1; in order to fully exploit the potentiality of GPS/GLONASS multi-constellation navigation, an equation representing the constancy of the inter-system bias is introduced. Horizontal and vertical errors of all considered GPS/GLONASS multi-constellation are shown in Figure 3.30. The use of such aiding does not help significantly the estimation process, i.e. there is no benefit in terms of position accuracy as clearly emerges comparing raw 2 and raw 5 of Table 3.16. Its effect is however notable its effect on solution availability, which reaches the maximum value of 89% when also altitude aiding is used. The use of the both aiding improved the performance in terms of RMS and maximum errors with respect to the base-line configuration for all the parameters considered, but does not improve the performance with respect to the configuration with only altitude aiding.

100


Figure 3.29. Horizontal (upper box) and vertical (lower box) errors as a function time. Comparison between configurations adopting altitude aiding and base-line configurations. The vertical component of the solution mainly takes advantage of aiding, because the equation adopted properly represents the slow altitude variations.

Figure 3.30. Horizontal (upper box) and vertical (lower box) errors as a function of time. Comparison between GPS/GLONASS base-line configuration and configuration adopting altitude aiding and configuration adopting both aiding.

101


3.2.2

Main results

GPS/GLONASS multi-constellation shows evident improvements with respect to GPS only in terms of solution availability and accuracy. The use of the altitude aiding improves significantly the performance in terms of both RMS and maximum position errors for both horizontal and vertical components. Inte-system bias aiding use, improves mainly the solution availability. The use of both type of aiding improves solution availability which is doubled with respect to the base-line configuration, while no imprvement are noted in terms of accuracy with respect to the use of altitude aiding only.

102

Chapter 4 Pseudolite Positioning In this chapter, an overview on pseudolite navigation system is provided. At first results obtained using synchronized pseudolites are analyzed and the problems relative to the synchronization process are investigated. A solution for the synchronization, using relative positioning is proposed. The algorithm developed is validated using simulated observables. Finally, the Received Signal Strength Indicator (RSSI) concept is introduced and positioning using Received Signal Strength (RSS) measurements is described.

4.1

Synchronous pseudolite navigation

A pseudolite system operating in synchronous mode extends the usage of satellitebased positioning methods as described in Section 2.5.3, into environments where Global Navigation Satellite System (GNSS) signal coverage is inadequate. Psudolites can operate in the Global Positioning System (GPS) L1 band and potentially enable indoor navigation with an accuracy comparable to that of standard GNSS receivers when synchronization is obtained. Decimeter level navigation was however demonstrated using pseudolite systems only in relatively benign environments [84] such as open-sky or in a large hangar where it was possible to mitigate the impact of multipath propagation using directive antennas. A schematic representation of the system adopted for this thesis is provided in Figure 4.1. The main components of the systems and their roles are: 4 pseudolites operating in the GPS L1 band and able to broadcast continuous and pulsed signals. Each pseudolite can be operated in synchronous and asynchronous manner; a Master Control Statio (MCS) along with a software tool able to coordinate and synchronize the different pseudolites and computing the synchronization

103

4 – Pseudolite Positioning

parameters for the different devices; radio modems used for the communication between the components of the system; 2 Fastrax receivers. The first one is connected to the MCS and is able to collect GPS and pseudolite measurements. The second is used as rover receiver: it is a modified receiver able to process GPS and pseudolite signals. A view of the Fastrax rover receiver is provided in Figure 4.2.

The pseudolite system is able to provide signals with the same format as that of GPS L1 signals; the system is a Commercial Off-the-Shelf (COTS) specifically it is provided by Space System Finland (SSF) all the details about the system are available in [85]. When used for this application, standard GPS receivers should be able to acquire and track the signals transmitted by the pseudolites and compute a navigation solution. The MCS can synchronize the system either to the GPS time scale or slave it to the clock of a single pseudolite denoted as Master Pseudolite (MPL). The limitation of such architecture is that the MCS has to be able to accurately measure the PR of the different pseudolites . In particular, the MCS performs synchronization process exploiting the knowledge of its relative distances with respect to the different pseudolites. In particular: the MCS must have all the pseudolites in Line Of Sight (LOS);

GPS and pseudolite signal reception PL control

Radio Modem

Radio Modem

Master Control Station

Radio Modem Serial port connection

Fastrax MCS receiver

Radio Modem

Figure 4.1.

Schematic representation of the architecture of the pseudolite system.

104

4.1 – Synchronous pseudolite navigation

multipath and other propagation errors have to be sufficiently small not to hinder the synchronization process.

The MCS software performs several checks to verify the synchronization level. If the checks are not passed, the synchronization process is restarted without achieving even partial results. When operated singularly, pseudolites can be used for asynchronous navigation using for example, an approach based on Carrier-to-Noise power spectral density ratio (C/N0 ) measurements which are not affected by clock errors. For this reason, two types of tests were conducted: Synchronous tests: the synchronous system has been tested using two different measurement units; the Fastrax receiver or a customized setup involving the use of two u-blox LEA-6T receivers. More details relative to the synchronous tests and the results achieved are provided in Section 4.1.1. Asynchronous tests: the RSS approach which will be described in Section 4.2 and is used with pseudolite system described above.

More details relative to the tests and the results achieved using synchronized pseudolites are provided in Section 4.1.1.

105


Figure 4.2. View of the rover Fasttrax receiver which is able to jointly process GPS and pseudolite signals.

4.1.1

Double Differences Approach

The synchronous pseudolite system described in Section 4.1 has been deployed under different configurations. Several problems, mostly related to the synchronization of the different nodes of the system, have been encountered. For this reason, several data collections were conducted in different environments. The first test was conducted in a large meeting room of about 7 m ×10 m. Four pseudolites were used and placed in the corners of the room. The control software of the MCS was used to manage the reference Fasttrax receiver. A view of the room with the system deployed is shown in Figure 4.3. A local reference frame is established with the origin in the upper left corner of the room and the axes oriented as indicated in Figure 4.4. Figure 4.4 also shows the positions of the four pseudolites (red dots) used for the experiment and the location of the antenna of the MCS (blue dot). The locations, in the local frame, of the four pseudolites and of the MCS are provided in Table 4.1. Several tests were conducted and measurements are obtained using a u-blox LEA-6T receiver. Two configurations are considered: using a laptop or an Android phone with a suitable Android application; no differences were expected and observed when using the two configurations. The 106


Figure 4.3. Experiment conducted in a large (7 m × 10 m) meeting room. Four pseudolites were placed at the corners while the antenna of the reference receiver was installed approximately in the centre of the room. Table 4.1.

Location of the four pseudolites and MCS used for the meeting room tests.

Device PL1 PL2 PL3 PL4 MCS

x [m] 5.36 6.57 0.2 0.87 3.74

y [m] 10.545 0.2 0.14 10.52 5.38

use of an Android phone simplifies the data collection operations reducing the load to be carried during the experiments. Two types of experiments were carried out: repeatability tests: the user performed several loops around a large table present in the meeting room trying to repeat always the same trajectory. The quality of the navigation solution is assessed by comparing the different trajectories estimated for the different loops. A high consistency level of the navigation solution indicates the good performance of the system. control point tests: several control points were placed in the meeting room. The locations of the control points were carefully determined by surveying the room. For each control point data were collected and used to estimate the user position.

107


Figure 4.4. Local reference frame established for the tests conducted in the large meeting room.

The location of the control points for the meeting room tests are provided in Table 4.2. A first series of tests was conducted in synchronous mode. To this end the software provided by SSF for managing the MCS and perform pseudolite synchronization was employed. According to [86], the MCS should require several minutes (about 30 minutes) to achieve precise synchronization. Unfortunately and despite several attempts, it was not possible to achieve the required level of synchronization. Despite significant efforts, precise synchronization was never achieved. The meeting room used for the first series of tests is characterized by a much lower size than the scenarios considered in [84]. Although the synchronization issue is still under 108


Table 4.2.

Location of the control points placed in the meeting room.

Control Point CP1 CP2 CP3 CP4 CP5 CP6 CP7 CP8

x 5.87 5.87 5.87 5.37 3.87 2.87 2.87 2.87

y 7.88 5.88 3.88 2.38 0.88 2.38 2.38 7.38

investigation, it is noted that this problem is probably inherent to the system and the environment selected for the tests. Multipath and fading are probably causing significant problems to the synchronization process. This fact highlights one of the limitations of indoor synchronous navigation. In order to overcome the synchronization problem and to analyze the measurement errors, a relative positioning approach has been implemented. Two u-blox LEA-6T devices were used as reference and rover receivers, respectively. The basic principle behind this approach is that reference and rover receivers are able to provide PR measurements modeled as: ρrov,i = drov,i + brov + bpl,i + ηrov,i ρref,i = dref,i + bref + bpl,i + ηref,i

(4.1)

where drov,i and dref,i are the geometric distances between rover/reference receivers and the ith pseudolite. brov and bref are the clock biases of the rover and reference receivers and bpl,i is the clock bias of the ith pseudolite. bpl,i is the synchronization error which should be compensated by the MCS. ηrov,i and ηref,i are residual unmodeled errors. The synchronization error, bpli , can be removed by considering single PR differences: ∆ρi = ρrov,i − ρref,i = drov,i − dref,i + brov − bref + ηrov,i − ηref,i .

(4.2)

Since, the geometric distance between the reference receiver and the ith pseudolite is known is then possible to construct new measurements free of pseudolite synchronization errors: ρ¯i = ∆ρi + dref,i = drov,i + ∆b + ∆ηi (4.3) where ∆b = brov − bref and ∆ηi = ηrov,i − ηref,i . Note that Eq. (4.3) has the same functional form of the PRs adopted for GNSS positioning [32] and in particular a single clock bias term, ∆b, is present. This term is common to all the pseudolite 109


measurements and can be estimated by adding it as unknown in the navigation solution Section 2.2.5 and Eq. (2.20). Note that the principle described above is valid only if the reference and rover receivers are accurately synchronized. In particular, the pseudolite clock bias term, bpl,i , is time-varying and imperfect cancellation will occur in Eq. (4.2) if synchronization errors are present. In order to collect valid pseudolite measurements using the u-blox receivers synchronization process performed by the MCS was disabled. In particular, the u-blox receivers experienced continuous losses of lock due to the jumps in the Doppler frequency of the transmitted pseudolite signals introduced by the MCS during the synchronization process. After disabling MCS synchronization, reference and rover receivers were able to correctly acquire and track the pseudolite signals. In this way, the system was effectively running in asynchronous mode. The two receivers used the time stamp embedded in one of the pseudolite signals to extract the system time and provide PR measurements. Corrected single differences (4.3) were formed and a custom navigation solution algorithm was developed to determine the user position. Unfortunately, the algorithm developed was unable to converge given the data collected due to unaccounted errors probably due to multipath and fading problems. As already mentioned these unaccounted errors were ascribed to residual synchronization errors. In order to investigate this hypothesis, double PR differences were formed: ∇∆ρi,j = ∆ρi − ∆ρj .

(4.4)

In order to verify the consistency of the observables, the double differences measured were compared with respect ot the simulated ones as described in Section 4.1.2.

4.1.2

Simulated Approach

In order to investigate the cause of the lack of convergence of the algorithm developed, a simple simulation has been carried out. The simulation scenario is shown in Figure 4.5: an area with size comparable to that of the meeting room, where the tests were performed, was considered along with a user moving along a square trajectory. Synthetic corrected single differences (4.3) were generated assuming the pseudolite locations indicated in Figure 4.5 and considering that the antenna of the reference receiver is co-located with that of the MCS. In this case, the navigation solution algorithm developed was always converging to the correct user location. This fact can be seen by the perfect agreement between the simulated (continuous blue line) and estimated (red circles) trajectories in Figure 4.5. This perfect agreement is also due to the fact that the term, ∆ηi , was ignored in the simulations. This test allowed debugging the navigation solution 110


algorithm developed and determining that the lack of convergence was due to unaccounted errors in the corrected single differences obtained using real data. The double differences obtained for the scenario simulated in Figure 4.5 are shown in Figure 4.6. Since the user is repeating the same trajectory describing a square, the double differences oscillate periodically. A similar behavior was expected for the measurements obtained experimentally. The double differences of the PRs collected from the four pseudolites during a repeatability test are shown in Figure 4.7. From Figure 4.7 it is noted that a clear oscillatory behavior is present, due to the periodic repetition of the same trajectory, but biases are clearly observable. In particular each measurement is characterized by a device dependent bias. This is likely due to the synchronization error mentioned before: measurements are taken at slightly different epochs and the clock drift of the pseudolite local oscillator introduces biases which can lead to errors up to 50 meters. This fact can be clearly observed Figure 4.7. In addition to this, the biases are time-varying and thus difficult to estimate. In order to overcome the difficulties encountered during the first test, i.e. the lack of synchronization between reference and rover measurements, a new pseudolite topology was considered. In the new approach an additional pseudolite, indicated as MPL, was introduced in order to synchronize both rover and reference receivers to a common time scale. Hence, the new configuration was composed by 5 pseudolites where an additional device denoted MPL was placed in front of the MCS. The coordinates of the MPL are provided in Table 4.3 in the local frame defined in the

12 PL3

PL2

10

y [m]

8

6

MCS

4

2 PL1

PL4 0 0

1

2

3

4

5

6

7

x [m]

Figure 4.5. Simulation scenario adopted to investigate the properties of the PR double differences.

