GNSS Navigation in Difficult Environments: Hybridization and Reliability
2 Giorni di Geomatica Firenze June 2015
Ciro Gioia