111


DD 1-1 DD 2-1 DD 3-1 DD 4-1

8

Pseudorange Double Differences [m]

6 4 2 0 -2 -4 -6 -8 50

100

150 Time [s]

200

250

Figure 4.6. Simulated PR double differences when considering the simulation scenario in Figure 4.5.

112

4.1 – Synchronous pseudolite navigation 20


10

0

-10

-20

-30

-40

-50 50

100

150 Time [s]

200

DD 1-1 DD 2-1 DD 3-1 DD 4-1 250

Figure 4.7. Double differences of the PR collected from the four pseudolites using two u-blox receivers. Meeting room, first data collection campaign, repeatability test.

previous section. The MPL is scarified to provide a common synchronization signal, i.e. timing information of the transmitted signal should have been used by the reference and rover receivers to initialize their local clocks and provide synchronous measurements. For this reason, the MPL was started before the other pseudolites. This strategy also provided relatively poor results. The reason was that the u-blox receivers were able to acquire also GPS signals and computed a position solution based only on GNSS measurements. After computing the position solution also GPS time was extracted and used to steer the receiver clocks. The High-Sensitivity (HS) of the u-blox receivers thus limited the use of the proposed approach and the receivers were resynchronized due to the presence of genuine GPS signals. Given the availability of GPS timing, a new approach was proposed where time synchronization was achieved using the GPS signals collected indoors. Although this approach solved the problem of resynchronization, the level of synchronization expected for the pseudolite measurements was not achieved. The reason is likely that the indoor

Table 4.3. Location of the MPL for the second data collection campaign performed in the meeting room.

Device MPL

x [m] 2.55 113

y [m] 5.38


the GPS measurements collected by the U-blox receivers are affected by gross errors due to multipath and propagation effects. For this reason, only poor navigation solutions are available and biases of several tens of meters are observed. These biases also affect the quality of the timing signal recovered from GPS. Even if GPS synchronization was achieved by both receivers, significant errors were still present in the measurements. In order to try to compensate for these residual errors, a two steps procedure was adopted. 1. During the first part of the tests, the antennas of the reference and rover receivers were co-located in a zero-base line configuration. The antennas were kept in this configuration for about 60 seconds: since the two antennas were co-located PR double differences contain only noise and residual biases due to synchronization errors. 2. After 60 seconds the user (carrying the rover receiver) started moving. Positioning was then attempted using the corrections computed during the first part of the tests. The PR double differences computed using the measurements from the two receivers and plotted in Figure 4.8.


10

5

0

-5

-10

-15 DD 1-1 DD 2-1 DD 3-1 DD 4-1

-20 50

100

150 Time [s]

200

250

Figure 4.8. Double differences of the PR collected from four pseudolites using two u-blox receivers. Meeting room, second data collection campaign, repeatability test. During the first 60 seconds, reference and rover receivers were kept in a zero-base line configuration.

114

4.2 – Asynchronous RSSI Positioning

10 x y

9 Reference Solution

Position Coordinates [m]

8 7 6 5 4 3 2 1 0

10

20

30

40

50

60

70

Time [s]

Figure 4.9. Position solution obtained using corrected PR measurements where initial synchronization biases were removed exploiting the zero-base line configuration adopted during the first 60 seconds of the test. When the user start moving, synchronization corrections were no longer valid and the position solution diverged.

From Figure 4.8, the presence of biases clearly emerges in the pseudolite measurements preventing the user to obtain a reliable position solution. The biases observed are due to the synchronization problems already discussed above. The biases observed were stable during the static phase of the test and thus they were removed exploiting the knowledge of the reference position. A reliable position solution was obtained using the corrected PR as shown in Figure 4.9. However, when the user start moving, synchronization corrections were no longer valid and the position solution diverged. Thus, this approach does not allow the computation of a reliable solution during the kinematic phase. The use of synchronous measurements in deep indoor environments is still an open issue and further investigations are required. The results obtained seem to indicated that this type of technology is not suitable for deep indoor navigation. For these type of scenarios and for the above mentioned reasons an asynchronous approach was adopted.

4.2

Asynchronous RSSI Positioning

The pseudolite system adopted for the previous data collections can be also used in an asynchronous way [85]. Different approaches for positioning using pseudolites 115


in asynchronous mode are available as mentioned in Section 2.5.3; in this thesis, an approach based on RSS measurements is adopted. In order to overcome the synchronization problems detailed in Section 4.1, the pseudolite system is used in asynchronous mode using a dedicated software which allows: to set the Pseudo Random Noise (PRN) which can be used to select different codes from the 1023 Gold code family; to set the signal power by adjusting the basic power level (either −115 and −73 dBm) and the attenuation; to control the Doppler shift and set some of the navigation message parameters such as the Z-count [32, 33]; to select the pulsing scheme.

RSS measurements, expressed in logarithmic units, are usually modeled as [87, 88, 89]: d P (d) = P0 − 10α log10 (4.5) d0 where P (d) is the RSS measured at the distance d from the emitter. α is the pathloss exponent and P0 is the power received at a short reference distance, d0 . RSS is easy to measure and can be obtained from, for example the Automatic Gain Control (AGC) levels [90, 91, 87]; C/N0 measurements [92].

In this thesis, C/N0 observables are used, hence Eq. (4.5) can be rewritten in terms of C/N0 measurements: C = Ki − α10 log10 (di ) (4.6) N0 i where the index, i, has been added to denote C/N0 measurements from the ith transmitter and Ki is a constant accounting for the power of the ith transmitted signal and the reference distance d0 . Unless specified, the C/N0 will always be expressed in units of dB-Hz. When the constants Ki and α are known, a direct relationship between the measured C/N0 and transmitter-receiver distance can be established. Transmitter-receiver distances can be expressed as a function of the user position: p di = (xu − xi )2 + (yu − yi )2 (4.7) 116

4.2 – Asynchronous RSSI Positioning

where (xu , yu ) and (xi , yi ) are the coordinates of the user and the ith pseudolite, respectively. Although Eq. (4.7) considers the case of two dimensional positioning, it can be easily extended to three dimensional case. Using Eq. (4.7), it is possible to rewrite Eq. (4.6) as C 1 = Ki − α10 log10 (xu − xi )2 + (yu − yi )2 (4.8) N0 i 2 where the user coordinates are the only unknowns. The user position can be determined only when a sufficient number of C/N0 measurements is available (i.e. ≥ 2). In order to determine the user position in the Least Squares (LS) the following cost function has to be minimized. A−1 X 2 1 C 2 2 (4.9) − Ki + α10 log10 (x − xi ) + (y − yi ) C(x, y) = N0 i 2 i=0 where A is the number of C/N0 measurements available. In this way, the user coordinates are obtained as (xu , yu ) = arg min J(x, y)

(4.10)

x,y

Eq. (4.9) is the Mean Squared Error (MSE) between the measured C/N0 values and the model in right-hand side of (4.8). The minimization problem in Eq. (4.10) is solved using a gradient descent algorithm where the initial user position can be set equal to the average of the pseudolite coordinates. The gradient of C(x, y) can be easily evaluated and is given by   ∂C(x,y) ∂x

 ∇C(x, y) = 

∂C(x,y) ∂y

 PA−1 i=0

 =

PA−1 i=0

  i) Ei ln1010 (x−x2α(x−x 2 2 i ) +(y−yi ) i) Ei ln1010 (x−x2α(y−y 2 2 i ) +(y−yi )



(4.11)

 .

where Ei is: Ei =

C N0

1 2 2 − Ki + α10 log10 (x − xi ) + (y − yi ) 2 i

Finally, the user position is computed by iterating the following equation x x = − µ · ∇C(x, y)|q y q+1 y q 117

(4.12)

(4.13)


where q is the iteration count and µ is the algorithm step empirically selected to guarantee algorithm convergence. It has been noted that when the C/N0 values are approaching zero, the measurements are affected by significant errors, reflecting the fact that low C/N0 measurements are unreliable. In the limit case, measurements with C/N0 values close to zero should be removed. In order to minimize the effect of the measurements with low C/N0 a new cost function is defined as follow: A−1 X C Ei2 Cw (x, y) = N 0 i i=0

(4.14)

where the subscript “w” was added to denote the fact that the cost function is now a form of Weighted MSE (WMSE) where each term in the summation in (4.14) is weighted by its relative C/N0 . The gradient of (4.14) is:  P  A−1 2α(x−xi ) C 10 E i 2 2  i=0 N0 i ln 10 (x−xi ) +(y−yi )   . ∇Cw (x, y) =  (4.15)  PA−1 C 2α(y−yi ) 10 Ei ln 10 (x−xi )2 +(y−yi )2 i=0 N0 i

and the position estimate is now computed iteratively according to the following update equation: x x = − µ · ∇Cw (x, y)|q (4.16) y q+1 y q where µ has been reduced to account for the scaling introduced by the C/N0 weighting. The WMSE algorithm significantly outperformed method (4.13) and for this reason only results considering (4.16) are presented in Section 5.2. This technique provided very encouraging results which will be presented in the next section.

118

Chapter 5 Results - Testing and Analysis The first part of this chapter is dedicated to the urban tests. First of all a static test is described and the results analyzed, then a pedestrian test is illustrated and the obtained results commented. Then solution obtained using a High-Sensitivity (HS) receiver is then presented. The parameter used to characterize the performance of the system are the reliable availability, Root Mean Square (RMS) and maximum error for both horizontal and vertical components. The second part of the chapter is devoted to the results achieved using the asynchronous pseudolite system described in Chapter 4. Data collections involving the use of several pseudolites were organized and the data collected were used to demonstrate indoor navigation adopting an Received Signal Strength Indicator (RSSI) approach. The performance of the system is tested in an office building: different data collections were performed to analyze the repeatability of the solution.

5.1

Urban Tests

In signal-degraded environments such as urban canyons or mountainous areas Global Navigation Satellite System (GNSS) signals are blocked or strongly degraded by natural or artificial obstacles. In these scenarios, the multi-constellation approach using Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS) together, as proposed in Section 3.2.1, is not able to provide accurate Position Velocity Time (PVT) solution due to the presence of gross errors in the measurement set. Hence a quality check on the measurements has to be introduced in order to identify and reject erroneous observables. Several data collections were performed, first of all a static campaign was carried out, as described in Section 5.1.1, in order to validate the Receiver Autonomous Integrity Monitoring (RAIM) schemes developed. Then kinematic tests were carried out, using standard and HS GNSS receivers, in order to evaluate the performance 119

5 – Results - Testing and Analysis

of the GPS/GLONASS multi-constellation approach in urban environments.

5.1.1

Static Campaign

In this section the performance of the RAIM algorithms developed, i.e. ForwardBackward, Subset and Danish methods is evaluated in a static test. The performance is analyzed in terms of: reliable availability; RMS and maximum horizontal and vertical position errors; RMS and maximum horizontal and vertical velocity errors.

A static test of about 6 hours was carried out on 24th February 2012. The antenna was placed on the roof of the PANG (PArthenope Navigation Group) laboratory building, at Centro Direzionale of Naples (Italy), a typical example of urban canyon. The antenna position and the environment is shown in Figure 5.1. In such environment many GNSS signals are blocked by skyscrapers or are strongly degraded by the multipath phenomenon. The only test performed in this section was static to simplify the error analysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixed, so its velocity was zero). A kinematic test needs a reference for the error analysis and thus it is more complicated to obtain. Kinematic tests are analyzed in Section 5.1.2.The static test choice does not limit the validity of the analysis because the operational environment is a typical signal-degraded scenario, i.e. an urban canyon. The equipment used for this test is composed by: a NovAtel FlexPak-G2, able to provide single frequency (L1) GPS/GLONASS measurements; a NovAtel 702-GG antenna.

The reference solution is computed by a post-processing geodetic method and the accuracy of the position is of mm order; the coordinates of the antenna are provided in Table 5.1. Eight different configurations are analyzed, combining the two GNSS considered and the different RAIM schemes developed:

Table 5.1.

Coordinates of the antenna placed on the roof of the PANG laboratory

Latitude [deg] 40.8565323

Longitude [deg] 14.2844166 120

Altitude [m] 90.6257

5.1 – Urban Tests

Figure 5.1. Antenna placed on the roof of the PANG (PArthenope Navigation Group) laboratory building, at Centro Direzionale of Naples (Italy)

GPS only without RAIM application (briefly indicated as GPS noRAIM); GPS/GLONASS without RAIM application (GG noRAIM); GPS only with Subset RAIM application (GPS Sub); GPS/GLONASS with Subset RAIM application (GG Sub); GPS only with Forward-Backward RAIM application (GPS FB); GPS/GLONASS with Forward-Backward RAIM application (GG FB); GPS only with Danish method applied (GPS Dan); GPS/GLONASS with Danish method applied (GG Dan).

The performance of the considered configuration is analyzed in terms of accuracy and availability. Specifically the metrics adopted for the evaluation of the accuracy are: RMS and maximum errors for horizontal and vertical components in the position and velocity domains. In order to evaluate the performance in term of 121


availability two different parameters are adopted depending on the application or not of RAIM techniques. The solution availability is used for the configuration without quality check and, in case of RAIM application, the reliable availability, defined as the time percentage when solution is reliable, is introduced. The mean number satellites available is 6 in the case of GPS only; in the multi-constellation case this value is 9.5. GPS only configuration is characterized by a mean Horizontal DOP (HDOP) of 5 and its maximum value reach 1600 due to the presence of obstacles which block the satellite signals as shown in Figure 5.1. The introduction of GLONASS measurements improve the satellites geometry and the HDOP mean value is 2.45, i.e., more than halved with respect to GPS only; the maximum value is 22. The tests session is characterized by a high solution availability, the inclusion of GLONASS observables provides only a slight improvements in terms of solution availability, which is improved of 2% with respect to the GPS only configuration. Availability values are detailed in the second column of Table 5.2. The test is also characterized by very large errors more than 1 km without RAIM application: this is due to geometry and multipath errors; in order to reduce such errors three different RAIM algorithms are applied. The developed RAIM schemes reduce the availability of the position solution. In the GPS only configuration the Subset test guarantees the highest reliable availability (76.2%); for Danish and ForwardBackward schemes the reliable availability is halved with respect to the solution availability. For the multi-constellation GPS/GLONASS, the Subset test guarantees a high reliable availability (only 3.5% of the solutions are rejected by the quality control) which is increased of 20% with respect to the GPS only configuration. The effect of the GLONASS inclusion is more evident in the Danish and ForwardBackward schemes; in these cases the reliable availability reaches about 75% with an improvement of 25% − 30% with respect to the GPS only configurations. The reliable availability of the position are summarized in the last column of Table 5.2. Similar results are obtained in the velocity domain, GLONASS measurements in-

Table 5.2.

Solution Availability and Reliable Availability of the position.

Configuration GPS noRAIM GG noRAIM GPS Sub GG Sub GPS FB GG FB GPS Dan GG Dan

Solution Availability [%] 98.1 100 98.1 100 98.1 100 98.1 100 122

Reliable Availability [%] N.A. N.A. 76.2 96.5 43.6 74.0 49.0 75.8

5.1 – Urban Tests

Table 5.3.

Solution Availability and Reliable Avaliability of the velocity solution.

Configuration GPS noRAIM GG noRAIM GPS Sub GG Sub GPS FB GG FB GPS Dan GG Dan

Solution Availability [%] 98.1 100 98.1 100 98.1 100 98.1 100

Reliable Availability [%] N.A. N.A. 70.5 97.8 56.3 72.9 56.3 73.4

crease the reliable availability for the three RAIM schemes with respect to GPS only configurations. As in the position domain, the Subset scheme guarantees the highest reliable availability (70.5% for GPS only and 97.8% for the multi-constellation case) with respect to the other schemes developed. The solution availability and the reliable availability of the velocity solution are summarized in Table 5.3. In the position and velocity domain, horizontal and vertical solutions are analyzed separately. At first, the performance of the developed RAIM algorithms is compared to the base-line configuration, using the classical representation for the horizontal component, i.e. East and North coordinates expressed in meters in order to have a clear amplitude of the clouds of the different configurations. In Figure 5.2, Figure 5.3 and Figure 5.4 the base-line configurations, i.e. without quality control, are represented by magenta dots (GPS only) and by blue dots (GPS/GLONASS case), the configurations with the RAIM algorithms are represented by green and yellow dots, respectively. The spread of the clouds provides an immediate representation of the magnitude of the error and allows a simple performance comparison between the configurations considered. In Figure 5.2 the horizontal scatter of the base-line configuration is compared with that of the Danish method. From Figure 5.2, Figure 5.3 and Figure 5.4 it clearly emerges that the configurations without RAIM are characterized by large errors: in the GPS only case, the maximum horizontal error exceeds 1 km and the inclusion of GLONASS measurements reduces it of almost 4 times. The Danish method improves all considered configurations, reducing both maximum and RMS errors, as shown in Figure 5.2 for the horizontal component; the clouds relative to the configurations using RAIM are significantly reduced with respect to the base-line configurations. The maximum error obtained with the Danish method is 159.7 meter. The error values linked to the Danish method are summarized in the third and fourth rows of Table 5.4. 123


Figure 5.2. Horizontal scatter of the base-line configuration compared with that of the Danish method.

In Figure 5.3, horizontal performance of the configuration using the Subset algorithm are compared with the base-line configuration. Also in this case, the GLONASS inclusion provides improvements with respect to the GPS case: the configuration that provides the best performance for all the parameters considered is the multiconstellation GPS/GLONASS using the Subset algorithm, i.e. the yellow cloud is more concentrated with respect to the other as shown in Figure 5.3. Using this configuration the RMS error is drastically reduced passing from 34.2 m to 15.1 m, without a significant availability reduction (only 2% of the solution are declared unreliable). Statistical values of the horizontal and vertical position error are summarized in Table 5.4. In Figure 5.4, the Forward-Backward performance in the horizontal plane is compared with the base-line configurations. The use of quality checks and the inclusion of the GLONASS observables clearly improve the performance with respect to the base-line case; also in this case the yellow cloud is the smallest, confirming the results obtained in the previous cases. The RMS error in this case is more than halved with respect to the configuration without RAIM. This fact clearly emerges comparing the fifth and sixth rows of Table 5.4 with respect to the first and the second ones of the same table. In order to have an immediate comparison, the horizontal solutions provided by the configuration using the different RAIM schemes are plotted in Figure 5.5. From Figure 5.5, the Danish method and 124

5.1 – Urban Tests

Figure 5.3. Horizontal scatter of the base-line configuration compared with that of the Subset test

Figure 5.4. Horizontal scatter of the base-line configuration compared with that of the Forward-Backward scheme.

125


Figure 5.5. Horizontal solutions provided by the configuration using the different RAIM schemes.

the Forward-Backward scheme seem to provide similar performance and the relative clouds are smaller than the Subset one. From a qualitative analysis the cloud relative to the GPS/GLONASS solution with Forward-Backward (magenta dots) scheme is more concentrated with respect to the others. A more detailed analysis can be performed comparing the values summarized in Table 5.4. In order to highlight the different behaviors of the three RAIM algorithms, a

Table 5.4. Statistical position error parameters: RMS and maximum errors for both horizontal and vertical components.

Configuration GPS Only GPS/GLONASS GPS Dan GG DAN GPS FB GG FB GPS Sub GG Sub

RMS[m] Horizontal Vertical 54.9 85.6 34.8 65.4 23.2 56.1 16.0 38.1 17.9 44.5 13.4 31.3 27.5 56.4 15.1 36.1 126

Max [m] Horizontal Vertical 1264.5 1685.9 245.6 372.2 159.7 343.1 159.7 284.3 159.7 285.8 159.7 284.3 299.0 327.0 321.6 398.5

5.1 – Urban Tests

Horizontal Position Error 18 GPS/GLONASS FB GPS/GLONASS Danish GPS/GLONASS Subset

16

Horizontal Position Error [m]

14 12 10 8 6 4 2 0 469987

470047

Figure 5.6. Detailed view of the horizontal error pertaining to the three best configurations

detailed view of the horizontal error pertaining the three best configurations is provided in Figure 5.6. In Figure 5.6, the rectangular area (on the left) within the dotted line shows the case where the Subset scheme provides the best solution. The rectangular area (on the right) within the dotted line shows the case where the Danish method provides the wrost performance with respect to the other methods due to an erroneous rejection. This effect is avoided in the Forward-Backward case due to the Backward phase of such algorithm. In order to have a comparison of the performance in the vertical channel, the vertical error of the considered configurations is plotted as a function of the local time in Figure 5.7, Figure 5.8 and Figure 5.9. From Figure 5.7, Figure 5.8 and Figure 5.9, it clearly emerges that the configurations without RAIM are characterized by larger errors: in the case of GPS only, the maximum vertical error exceeds 1.5 km and the inclusion of GLONASS measurements reduce it by almost a factor 4 as for the horizontal case. The use of quality control algorithms improves significantly the performance in terms of both RMS and maximum position errors and such enhancements are clear for both GPS only and GPS/GLONASS cases. As expected the vertical error has values usually bigger than the horizontal ones due to the satellite geometry. Statistics of the vertical error for the different methods are detailed in the second and fourth column of Table 5.4.

127


Figure 5.7.

Danish and base-line vertical errors as a function of the local time.

Figure 5.8.

Subset and base-line vertical errors as a function of the local time.

128

5.1 – Urban Tests

Figure 5.9. Forward-Backward and base-line vertical errors as a function of the local time.

A comparison among the RAIM algorithms in the vertical channel is carried out in Figure 5.10. From Figure 5.10, it emerges that vertical position errors for GPS/GLONASS Subset configurations are degraded (i.e. the maximum value in the case of GPS only is 327 m and in the multi-constellation case it reaches 398 m). This behavior is due to an erroneous measurement rejection in the presence of multiple blunders; better results are obtained with the Forward-Backward and Danish methods. Statistical parameters of the vertical error are summerized in Table 5.4. As for the position errors, the RAIM schemes are first compared with the no RAIM configurations. In Figure 5.11, the perfomance of the Danish method is evaluated; Subset scheme is analyzed in Figure 5.12 and finally the accuracy of the Forward-Backward algorithm is investigated in Figure 5.13. Then the performance of the three Fault Detection and Exclusion (FDE) techniques are compared in the horizontal and vertical channels in Figure 5.14. In the upper boxes of Figure 5.11, Figure 5.12 and Figure 5.13, the horizontal velocity errors of the base-line configuration are compared to tose of the configurations using the three different RAIM schemes. From these pictures, it can be noted that none of the RAIM configurations is characterized by high errors: for the GPS only case they are higher than 50 m/s; the GLONASS inclusion reduces the errors down to 0.44 m/s. Figures of merits of the horizontal and vertical velocity errors for the base line configurations are summarized in the first two rows of Table 5.5. 129


Figure 5.10. Vertical error pertaining to the six configurations using the three different RAIM schemes

As in the position domain, RAIM methods improve all the configurations considered, reducing both maximum and RMS errors for the horizontal and vertical components; however in the velocity domain the benefits of RAIM are less evident with respect to the position domain due to the robustness of the Doppler observable. In the upper box of Figure 5.14, the horizontal velocity errors obtained with the FDE techniques are compared; in the lower box of Figure 5.14 the vertical velocity error of the three schemes are plotted with respect to the local time. As in the position domain, the Subset test is characterized by the highest reliable availability but also by the highest errors, the other schemes provide similar performance for both horizontal and vertical components. The number of exclusions performed by the three RAIM schemes is plotted as a function of time in order to demonstrate the ability to identify and reject multiple blunders. In Figure 5.15, the number of PRs excluded by the three methods is plotted separately as function of time; from Figure 5.15, emerges that the Forward-Backward method was able to reject up to six simultaneous measurements in the multiconstellation GPS/GLONASS configuration (red dots), while the maximum number of simultaneous exclusions for the other methods is 5. In the case of GPS only, the 130

5.1 – Urban Tests

Figure 5.11. Danish method horizontal and vertical velocity error as a function of local time Table 5.5. Statistical position error parameters: RMS and maximum errors for both horizontal and vertical components.

Configuration GPS Only GPS/GLONASS GPS Dan GG DAN GPS FB GG FB GPS Sub GG Sub

RMS[m/s] Horizontal Vertical 0.968 1.573 0.042 0.060 0.046 0.073 0.035 0.054 0.047 0.074 0.036 0.055 0.053 0.084 0.042 0.067

Max [m/s] Horizontal Vertical 68.750 108.240 0.442 0.822 0.649 1.251 0.295 0.642 0.649 1.251 0.367 0.653 0.669 1.251 0.928 1.337

methods were able to perform 4 simultaneous PR exclusions. In Figure 5.16, the number of PR-rate measuremetns excluded by the three methods is plotted separately as a function of time; from Figure 5.16, it clearly emerges that the number of PR rate exclusions is lower than in the PR case: in this case the maximum number of measurements rejected is 5 in the case of GPS/GLONASS multi-constellation 131


Figure 5.12. Subset test horizontal and vertical velocity error as a function of local time

approach using the Danish method. This confirms the robustness of the Doppler measurements to the multipath effect. From the analysis performed, it emerges that the Forward-Backward method provides the best performance with respect to the other techniques. It guarantees a good compromise between accuracy and availability. Such method provides a more accurate solution with respect to the Subset test and with respect to the Danish method. It has the advantage of the Backward phase that limited erroneous exclusions. For these reasons, only the Forward-Backward scheme is used in the next sections.

132

5.1 – Urban Tests

Figure 5.13. Forward-Backward horizontal and vertical velocity error as a function of local time

Figure 5.14.

Horizontal and vertical velocity errors for the trhee RAIM schemes

133


Figure 5.15. Number of the PRs excluded by the three RAIM algorithms plotted as a function time.

Figure 5.16. Number of the PR rate measurements excluded by the three RAIM algorithms considered.

134

5.1 – Urban Tests

5.1.2

Kinematic Test

The data collection considered in this section was a pedestrian test and is illustrated in Figure 5.17. It was carried out on 21st June 2012 around 10:00 am in Centro Direzionale of Naples (Italy), that is, as already mentioned, a typical example of urban canyon. The trajectory followed was the same described in Section 3.2 and the reference path was obtained using the method already described in Section 3.2 using pre-surveyed vertexes. The NovAtel receiver was equipped with an external device (a button) used to mark the transit on the vertexes in order to associate a time epoch to each surveyed vertex. Data were collected with a 1 Hz frequency, the total duration of the test was about 30 minutes, the speed varied from 0 to about 5 km/h without stops and the total distance travelled was about 2.5 km. The kinematic tests were performed with two different receivers: a NovAtel OEM615, which is a multi-constellation GPS/GLONASS dualfrequency receiver: L1 and L2 for GPS and GLONASS; a u-blox LEA 6-T device which is a single frequency GPS only HS receiver.

The two devices were connected to the same antenna (a NovAtel 702-GG antenna). The performance is evaluated in terms of: Position reliable availability (availability for configurations without RAIM); Position accuracy, i.e. RMS and maximum error for both horizontal and vertical components.

Figure 5.17. Pedestrian test carried out on 21st June 2012 around 10:00 am in Centro Direzionale of Naples (Italy), a typical example of urban canyon.

135


In this section, the results obtained using the standard NovAtel receiver are detailed; the results obtained using the HS receiver are summarized in Section 5.1.3. Eight different configurations are analyzed: GPS only without RAIM application (indicated as GPS noRAIM); GPS/GLONASS without RAIM application (GG noRAIM); GPS only with Forward-Backward RAIM application (GPS RAIM); GPS/GLONASS with Forward-Backward RAIM application (GG RAIM); GPS only with altitude aiding without RAIM (GPS Aid H); GPS/GLONASS with altitude and inter-system bias aiding without RAIM (GG Double Aid); GPS only with altitude aiding with RAIM (GPS RAIM Aid H); GPS/GLONASS with altitude and inter-system bias aiding without RAIM (GG RAIM Double Aid).

The data collected using the NovAtel receiver are characterized by a solution availability that varies from 53% for GPS standalone to 74% for GPS/GLONASS; the use of aiding improves GPS availability up to the level of GPS/GLONASS, which reaches 84% with aiding information inclusion. The data pertaining the solution availability and reliable availability are summarized in Table 5.6. For the first three configurations, the reliable availability is more than halved with respect to the solution availability, while aiding inclusion allows GPS/GLONASS multi-constellation solution to obtain a high reliable availability. Specifically, the Table 5.6. Solution Availability and Reliable Availability of the position using Novatel OEM625 receiver

Configuration GPS noRAIM GG noRAIM GPS Aid H GG Double Aid GPS RAIM GG RAIM GPS RAIM Aid H GG RAIM Double Aid

Solution Availability [%] 53 73 74 84 53 73 74 84 136

Reliable Availability [%] N.A. N.A. N.A. N.A. 19 38 31 62

5.1 – Urban Tests

use of quality checks reduces the availability of the solution which can be very low in the case of GPS only (reliable availability around 19%). The inclusion of GLONASS measurements or of aiding on the altitude improves the reliable availability which is doubled with respect to the base-line configuration; the configuration using GPS along with GLONASS and double aiding further improves the reliable availability which reaches a maximum value of 62%. Although, in the scenario selected, many GNSS signals are blocked or degraded by multipath, positioning results in the GPS only case are characterized by reasonable RMS values. On the contrary large maximum errors can be present as shown in Figure 5.19. The GLONASS and pseudo-measurement inclusion (without RAIM application) increases the availability but degrades the solution with respect to various parameters, most of all for the lack of blunder check. In Figure 5.19, both horizontal (in the upper box) and vertical (in the lower box) position errors are plotted as a function of time. In Figure 5.19, the performance of the configurations without RAIM is analyzed. All the available solutions are considered; it clearly emerges that in this scenario all the configurations are characterized by very high errors. The maximum error is 500 m in the horizontal plane for the GPS configuration with aiding on the altitude. This value is due to the use of aiding on the altitude, which is adapted to improve the redundancy of the system and reduce the vertical error. Geometrically the altitude pseudo-measurement can be interpreted as a satellite at the zenith as shown in Figure 5.18. Hence the main information provided by the pseudo-measurement is related to the altitude. In same cases, however, when the geometry of the system is very weak, the pseudomeasurement contributes to the estimate of the horizontal component, providing erroneous information and so degrading the solution. From the upper box of Figure 5.19, it emerges that the GPS only configuration (red dots) provides the best performance in the horizontal plane, however with the lowest solution availability. The inclusion of GLONASS measurements mainly improve the availability of the solution but all the considered error parameters are higher than in the GPS case. Finally, the use of the multi-constellation and of the two aidings (i.e. GPS/GLONASS with double aiding, blue dots) provides performance similar to that of the GPS case but with a very high solution availability, demonstrating the potentiality of the multiconstellation approach. From the lower box of Figure 5.19, it can be noted that the configuration with aiding (blue and magenta dots) in urban canyons improves the performance of the vertical component for both RMS and maximum values which are strongly reduced with respect to the base-line configuration. Statistical parameters of the horizontal and vertical errors for the configurations without RAIM application are summarized in Table 5.7. In order to have a direct comparison between the base-line configuration and to analyze the benefits of the RAIM algorithm in urban navigation, horizontal and vertical errors of the 137


7

Aid 10

8

GDOP=65.0098; PDOP=49.3303; HDOP=25.9535; EDOP=19.489; NDOP=17.1395; VDOP=41.9511; TDOP=42.3414

Figure 5.18. Sky plot pertaining an epoch where only three GPS satellites were available and the solution was obtained exploiting aiding information. Geometrically, the pseudo-measurement can be interpreted as a satellite at the zenith.

Table 5.7. Statistic parameters of the errors for the base-line configurations without RAIM application.

Configuration GPS noRAIM GG noRAIM GPS Aid H GG Double Aid

RMS[m] Horizontal Vertical 6.9 6.2 18.9 13.8 25.2 3.7 8.2 3.7

Max [m] Horizontal Vertical 122.6 112.0 482.8 284.1 500.0 7.9 134.4 8.3

base-line configuration with (magenta and blue dashed lines) and without RAIM (green and red lines) are plotted as a function of time in Figure 5.20. In order to have a fair comparison, configurations are considered at common epochs, i.e. only when the configuration with RAIM is declared reliable. From Figure 5.20, the benefits of the RAIM application clearly emerges: the dashed lines representing the configuration with RAIM are ever lower than the continuous lines representing the configurations without quality checks. The RAIM application improves significantly 138

5.1 – Urban Tests

Figure 5.19. Horizontal and vertical positition error of the configurations considered without RAIM application.

the system performance in terms of RMS and maximum errors for both horizontal and vertical components. The best performance is obtained combining GPS and GLONASS measurements. The RMS of the horizontal error is limited to 3.7 m. The best performance in the vertical channel is obtained in the GPS only case with RAIM. In this case, RMS and maximum values are reduced even with respect to the GPS/GLONASS multi-constellation case. This is only due to the limited reliability of the solution in the case of GPS only. In fact the maximum error in the vertical components in the multi-constellation case corresponds to an epoch where GPS solution is not available, but the performance in terms of RMS are very close: the difference is of only 0.5 m confirming the potentiality of the multi-constellation . The behavior of the horizontal error is shown in the upper box of Figure 5.20. Vertical errors are shown in the lower box of the same figure. Statistical parameters of the horizontal and vertical errors for the base-line configurations, considering only reliable epochs, are summarized in Table 5.8. A comparison among the configurations with RAIM is performed to demonstrate the benefits of the inclusion of aiding in urban navigation and to evaluate their impact on RAIM algorithms. The analysis is also useful to demonstrate the needs of quality checking for avoiding the use of erroneous values for aiding. The performance of each configuration is evaluated in the reliable epochs. The behavior of the horizontal and vertical errors are analyzed separately in Figure 5.21. From Figure 5.21, the benefits 139

5 – Results - Testing and Analysis Horizontal Error 50

Error [m]

40 30

GPS Only No RAIM GPS Only RAIM GPS\GLONASS No RAIM GPS\GLONASS RAIM

20 10

0 379100 11:18

379400 11:23

379700 11:28

380000 11:33

380300 11:38

380600 11:43

380300 11:38

380600 11:43

Vertical Error 50

Error [m]

40 30 20 10 0 379100 11:18

379400 11:23

379700 380000 11:28 Local Time 11:33

Figure 5.20. Horizontal and vertical errors for base-line configurations with and without RAIM, considering only reliable epochs and using the NovAtel OEM615 receiver

of the inclusion of aiding clearly emerges; in fact the configurations with aiding, i.e. GPS with altitude aiding (magenta dashed line) and GPS/GLONASS with double aiding (blue dashed line), are characterized by smaller errors with respect to the base-line configurations, (green continuous line) for GPS only and (red continuous line) for GPS/GLONASS multi-constellation . The use of altitude aiding reduces significantly the vertical error: the RMS value is of metric order for both configurations. The use of aiding improves also the performance in the horizontal channel, this is due to the enhanced redundancy of the system which improves the performance of the RAIM algorithm. Statistical parameters of horizontal and vertical

Table 5.8. GNSS performance in the kinematic test with RAIM, using Novatel OEM615 receiver and considering only reliable epochs

Configuration GPS noRAIM GPS RAIM GG noRAIM GG RAIM

RMS[m] Horizontal Vertical 5.1 4.2 4.1 2.7 4.2 3.9 3.7 3.2 140


5.1 – Urban Tests Horizontal Error 50 GPS Only RAIM GPS Only Aid H RAIM GPS\GLONASS RAIM GPS\GLONASS Aiad H and CDT RAIM

Error [m]

40 30 20 10 0 379100 11:18

379400 11:23

379700 11:28

380000 11:33

380300 11:38

380600 11:43

380300 11:38

380600 11:43

Vertical Error 20

Error [m]

15 10 5 0 379100 11:18

379400 11:23

379700 380000 11:28 Local Time 11:33

Figure 5.21. Horizontal and vertical errors for the configurations with RAIM each configuration is analyzed in the relative reliable epochs and using Novatel OEM615 receiver.

Table 5.9. Statistical parameters of horizontal and vertical errors for the configurations with RAIM using NovAtel OEM615 receiver and considering only reliable epochs.

Configuration GPS RAIM GPS RAIM Aid H GG RAIM GG RAIM Double Aid

RMS[m] Horizontal Vertical 4.1 2.7 4.1 0.6 4.2 3.9 3.3 0.7


errors for the configurations using RAIM, considering reliable epochs, are summarized in Table 5.9. The RAIM application improves significantly the performance of aided configurations, in terms of RMS and maximum errors. The best performance is obtained combining GPS and GLONASS measurements with aid implementation, limiting the vertical error to a meter level, while the horizontal one is characterized by a 3.3 m RMS error and a 17.6 m maximum error, with a reliable availability of 62%. 141


5.1.3

High Sensitivity solution

In this section, the results obtained using the HS GPS receiver are analyzed. The performance is evaluated in terms of solution availability (without RAIM application) or reliable availability (when quality checking is performed); the accuracy is analyzed in terms of RMS and maximum error for both horizontal and vertical components. The data collected using the u-blox receiver are characterized, as expected, by a high solution availability (about 98% for GPS and 100% for GPS with altitude aiding) confirming the ability of this type of receiver to acquire and track very weak signals. Values of the solution availability and reliable availability for the configurations considered are summarized in Table 5.10. In the test scenario, due to low Signal-to-Noise Ratio (SNR) values and multipath effects, the navigation accuracy is degraded and the increased measurement noise prevents HS receivers from achieving the level of accuracy performance demonstrated in the previous section using a standard receiver. The solution provided by the u-blox receiver is characterized by very large errors, in the order of several hundreds of meters; horizontal and vertical errors are plotted as a function of time in Figure 5.22. From the upper box of Figure 5.22, it emerges that the two configurations GPS (red line) and GPS with altitude aiding provide similar performance: the two lines are very close to each other. In the base-line configuration case, i.e. GPS only without RAIM application, the horizontal error reaches a maximum value of 176.8 m. Also the configuration with aiding on the altitude provides similar performance and only 7 m of difference can be observed; a sub-metric difference emerges for the RMS value. From the lower box of Figure 5.22, the benefits of aiding clearly emerges: the maximum vertical error is strongly reduced passing from 788 m to 111.8 m. However, as highlighted in the previous section, when a blunder is presents, it produces a degradation of the performance of the aided configurations. In this case, this phenomenon is less evident because the accuracy of the unaided solution is very poor. These results are summarized in Table 5.11. In order to evaluate the benefits of the use of RAIM in urban scenarios and with a Table 5.10. Solution Availability and Reliable Availability of the position using the u-blox receiver

Configuration GPS noRAIM GPS Aid H GPS RAIM GPS RAIM Aid H

Solution Availability [%] 98 100 98 100 142

Reliable Availability [%] N.A. N.A. 70 82

5.1 – Urban Tests

Table 5.11. Statistical parameters of the horizontal and vertical errors for the configurations without RAIM using the u-blox receiver.

Configuration GPS RAIM GPS RAIM Aid H

RMS[m] Horizontal Vertical 51.0 64.1 51.3 58.4


HS receiver, the horizontal and vertical errors of the two configurations considered are plotted separately in Figure 5.23. From the upper box of Figure 5.23, it can be noted that aiding on the altitude slightly degrades the horizontal solution. In fact the blue line is higher than the red one. The two configurations are however very close and the differences in term of RMS error is only two meters. The degradation is more evident in the maximum error, which passes from 154 m to 283 m. RAIM improves significantly the performance in terms of RMS error for the vertical and horizontal components, maintaining a high reliable availability. RMS horizontal errors are halved and even better results are observed in the vertical component. The maximum horizontal error of the GPS aided configuration is degraded due to an erroneous measurement rejection in the presence of multiple blunders. From the lower box of Figure 5.23, the benefits of Horizontal Error 200

Error [m]

150 100 50 0

379300 11:22

379600 11:27

379900 11:32

380200 11:37

380500 11:42

Vertical Error 250

Error [m]

200

GPS (no RAIM) GPS aid (no RAIM)

Error up to 788 m

150 100 50 0

379300 11:22

379600 11:27

379900 11:32 Local Time

380200 11:37

380500 11:42

Figure 5.22. Horizontal (upper box) and vertical (lower box) errors as a functin of time using u-blox receiver without RAIM application.

143


Table 5.12. Statistical parameters of horizontal and vertical errors for the configurations with RAIM using u-blox receiver, considering only reliable solutions

Configuration GPS RAIM GPS RAIM Aid H



aiding and of the application of RAIM clearly emerges: the blue line is always lower than the red one. The maximum vertical error is reduced passing from 126 m to 5 m, and the RMS value is reduced by 15 times passing from 19.2 m to 1.3 m. The statistical parameters of the horizontal and vertical errors considering only reliable solutions are summarized in Table 5.12. In order to highlight the benefits of RAIM in the case of aiding, a comparison between the aided configurations is performed. The behavior of the horizontal and vertical error is shown in Figure 5.24. From the lower box clearly emerges that the use of RAIM provides a significant improvement in the vertical error. When a blunder is present in the measurement set, an erroneous value is assigned to the aiding degrading the parameter that is directly observed by the pseudo-measure. For a quantitative analysis, statistical parameters of the position error for the aided configurations, considering only the Horizontal Error 200

Error [m]

150

GPS (RAIM) GPS aid (RAIM)

100 50 0

379300 11:22

379600 11:27

379900 11:32

380200 11:37

380500 11:42

380200 11:37

380500 11:42

Vertical Error

Error [m]

150

100

50

0

379300 11:22

379600 11:27

379900 11:32 Local Time

Figure 5.23. Horizontal (upper box) and vertical (lower box) errors as a function of time using the u-blox receiver with RAIM application.

144

5.1 – Urban Tests Horizontal Error

Error [m]

300

200

100

0

379300 11:22

379600 11:27

379900 11:32

380200 11:37

380500 11:42

380200 11:37

380500 11:42

Vertical Error 120

Error [m]

100

GPS aid (no RAIM) GPS aid (RAIM)

80 60 40 20 0

379300 11:22

379600 11:27

379900 11:32 Local Time

Figure 5.24. Horizontal (upper box) and vertical (lower box) errors as a function of time using the u-blox receiver. Performance conparison between configuration with and without RAIM shows the advantages of the use of the quality checks and of aiding. Table 5.13. Statistical parameters of horizontal and vertical errors for the aided configurations using u-blox receiver, considering only reliable solutions

Configuration GPS Aid H GPS RAIM Aid H



reliable epochs, are summarized in Table 5.13

5.1.4

Main results for the urban scenarios

From the results presented above, it is possible to conclude that GPS/GLONASS multi-constellation shows evident improvements with respect to stand-alone GPS in terms of solution availability, accuracy and integrity. The use of aiding without quality control imporves mainly the solution availability and, in some cases, degrades the solutions accuracy. In urban application, RAIM algorithms are necessary to identify and reject several gross errors; moreover the Forward-Backward and the Danish methods are characterized by similar performance and by the smallest 145


errors, demonstrating the usefulness of the separability check module (which cannot be applied to Subset method). Subset method in characterized by highest value of reliable availability but also by the largest errors. The use of aiding on the altitude along with RAIM, improves the performance of the navigation solution for all parameters considered. Finally the comparison between a standard receiver and a HS device shows that the first receiver guarantees more accurate positioning but with a lower reliable availability. The usage of a HS receiver is justified only when the RAIM quality check is carried out.

5.2

Indoor Tests

Indoor navigation using radio navigation systems is a challenging task which involves the solution of several problems such as signal attenuation, fading and measurements biases due to multipath propagation. Although the range of operations of GNSS significantly extended by the development of new techniques such as HS, indoor location using GNSS alone is still very challenging. In order to demonstrate indoor location, the use of a HS GNSS receiver, which is able to track very weak signals, was considerd. The results obtained using a HS GNSS receiver are discussed in Section 5.2.1. Then the opportunity of using pseudolites for indoor navigation is investigated; results obtained in different indoor scenarios are analyzed. The goals and the results of the tests performed using pseudolites are detailed in Section 5.2.2 and in Section 5.2.5, respectively.

5.2.1

Indoor High Sensitivity solution

The first solution tested for indoor navigation was the use of a HS GNSS receiver able to track very weak signals. So a data collection has been carried out in the corridor on the first floor of a large office building on the Joint Research Centre (JRC) premises (Ispra, Italy) on July 2013. Several control points were placed in the corridor to verify the accuracy of the navigation solution. The equipment used for this test is composed by: a u-blox LEA-6T single frequency HS GPS receiver; a GPS patch antenna; a laptop for the storage of the measurements.

The equipment adopted is shown in Figure 5.25. The user equipped with the above mentioned devices, followed a straight-line trajectory in the corridor of the aforesaid building. The building was carefully surveyed in order to determine the coordinates of the control points used for performance evaluation. Ten control points were placed 146

5.2 – Indoor Tests

Control Points Rx Antenna

USB Connections: - U-blox LEA-6T - Realtek RTL2832U Figure 5.25. Equipment used for indoor positioning: a u-blox LEA-6T single frequency HS GPS receiver and a GPS antenna. The test was carried out in the corridor of the first floor of a large office building in the JRC premises (Ispra, Italy) on July 2013. Several control points were placed in the corridor for performance evaluation.

in the corridor and their coordinates are provided in Table 5.14. PRs provided by the u-blox receiver were used as input to the navigation algorithms described in Section 2.2.5. In Figure 5.2.1, the navigation solution obtained using ublox measurements (yellow markers) are plotted along with the control points (blue markers). From Figure 5.2.1, it clearly emerges that the GNSS solution is characterized by a very poor accuracy, the fixes are spread over the JRC campus and only occasionally the solutions are within the building. This demonstrates that GNSS alone may be completely unable to provide positioning information in these scenarios.

147


Table 5.14. Coordinates of control points placed on the corridor of the first floor of the building selected for the data collection.

Control Point 1 2 3 4 5 6 7 8 9 10

Latitude[deg] 45.80957863 45.80961859 45.80965153 45.80968534 45.80971853 45.80975222 45.80978156 45.80980333 45.80983036 45.80984677

Longitude [deg] 8.629906014 8.629904213 8.629902411 8.629900738 8.629898696 8.629896398 8.629895365 8.629893972 8.629892539 8.629891778

Figure 5.26. Indoor GNSS navigation solution. Position fixes obtained using the measurements from a HS GNSS receiver. Although the measurements were taken indoors, position fixes are only occasionally inside the building seleceted.

148


5.2.2

Indoor navigation asynchronous pseudolite solution, control point test

Considering the limitations of GNSS solution in indoors and considering the problems encountered using a synchronous pseudolite system aand detailed in Section 4.1, an alternative solution is adopted for indoor location and an asynchronous pseudolites network is used. In this section the position results obtained using an asynchronous pseudolite system and the RSSI approach, described in Section 4.2, are presented. Several tests were carried out in the same large office building mentioned above. The first test is similar to the one described in Section 5.2.1. The measurement unit used for the test is the same as that shown in Figure 5.25 and is composed by: a u-blox LEA-6T receiver able to collect pseudolite signal; a GNSS patch antenna; a laptop for the storage of the measurements.

For the first series of tests, the transmitter were the three Universal Software Radio Platform (USRP) pseudolites , described in [93] deployed as shown in Figure 5.28. The two configurations used for signal transmission are shown in Figure 5.27. In particular, a passive GNSS antenna was initially used for signal transmission as indicated in Figure 5.27 a). Although the antenna was passive and no additional amplifier (only the USRP internal amplifiers were used) was present in the transmission chain, the transmitted signal was too strong and saturated the receivers used for the data collection. In this way, information on the signal strength was lost. To limit the transmit power, a second configuration, with the transmit antenna removed was adopted Figure 5.27 b). The transmit power was reduced significantly and saturation in the receiver front-end was avoided. When configuration b) was used, it was possible to obtain useful information on the Received Signal Strength (RSS) and perform RSSI based positioning; so configuration b) was used for test analyzed in the following. The pseudolite coordinates are provided in Table 5.15. Table 5.15.

Device Pseudolite 1 Pseudolite 2 Pseudolite 3

Pseudolite coordinates

Latitude[deg] 45.80960246 45.80970315 45.80988520

149

Longitude [deg] 8.629953294 8.629947785 8.629839534


USRP Pseudolite

Antenna removed

a)

b)

Figure 5.27. USRP pseudolites. Two configurations used for signal transmission. A passive GNSS antenna was initially used for signal transmission as indicated in a). To limit the transmit power, a second configuration, with the transmit antenna removed was adopted b)

150


Control Points

Figure 5.28.

Location of the control points and of the three USRP pseudolites .

151


5.2.3

Calibration Stage for the corridor test

In order to use the RSSI approach described in Section 4.2, the parameters K (the constant accounting for the power of the transmitted signal) and α (the path-loss exponent) have to be knwon. This calibration process was performed by exploiting the knowledge of the control point positions and their distances from the pseudolites. The distances of the 3 pseudolites from the different control points are shown −1 in Figure 5.29 and have been used for estimating α and {Ki }N i=0 Eq. (4.8). The calibration of the parameters was performed using the data in a trial data collection. The Carrier-to-Noise power spectral density ratio (C/N0 ) values depicted in Figure 5.30 are associated to the different control points. Thus it is possible to plot the average C/N0 , observed at a specific control point, as a function of distance. The different measurements were then fitted according to model (4.6). The experimental points obtained are depicted in Figure 5.31 as small empty circles whereas continuous lines represent the interpolated model. Model (4.6) effectively interpolates experimental measurements and the values obtained for the different parameters are provided in Table 5.16. Note that a single α has been determined for all the measurements whereas Ki is a parameter specific to each pseudolite . The adoption of pseudolite specific Ki is justified by the fact that the USRPs are not calibrated and each device can transmit a slightly different power. This phenomenon clearly

PL - 1 PL - 2 PL - 3 30

Distances [m]

25

20

15

10

5 1

2

Figure 5.29.

3

4

5 6 Control Point ID

7

8

9

10

Control point distances from the different pseudolites .

152


45 CP4

CP5 CP8

40 CP6

CP3 35 C/N0 [dB-Hz]

CP9

CP7

30 CP2 25

CP1

20 15 10 PL - 1 PL - 2 PL - 3

5 0

50

Figure 5.30.

100

150 Time [s]

200

Estimated C/N0 values as a function of the control point location. PL1 - Experimental PL2 - Experimental PL3 - Experimental PL1 - Model fit PL2 - Model fit PL3 - Model fit

45

40

C/N0 [dB-Hz]

250

35

30

25

20

4

Figure 5.31.

6

8

10

12 Distance [m]

14

16

18

20

Calibration results interpolating C/N0 values as a function of distance.

153


Table 5.16.

Parameters for RSSI positioning obtained through calibration.

Parameter α K1 K2 K3

Value 5.1 82 dB(Hz·m) 75.5 dB(Hz·m) 87.2 dB(Hz·m)

emerges from Figure 5.31 which shows that pseudolite 3 has a larger Ki than pseudolite 2: experimental data lay on parallel curves and the adoption of a single Ki it is not possible. Using the values reported in Table 5.16, it was finally possible to perform indoor location using C/N0 measurements.

5.2.4

Corridor test: results

Further tests were carried out after the calibration step. During the considered test, the user moved along the trajectory defined by the control points: the user was static on each control point for about 20 seconds. The C/N0 values estimated using the u-blox receiver are plotted as a function of time in Figure 5.32. During the first phase of the test (0-55 second), the user was outside the building and the pseudolite signals were attenuated by walls and thus were too weak to be acquired. As shown in Figure 5.32, during the first part of the test no information was available to perform RSSI positioning. Therefore results are presented only for the portion of the test where valid measurements are available. The C/N0 values seem to represent the user’s location correctly; for instance, the blue curve of pseudolite 1 shows C/N0 values reaching their maximum (48 dB-Hz) when the user is on the third control point placed in front of the door of the room where the first pseudolite was placed. When the user passes the third control point a progressive decrease in C/N0 can be observed. The C/N0 values are provided in Figure 5.32 to facilitate interpretation of the results obtained in the position domain and discussed below. In particular, an anomalous behavior is noted in correspondence of control point 7. The C/N0 values depicted in Figure 5.32 were used to compute the user’s position based on the Weighted MSE (WMSE) algorithm presented in Section 4.2. The position fixes are shown in Figure 5.33 along with the pseudolite and control point coordinates which were represented in the local frame, East North Up (ENU). The origin of the local frame is pseudolite 1, the Y axis is coincident with the North direction whereas the X axis is directed along the East direction. The trajectory along the corridor was characterized by a displacement of about 154


50 45

CP6 CP1

40

PL1 PL 2 PL 3

CP9

CP5 CP8 CP3 CP4

C/N0 [dB-Hz]

35 30

CP7 CP2

25 20 15 10 5 0 0

50

100 Time [s]

150

200

Figure 5.32. Estimated C/N0 values as a function of time. The measurements presented were used for demonstrating RSSI positioning.

25 meters in the North-South direction and only 5 meters in the East-West direction. Note that the location of the pseudolites was dictated by the geometry of the building which is mainly oriented along the North-South direction. Consequently, the 3 devices were able to provide useful information mainly for the estimation of the North coordinate. In fact, they were mainly distributed along the user trajectory. Thus the position fixes depicted in Figure 5.33 are mainly scattered along the East-West direction. As already mentioned, the geometry along the East-West direction is quite poor due to the pseudolite displacement, i.e. the difference between pseudolite 1 and pseudolite 2 East coordinates is less than half a meter, and the only device placed on the opposite side of the building was pseudolite 3. For this reason, the error along the East-West direction reaches a maximum value of about 10 meters. This occurs in correspondence of control point 7 which is characterized by anomalous C/N0 measurements as highlighted in Figure 5.32. When excluding the position fixes corresponding to control point 7, the East-West error is however lower than 5 meters. This result is considered positive given the geometry of the system and the quality of the measurements. Quality checks of the measurements were not performed and no additional constraints, such as mapping and time domain filtering, were implemented. Improved performance is expected by enhancing the WMSE algorithm developed by introducing constraints and measurements from 155


40 Computed Position Pseudolite Control Point

35 30

North [Meters]

25 20 15 10 5 0 -5 -15

Figure 5.33.

-10

-5 East [Meters]

0

5

Horizontal position estimates obtained using an RSSI based algorithm.

other sensors. To demonstrate the impact of the pseudolite geometry on the position solution, performance along the North direction was analyzed separately in Figure 5.34, where the blue line represents the estimated North coordinates and the red dotted line represents the North coordinates of the control points expressed in the ENU frame. Form Figure 5.34, it emerges that the maximum error for the North coordinate has a maximum values of about 7 meters in correspondence of control point 7. Again, the error is probably due to the anomalous behavior of the C/N0 values shown in Figure 5.32. For the remaining part of test the North component is characterized by metric order accuracy.

156

5.2 – Indoor Tests 30 Estimated Reference 25 Control Point 7

North [Meters]

20

15

10

5

60

80

100

120

140 Time [s]

160

180

200

220

Figure 5.34. North coordinate evolution as a function of time. The red dotted line indicates the position of the control points.

5.2.5

Indoor navigation using asynchronous pseudolite system, repeatability test

Additional tests were carried out using a different pseudolite system, selecting different environments and adding a prefiltering stage to smooth C/N0 measurements. The consistency of the navigation solution is investigated with the repeatability tests described in Section 4.1.1. Although several experimetns were performed the results of a single test are presetned to avoid repetition of similar findings. During the test carried out the user performed five loops around a table present in a large meeting room trying to repeat always the same trajectory. This type of test has been carried out in order to verify the repeatability of the solutions. The quality of the navigation solution is assessed by comparing the different trajectories estimated for the different loops. A high consistency level of the navigation solution indicates the good performance of the system. The equipment used for the test is composed by: 4 pseudolites operating in the GPS L1 band and able to broadcast continuous and pulsed signals, the pseudolites are deployed as shown in Figure 4.3; a u-blox LEA-6T receiver able to collect pseudolite signals;

157


a GNSS patch antenna; an Android mobile phone, equipped with a suitable application, used to storage the data.

The pseudolites are Commercial Off-the-Shelf (COTS) devices procured from Space System Finland (SSF) and described in [93].

5.2.6

Calibration Stage for repeatability test

The calibration of the system has been performed using measurements collected during experiments involving control points as discussed in Section 4.1.2. The calibration process was performed by exploiting the knowledge of the control point positions and their distances from the pseudolites; the coordinates of the control points are provided in Table 4.2. Two different approaches were considered for the calibration: the first one considered different Ki for each pseudolite. In a second attempt, a common K value was considered. The power parameters, Ki and the path loss exponent, α, obtained for the first approach are summarized in Table 5.17. Calibration results interpolating C/N0 values as a function of distance are shown in Figure 5.35: the C/N0 values depicted are associated to the different control points. The experimental points obtained for the four pseudolites are depicted in Figure 5.35 as small empty circles whereas dashed lines represent the interpolated model. The Ki parameters obtained are very similar confirming that the devices are calibrated, i.e., broadcast similar power levels under similar propagation conditions. In order to exploit the fact that the SSF devices are calibrated and interpolation was performed considering a single K value (the index, i, was dropped for clarity). The value obtained using this second approach are reported in Table 5.18. The curve representing the interpolated model using the same K for all the pseudolites is depicted in Figure 5.36: the results are very close to the ones depicted in Figure 5.35, confirming that the two models are practically equivalent.

Table 5.17. Power parameters and path loss exponent for the meeting room experiments considering different received power levels.

Parameter α K1 K2 K3 K4

Value 2.95 63.43 dB(Hz·m) 61.14 dB(Hz·m) 60.94 dB(Hz·m) 59.00 dB(Hz·m) 158


50

45

C/N0 [dB-Hz]

40

35

PL1 - Experimental PL2 - Experimental PL3 - Experimental PL4 - Experimental PL1 - Model Fit PL2 - Model Fit PL3 - Model Fit PL4 - Model Fit

30

25

20

15

3

4

5

6 7 Distance [m]

8

9

10

Figure 5.35. Calibration results interpolating C/N0 values as a function of distance considering different power parameters, Ki . Meeting room tests.

Table 5.18. Power parameter and path loss exponent for the meeting room experiments considering a single, K.

k 60.66

159

α 3.02


50

45

C/N0 [dB-Hz]

40

35

30

25 PL1 - Experimental PL2 - Experimental PL3 - Experimental PL4 - Experimental Model Fit

20

15

3

4

5

6

7 Distance [m]

8

9

10

11

Figure 5.36. Calibration results interpolating C/N0 values as a function of distance considering a single power parameter, K. Meeting room tests.

160


5.2.7

Repeatability test results analysis

The raw C/N0 measurements collected during the repeatability test carried out in the meeting room are depicted in Figure 5.37 as a function of time. Measurements are not pre-processed and are characterized by high frequency noise variations. From Figure 5.37 it is possible to identify the laps performed from the periodicity of the signals. Raw measurements were used to compute position using the approach described in Section 4.2. Positioning results obtained using the raw measurements are shown in Figure 5.38. Although, the position solution obtained using these measurements is contained inside the room, it is not possible to identify the trajectory followed by the user. In order to improve the solution, a pre-filtering stage was introduced on the measurements. A Butterworth filter of order 13 was adopted. The cut-off frequency was determined by considering the spectral content of the C/N0 measurements: only the main lobe of the C/N0 Power Spectral Density (PSD) was retained. The filtered measurements are depicted in Figure 5.39 whereas their normalized PSDs are provided in Figure 5.40 along with the transfer function of the filter. Filtering removes high frequency noise components without distorting the low frequency variations of the C/N0 measurements. These variations are due to the user motion. The laps performed by the user clearly appear in the smoothed measure-

60

LAP 2

LAP 3

LAP 1

LAP 4

LAP 5

C/N0 [dB-Hz]

50

40

30

20

10

0

PL 1 PL 2 PL 3 PL 4 20

40

60

80 100 Time [s]

120

140

160

Figure 5.37. Estimated C/N0 values as a function of time. The measurements were used for RSS positioning.

161


Estimated Position PL

PL 4 10

PL 1

9 8

North [Meters]

7 6 5 4 3 2 1 0 -2

PL 3 -1

0

1

2

3 4 East [Meters]

5

6

PL 2 7

8

Figure 5.38. Position estimates obtained using the RSS algorithm and processing raw C/N0 measurements.

ments. It can be noted that after the second lap, a loss of lock occurred on the signal broadcast by pseudolite 3. This is clearly indicated in Figure 5.39. The filtered measurements were used to compute the position solution using RSS algorithm described in Section 4.2: the position estimated using the smoothed measurements is plotted in Figure 5.41. From Figure 5.41, the impact of filtering clearly emerges: the user trajectory can be easily identified with a high level of consistence among the different laps. In order to further analyze the repeatability of the results, each lap is plotted singularly in Figure 5.42. The position solution estimated for the four laps in Figure 5.42 is very consistent; only a slight difference (sub-meter level) between the different laps emerges, demonstrating the high repeatability and consistence of the test. In order to investigate the effect of the loss of lock highlighted in Figure 5.39, the solution of lap 3 is depicted in Figure 5.43. Although the loss of lock on the signal of pseudolite 3 in the first part of the third lap degrades the position solution, the error is still of metric order demonstrating the robustness of the algorithm developed which is able to provide reliable solutions using only three pseudolites. Only a slight degradation of the position accuracy is observed and is due to the change of the geometry. Exploiting the knowledge of the absolute position of the origin of the local frame, the solution computed can be easily transformed from the local frame to the WGS84 162


60 55

LAP 3

LAP 2

LAP 1

LAP 4

LAP 5

50 45

C/N0 [dB-Hz]

40 35 30 25 20 15

PL1 PL 2 PL 3 PL 4

Loss of Lock PL 3

10 5 20

40

60

80 100 Time [s]

120

140

160

Figure 5.39. Estimated C/N0 values as a function of time. Filtered C/N0 measurements using a Butterworth filter of order 13.

frame. The obtained solution is plotted using the Google Earth software in Figure 5.44. From the analysis, it emerged that 3 pseudolites are sufficient to enable indoor navigation in a large meeting room with meter level accuracy. The use of 4 pseudolites improves the geometry of the system further enhancing the accuracy of the solution.

163


15

10 Filter Transfer Function

Normalized PSD [dB]

5

0

-5

-10

-15

-20 0

0.05

0.1

0.15

0.2 0.25 0.3 Frequency [Hz]

0.35

0.4

0.45

0.5

Figure 5.40. PSDs of the C/N0 measurements and transfer function of the Butterworth filter used to pre-process raw observations.

10

Estimated Position PL

9 8

North [Meters]

7 6 5 4 3 2 1 1

Figure 5.41.

2

3

4 East [Meters]

5

6

7

Position estimates obtained using filtered C/N0 measurements.

164


LAP 2

10

10

8

8

North [Meters]

North [Meters]

LAP 1

6 4 2

4 2

1

2

3 4 East [Meters]

5

6

LAP 4

10

2

Estimated Position PL 10

8

North [Meters]

North [Meters]

6

6 4 2

4 East [Meters]

6

LAP 5

8 6 4 2

1

2

3 4 East [Meters]

5

6

1

2

3 4 East [Meters]

5

6

Figure 5.42. Position estimates obtained using filtered C/N0 measurements, each lap is analyzed separately. Lap 3 is considered separately in Figure 5.43 in order to better investigate the impact of loss of lock.

165


LAP 3 10 Estimated Position PL

9 8

North [Meters]

7 6 5 4 3 2 1 1

2

3 4 East [Meters]

5

6

Figure 5.43. Effect of the loss of lock of one pseudolite signal in the position estimates obtained using filtered C/N0 measurements. Third lap.

166


Figure 5.44. Position solution in the WGS84 absolute coordinate system. Meeting room, repeatability test.

167

168

Chapter 6 Conclusions and future work In this thesis, the performance of different Global Navigation Satellite System (GNSS) configurations, such as multi-constellation GPS/GLONASS and multi-constellation GPS/Galileo was assessed, in several environments from open-sky to indoors. Specific interest was devoted to Location Based Service (LBS) in urban environments. Three different Receiver Autonomous Integrity Monitoring (RAIM) algorithms were developed and the benefits of their use was evaluated in signal degraded scenarios in both position and velocity domains. The main motivation behind the multiconstellation approach is the lack of coverage of GPS in signal-degraded environments such as urban canyons. These scenarios are characterized by the presence of multiple blunders within the measurement set which signifincately degrade the location accuracy. The recent development of several GNSSs, such as the Erupean Galileo and the Russian satellite system GLONASS, suggest the combined use with GPS to increase continuity, accuracy and integrity of the navigation solution. GLONASS is currently the main candidate as component of a GNSS multi-constellation and it is the only system fully operational along with GPS. Galileo has only 4 satellites and is still in its In Orbit Validation (IOV) phase. This thesis analyzed the multi-constellation opportunity, investigating GPS/Galileo multi-constellation solution using real data collected in open-sky. The performance of multi-constellation GPS/GLONASS solution was investigated in urban canyon with pedestrian data collections, highlighting the improvements provided by the inclusion of the second GNSS measurememts. Although reliability and quality monitoring are not always available in signal degraded environments due to a lack of redundancy, when available, they provide significant enhancements to navigation reliability and accuracy. Reliability theory, in terms of reliability testing and statistical reliability conditions of a navigation system, was discussed. Classical RAIM techniques were analyzed and their limitations 169

6 – Conclusions and future work

in signal degraded scenarios were investigated; such limitations pushed the development of modified algorithms suitable to identify and reject multiple blunders. In order to improve the performance of the classical RAIM schemes, several additional checks were introduced to verify the geometry of the system and the correlation among the measurements. The application of reliability theory in the Fault Detection and Exclusion (FDE) schemes developed was demonstrated using real-life data in different configurations. Performance of multi-constellation GPS/GLONASS navigationn in urban environments in static and kinematic tests was evaluated applying the three schemes proposed, i.e., the Forward-Backward, the robust Danish estimation method, and the Subset Testing. The procedures (i.e., the Forward-Backward, the robust Danish estimation method, and the Subset Testing) considered demonstrated significant reliability and accuracy improvements in signal degraded environments navigation. Although epoch-byepoch Weighted LS (WLS) estimation was used to assess the reliability enhancement methods implemented. The ideas introduced can be easily extended to Kalman filtering and, thus, widely applicable to various dynamic navigation applications. Exploiting the concept adopted in a Kalman filter, i.e., hypotheses on the behavior of the unknowns, augmentation techniques, such as the use of pseudo-measurements, were introduced. The effects of pseudo-measurements, i.e. aiding on altitude and on inter-system bias, was evaluated using real data collected with different types of receivers. The advantages and the limitations of High-Sensitivity (HS) receivers were analyzed using real data, and the performance of this type of receiver was compared to standard devices. The extension of GNSS positioning to indoors, using HS receivers, was also evaluated and alternative solutions using pseudolites were discussed. Performance of synchronous pseudolite systems were investigated and problems relative to the synchronization process discussed. Finally asynchronous pseudolite positioning using a Received Signal Strength Indicator (RSSI) approach was analyzed.

6.1

Main results

This thesis considered reliability and quality monitoring at the user level for personal navigation applications. Reliability monitoring was conducted on both position and velocity solutions. The failure detection and exclusion methods developed proved to be of great importance in signal degraded environments in order to provide reliable and accurate navigation solutions. Navigation errors were analyzed with real data acquired in open-sky, urban canyon, and indoor scenarios. The main results obtained in this thesis can be conveniently summarized with respect 170

6.1 – Main results

to the scenarios considered. Open-sky The quality of Galileo PRs and PR rates on the E1BC and E5a frequencies was analyzed. From the analysis of the Galileo observables the following conclusions can be drawn: PR analysis demonstrates that IOV measurements are characterized by similar accuracies: for E1BC the PR RMS error varies from 0.31 m to 0.37 m and the maximum error is of metric order. The analysis on the E1BC and E5a demonstrated that the E5a signal has performance similar to that of the E1bc signal. A performance degradation is observed in the Galileo E5a measurements. This degradation was not expected but a similar phenomenon was observed for GIOVE-A measurements. PR-rates analysis demonstrates that the four Galileo satellites provide similar measurement accuracies and differences are of mm/s order. Differences between E1 and E5a measurements are less evident than in the PR case. Galileo PR errors are reduced by almost 50% with respect to Global Positioning System (GPS). The advantages of the European GNSS clearly emerge in terms of maximum and Root Mean Square (RMS) errors. In both position and velocity domains the comparison between Galileo and GPS demonstrates the Galileo potentiality: the mean error is reduced of 2 meters in the position domain whereas in the velocity domain the configurations considered are characterized by similar performance with differences lower than 2 cm/s. The use of multi-constellation GSP/Galileo shown that the maximum positioning error is only slightly reduced with respect to the GPS-only case.

Urban canyon Combined GPS/GLONASS positioning was attempted in urban scenarios and the following conclusions were obtained: GPS/GLONASS multi-constellation solution shows evident improvements with respect to stand-alone GPS in terms of solution availability and accuracy, parameters which are usually considered critical in urban scenarios. The use of the GLObal NAvigation Satellite System (GLONASS) observables provide an improvements of the solution availability of almost 10% with respect to the GPS only case.

171


A reduction of RMS and maximum errors can be noted when GPS/GLONASS measurements are used together. The RMS values are reduced of one meter for both horizontal and vertical components; more evident is the improvements in the maximum error which is reduced of 8 meters in the horizontal plane. The use of aiding, i.e. pseudo-measures on the altitude and on the intersystem bias, without quality control improves the solution availability, which is doubled with respect to the base-line configuration. Without RAIM application, aided configurations can degrade the navigation solution with respect to various aspects, above all for the lack of blunder check. In urban scenarios the application of RAIM algorithms is necessary to identify and reject several gross errors, which strongly degrade the navigation solution. The proposed RAIM (Forward-Backward, Danish and Subset methods) algorithms are analyzed in terms of reliable availability and of RMS and maximum errors. The reliable availability is the percentage of time when the solution is declared reliable by the RAIM schemes adopted. Subset method in characterized by the highest value of reliable availability but also by the largest errors. The Forward-Backward and the Danish methods are characterized by similar performance and by the smallest errors, demonstrating the validity of the separability check module (which cannot be applied to Subset method). The three methods have been tested on both position and velocity domains, showing comparable robustness. The inclusion of GLONASS measurements provides benefits in terms of reliable availability, accuracy and integrity due to the augmented redundancy which also improves the RAIM performance. In urban canyon, the use of the aid on the altitude along with RAIM, improve the performance of the vertical component for both RMS and maximum values which are strongly reduced with respect to the baseline configuration. Such enhancements are clear for both GPS only and GPS/GLONASS cases. The use of aiding, along with RAIM algorithms, improves significantly the performance in terms of both RMS and maximum position errors for horizontal and vertical components.

172

6.2 – Future Work

The comparison between a standard receiver and a HS device shows that the first receiver guarantees more accurate positioning but with a lower reliable availability with respect to the other one. The use of a HS device seems justified for urban scenarios only when RAIM quality checks are implemented.

Indoors The results obtained when investigating indoor navigation show that GNSS signals are currently inadeguate for this task, due to several problems such as signal attenuation, fading and measurements biases due to multipath. More specifically the following finding were obtained. An alternative solution for indoor navigation is required. Pseudolite was thus considered for its ability to provide GNSS-like signals, hence only little modifications are required to the classical GNSS receivers. A pseudolite system was used in synchronous and asynchronous mode and performance analysis was carried out. The limitations of synchronous pseudolite systems were analyzed and it was shown that multipath and other propagation problems can prevent the system from achieving the level of synchronization required for determining travel time measurements. The results obtained indicated that synchronous pseudolite system is not suitable for deep indoor navigation: the performance of an indoor navigation system can be significantly degraded by poor geometries and interference problems. Althoug a solution based on differential positioning was proposed, it was not possible to achieve reliable solution. Using asynchronous pseudolites , indoor navigation with meter level accuracy is possible and has been demonstrated. From the analysis, it emerged that 3 pseudolites are sufficient to enable indoor navigation in an office area of about 350 square meters with meter level accuracy.

6.2

Future Work

The results obtained demonstrate the benefit of the GPS/GLONASS multi-constellation with respect to the GPS only case in urban scenarios; with this in mind a future development of this research will include the Galileo system considering a multiconstellation GPS/GLONASS/Galileo. 173


The obtained results show the effectiveness of the algorithms adopted in terms of reliable availability and of RMS and maximum errors. A possible extension of the work presented here is the adoption of reliability and quality monitoring for Kalman filtering, which provide improved estimations of the navigation parameters for a dynamic user (assuming that the state and observation models are correct). Additional sensors, such as inertial units, and cellular network observables, Digital Video Broadcasting - Terrestrial (DVB-T) signals can be integrated as aiding to GNSS navigation in order to reach sufficient availability of navigation solution in urban and indoor scenarios. The results obtained in indoor environments are particularly encouraging, since they were obtained without exploiting map constraints and prior knowledge of the user position. The inclusion of such constraints and the propagation of the user position, for example using a Kalman filter, are currently under investigation and will be analyzed in future work. The integration between pseudolite and GNSS measurements is still an open issue.

174

Bibliography [1] J. F. Raquet. Navigation using pseudolites, beacons, and signals of opportunity. In Navigation Sensors and Systems in Global Navigation Satellite Systems (GNSS) Denied Environments, 2013. [2] Cillian O’Driscoll, Daniele Borio, and Joaquim Fortuny. Scoping study on pseudolites. Technical report, EC Joint Reseach Centre, March 2011. [3] Septentrio Satellite Navigation. PolaRxS Application Manual, Version 2.1.0 September 30, 2010, 2010. [4] JAVAD RIng Antenna. [5] U.S. Department of Defense, U.S. Department of Homeland Security, and U.S. Department of Transportation. 2008 federal radionavigation plan. Technical report, U.S. Department of Defense and U.S. Department of Homeland Security and U.S. Department of Transportation, 2008. [6] C. ODriscoll, G. Lachapelle, and M. E. Tamazin. Investigation of the benefits of combined gps/glonass receivers in urban environments. In NAV10, London, 2010. Royal Institute of Navigation. [7] H. Kuusniemi. User-Level Reliability and Quality Monitoring in Satellite-Based Personal Navigation. PhD thesis, Tampere University of Technology, Finland, 2005. Publication 544. [8] A. Wieser. High-sensitivity gnss: the trade-off between availability and accuracy. In 3rd Symposium Geodesy for Geotechnical and Structural Engineering, 2006. [9] Z. He. High-Sensitivity GNSS Doppler and Velocity Estimation for Indoor Navigation. PhD thesis, Department of Geomatics Engineering, The University of Calgary, Calgary, Canada, 2013. [10] M. B. Kjrgaard, H. Blunck, T. Godsk, T. Toftkjr, D. L. Christensen, and K. Grnbk. Indoor positioning using gps revisited. In 8th international conference on Pervasive Computing, 2010. [11] Y. C. Lee and K. L. Van Dyke. Analysis performed in support of the ad-hoc working group of rtca sc-159 on raim/fde issues. In ION NTM, page 639654, San Diego, CA, 2002. Institute of Navigation. [12] US Department of Defense. Global positioning system standard positioning 175

Bibliography

[13] [14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

service performance standard. Technical report, US Department of Defense, September 2008. T. Walter and P. Enge. Weighted raim for precision approach. In ION GPS, page 19952004, Palm Springs, CA, September 1995. Institute of Navigation. Brown and R. Grover. A baseline gps raim scheme and a note on the equivalence of three raim methods. NAVIGATION, Journal of The Institute of Navigation, 39(3):301–316, 1992. T. Walter, P. Enge, J. Blanch, and B. Pervan. Vertical guidance of aircraft based on modernized gps and new integrity augmentations. In IEEE Special Issue on Aviation Information Systems, volume 96, December 2008. A. Ene. Further development of galileo-gps raim for vertical guidance. In Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), pages 2597–2607, Fort Worth Convention Center, Fort Worth, TX, September 2006. The Institute of Navigation. M. A. Sturza and A. K. Brown. Integrated gps/glonass for reliable receiver autonomous integrity monitoring (raim). In Proceedings of the 46th Annual Meeting of The Institute of Navigation, pages 9–13, Atlantic City, NJ, June 1990. The Institute of Navigation. P. B. Ober and D. Harriman. On the use of multiconstellation-raim for aircraft approaches. In Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), pages 2587– 2596, Fort Worth, TX, September 2006. A. Angrisano, S. Gaglione, and G. Del Core C. Gioia. Gnss reliability testing in signal-degraded scenario. Internation Journal of Navigation and Observation, 1:1–12, 2013. B. S. Pervan, D. G. Lawrence, and B.W. Parkinson. Autonomous fault detection and removal using gps carrier phase. IEEE Trans. Aerospace and Electronic Systems, 3:897906, July 1998. R. Hatch, T. Sharpe, and Y. Yang. A simple raim and fault isolation scheme. In ION GPS, page 801808, Portland, OR., September 2003. Institute of Navigation. S. Ryan. Augmentation of DGPS for Marine Navigation. PhD thesis, Department of Geomatics Engineering, The University of Calgary, Calgary, Canada, 2002. G. MacGougan and J. Liu. Fault detection methods and testing for marine gps receivers. In ION GPS, page 26682678, Portland, OR, September 2002. Institute of Navigation. H. Kuusniemi, A.Wieser, G. Lachapelle, and J. Takala. User-level reliability monitoring in urban personal satellite-navigation. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 43(4):1305–1318, October 176

Bibliography

[25]

[26]

[27]

[28] [29]

[30]

[31]

[32] [33]

[34] [35]

[36]

[37]

[38]

2007. A. Angrisano, S. Gaglione, and C. Gioia. Raim algorithms for aided gnss in urban scenario. In Ubiquitous Positioning, Indoor Navigation, and Location Based Service (UPINLBS), 2012. ISBN: 978-1-4673-1908-9. C. Cai and Y. Gao. A combined gps/glonass navigation algorithm for use with limited satellite visibility. THE JOURNAL OF NAVIGATION, 62:671–685, 2009. A. Angrisano, S. Gaglione, and C. Gioia. Performance assessment of gps/glonass single point positioning in an urban environment. Acta Geodaetica et Geophysica, 48:149–161, June 2013. B. Hoffmann-Wellenhof, H. Lichtenegger, and J. Collins. Global Positioning System: Theory and Practice. Springer, 1992. B. Parkinson, J. Spilker Jr., P. Axelrad, and P. Enge (Author). Global Positioning System: Theory And Applications, volume I. American Institute of Aeronautics and Astronautics, Washington D.C., USA, 1996. DoD Positioning Navigation and Timing Executive Committee. Gps standard positioning service performance standard. Technical report, DoD Positioning Navigation and Timing Executive Committee, September 2008. Russian Institute of Space Device Engineering. Global navigation satellite system glonass interface control document. Technical Report Edition 5.1, Russian Institute of Space Device Engineering, Moscow, 2008. E. D. Kaplan. Understanding GPS: Principles and Applications. Second Edition. Artech House, November 2005. Navstar GPS Directorate. Global positioning systems directorate systems engineering & integration interface specification is-gps-200. Technical report, Navstar GPS Directorate, September 2012. European Union. European gnss (galileo) open service signal in space interface control document. OS SIS IC 1.1, European Union, September 2010. J. F. Raquet. Development of a Method for Kinematic GPS CarrierPhase Ambiguity Resolution Using Multiple Reference Receivers. PhD thesis, University of Calgary, 1998. UCGE Report 20116 http://www.ensu.ucalgary.ca/links/GradTheses.html. J. A. Klobuchar. Ionospheric time-delay algorithm for single-frequency gps usersionospheric time-delay algorithm for single-frequency gps users. IEEE Transactions on aerospace and electronic systems, AES- 23, N. 3:325–331, 1987. A. Angrisano, S. Gaglione, C. Gioia, M. Massaro, and U. Robustelli. Assessment of nequick ionospheric model for galileo single-frequency users. Acta Geophysica, 2:1–20, April 2013. J. Sastamoinen. Contribution to the theory of atmospheric refraction, part ii refraction correction in satellite geodesy. Bulletin Geodesique, 107:13–34, 1993. 177

Bibliography

[39] D. A. Vallado. Covariance transformations for satellite flight dynamics operations. In AAS/AIAA Astrodynamics Specialist Conference, 2003. [40] O. Mezentsev. Sensor Aiding of HSGPS Pedestrian Navigation. PhD thesis, Department of Geomatics Engineering, University of Calgary, Canada, 2005. UCGE Report No. 20212. [41] S. Godha. Performance evaluation of low cost mems-based imu integrated with gps for land vehicle navigation application. Master’s thesis, Department of Geomatics Engineering, University of Calgary, Canada, 2006. UCGE Report No. 20239. [42] J. A. Farrell and M. Barth. The Global Positioning System & Inertial Navigation. McGraw-Hill Professional, 1998. [43] Y. Bar-Shalom, X. Rong Li, and T. Kirubarajan. Estimation with Applications to Tracking and Navigation. John Willey and Sons, New York, June 2001. [44] E. M. Mikhail. Observations and Least Squares. IEP, 1976. [45] R. G. Brown and P. Y. C. Hwang. Introduction to Random Signals and Applied Kalman Filtering. Wiley, 1996. [46] N. El-Sheimy. Inertial techniques and ins/dgps integration, 2004. ENGO 623Course Notes, Department of Geomatics Engineering, University of Calgary, Canada. [47] B. W. Remondi. Computing satellite velocity using the broadcast ephemeris. GPS Solutions, III:181–183, 2004. [48] H. S. Hopfield. Two quartic tropospheric reflectivity provile for correcting satellite data. Journal of Geophysical Research, Vol. 74:4487–4499, 1986. [49] Special Committee 159. Minimum operational performance standards for global positioning system/wide area augmentation system airborne equipment, rtca. Technical Report Document DO-229D, RTCA, 1828 L Street, NW, Suite 805 Washington, DC 20036, November 2001. [50] S. Kuang. Geodetic Network Analysis and Optimal Design: Concepts and Applications. Ann Arbor Press, 1996. [51] J. L. Farrell and F. V. Graas. Statistical validation for gps integrity test. NAVIGATION, Journal of The Institute of Navigation, V:89102, 1998. Red Book of RAIM. [52] A. K. Brown. Receiver autonomous integrity monitoring using a 24-satellite gps constellation. NAVIGATION, Journal of The Institute of Navigation, V:2133, 1998. Red Book of RAIM. [53] M. Petovello. Real-time Integration of a Tactical-Grade IMU and GPS for HighAccuracy Positioning and Navigation. PhD thesis, Department of Geomatics Engineering, University of Calgary, Calgary, 2003. UCGE Report No. 20173. [54] W. Baarda. A testing procedure for use in geodetic networks. Publication on Geodesy New Series 2. No. 5, Netherlands Geodetic Commission, Delft, Netherlands, 1968. 178

Bibliography

[55] J.Wang S. Hewitson. Impact of dynamic information on gnss receiver integrity monitoring. In International Symposium on GNSS/GPS, Sydney, Australia, December 2004. [56] G. Lachapelle S. Ryan. Augmentation of dgnss with dynamic constraints for marine navigation. In ION GPS, Nashville, TN,, September 1999. Institute of Navigation. [57] G. Lachapelle A. Wieser, M. Petovello. Failure scenarios to be considered with kinematic high precision relative gnss positioning. In ION GNSS, 2004. [58] P. J. G. Teunissen. GPS for Geodesy. Springer, 2nd edition edition, 1998. [59] J. H. KRAEMER G. Y. CHIN. Gps raim: Screening out bad geometries under worst-case bias conditions. NAVIGATION: Journal of The Institute of Navigation, 39:117–137, 1992. [60] G.Y: Chin R.G. Brown. Gps raim calculation of threshold and protection radius using chi-square methods - a geometric approach. NAVIGATION, Journal of The Institute of Navigation, V:155179, 1997. [61] J. Wang S. Hewitson. Gnss receiver autonomous integrity monitoring (raim) performance analysis. GPS Solutions, 10:155–170, 2006. [62] T. Y. Shih C. S. Hsieh. On gross error detection methods for control points in image registration. Journal of C.C.I.T., 34:1–17, 2006. [63] S.M. Chamberlain. Combined gps/glonass navigation,. In Proceedings, Telesystems Conference, 1991. [64] C. Cai. Precise point positioning using dual-frequency gps and glonass measurements. Master’s thesis, UNIVERSITY OF CALGARY DEPARTMENT OF GEOMATICS ENGINEERING, 2009. [65] Z. Wang Y. Zhang. Analyses and solutions of errors on gps/glonass positioning. Goa-spatial Information, Volume 5, Issue 2, June 2002:6–12, 2002. [66] M. P. Stewart A. Leick J. Wang, C. Rizos. Gps and glonass integration: Modeling and ambiguity resolution issues. GPS Solutions, Vol. 5, No. 1:55–64, 2001. [67] C. Gioia D. Borio J. Fortuny-Guasch A. Angrisano, S. Gaglione. Testing the test satellites: the galileo iov measurement accuracy. In International Conference on Localization and GNSS (ICL-GNSS), 2013. [68] B. Burke P. Misra, M. Pratt. Augmentation of gps/laas with glonass: performance assessment. In ION GPS-98. 11th Int. Technical Meeting of the Satellite Division of the Institute of Navigation, 1998. [69] Z. Altamimi C. Boucher. Itrs, pz-90 and wgs 84: current realizations and the related transformation parameters. Journal of Geodesy, 75:613–619, 2001. [70] C. Gioia A. Angrisano, S. Gaglione. Performance assessment of aided global navigation satellite system for land navigation. IET Radar, Sonar & Navigation, 7:671680, 2013. [71] Stewart H. Cobb. GPS pseudolites: Theory, Design and Applications. Phd thesis, Stanford University, September 1997. 179

Bibliography

[72] T. A. Stansell. Rtcm sc-104 recommended pseudolite signal specification. NAVIGATION: Journal of The Institute of Navigation, 33(1):42–59, 1986. [73] D. Borio C. O’Driscoll and J. Fortuny-Guasch. Investigation of pulsing schemes for pseudolite applications. In In Proc. of the ION/GNSS, Portland, OR, September 2011. [74] M. Ishii H. Torimoto S. Kogure-H. Maeda. D. Manandhar, K. Okano. Development of ultimate seamless positioning system based on qzss imes. In In Proc. of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), 2008. [75] A. Dempster. Qzss’s indoor messaging system gnss friend or foe? Inside GNSS, 4(1) January/February:37–40, 2009. [76] Japan Aerospace Exploration Agency. Interface specification for qzss (is-qzss),. Technical report, JAXA, 2010. [77] A. ANGRISANO, S. GAGLIONE, C. GIOIA, U. ROBUSTELLI, and M. VULTAGGIO. Giove satellites pseudorange error assessment. JOURNAL OF NAVIGATION, 65:29–40, 2012. [78] J. T. Curran, Petovello M., and Lachapelle G. Plan group tracks galileo satellites for positioning in canada. GPS World, March:1, 2013. [79] P. Steigenberger, U. Hugentobler, O. Montenbruck, and A. Hauschild A. Precise orbit determination of giove-b based on the congo network. Journal of Geodesy, 85:357365, 2011. [80] A. Simsky, D. Mertens, J-M. Sleewaegen, M. Hollreiser, and M. Crisci. Experimental results for the multipath performance of galileo signals transmitted by giove-a satellite. International Journal of Navigation and Observation, I:13, 2008. [81] A. Simsky, D. Mertens, J-M. Sleewaegen, M. Hollreiser, and M. Crisci. Multipath and tracking performance of galileoranging signals transmitted by giove-a. In 20th International Technical Meeting of the Satellite Division of The Institute of Navigation, 2007. [82] J. A. A. Rodriguez, G. W. Hein, IM. rsigler, and T. Pany. Combined galileo/gps frequency and signal performance analysis. In ION GNSS 2004 Long Beach California, 2004. [83] G. Xu. GPS: Theory, Algorithms and Applications. Springer-Verlag Berlin Heidelberg, 2003. [84] H. Laitinen and M. Str¨om. Single-frequency carrier navigation in a synchronised pseudolite network. In Proc. of the European Navigation Conference ENCGNSS, pages 1–8, Naples, Italy, May 2009. [85] Space System Finland. GSG-L1 GPS Signal Generator User’s Manual, February 2007. [86] Space System Finland. User’s Manual Pseudolite Navigation System, March 2010. 180

Bibliography

[87] Jonas Lindstr¨om, Dennis M. Akos, Oscar Isoz, and Marcus Junered. GNSS interference detection and localization using a network of low cost front-end modules. In Proc. of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation ION/GNSS, pages 1165–1172, Fort Worth, TX, September 2007. [88] D. Fontanella, R. Bauernfeind, and B. Eissfeller. In-car GNSS jammer localization with a vehicular ad-hoc network. In Proc. of the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation ION/GNSS, pages 2885–2893, Nashville, TN, September 2012. [89] N. Patwari, J.N. Ash, S. Kyperountas, A.O. Hero III, R. L. Moses, and N.S.Correal. Locating the nodes: cooperative localization in wireless sensor networks. 22(4):54–69, July 2005. [90] Logan Scott. J911: The case for fast jammer detection and location using crowdsourcing approaches. In Proc. of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation ION/GNSS, pages 1931– 1940, Portland, OR, September 2011. [91] Oscar Isoz, Asghar T. Balaei, and Dennis Akos. Interference detection and localization in the GPS l1 band. In Proc. of the International Technical Meeting of The Institute of Navigation (ITM/ION), pages 925–929, San Diego, CA, January 2010. [92] I. Kraemer, P. Dykta, R. Bauernfeind, and B. Eissfeller. Android GPS jammer localizer application based on C/N0 measurements and pedestrian dead reckoning. In Proc. of the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation ION/GNSS, pages 3154–3162, Nashville, OR, September 2012. [93] D.Borio and C.Gioia. Indoor navigation using asynchronous pseudolites. In 6th European Workshop on GNSS Signals and Signal Processing, 2013.

181

GNSS Navigation in Difficult Environments - PANG - Parthenope

GNSS Navigation in Difficult Environments - PANG - Parthenope

Suggest Documents

GNSS Navigation in Difficult Environments - PANG - Parthenope

gnss navigation in difficult environments: hybridization and ... - PANG

GNSS Navigation in Difficult Environments ...

A Galileo IOV assessment: measurement and ... - PANG - Parthenope

Assisted GNSS Navigation in Lunar Missions

Assisted GNSS Navigation in Lunar Missions

Robust Navigation In GNSS Degraded Environment

Constrained Navigation Environments - CiteSeerX

Navigation Message Authentication Schemes - Inside GNSS

GNSS Navigation Performance with Long-Term ...

Navigation Message Authentication Schemes - Inside GNSS

Spatial Navigation in Virtual Reality Environments

Autonomous navigation in natural environments - Springer Link

Reactive Navigation in Outdoor Environments using ... - CiteSeerX

Mobile Robots Navigation in Indoor Environments ...

Navigation and Mapping in Large Unstructured Environments

Constrained Navigation Environments - Semantic Scholar

Autonomous MAV Navigation in Complex GNSS ... - ais.uni-bonn.de

Implementation of GNSS/GPS Navigation and its Attacks in UAVSim ...

Autonomous Navigation for Micro Aerial Vehicles in Complex GNSS ...

Autonomous MAV Navigation in Complex GNSS-denied 3D ...

Simulation of GNSS Availability in Urban Environments Using a

Snapshot Software Receiver for GNSS in Weak Signal Environments ...

23 Prediction of GNSS Availability and Accuracy in Urban Environments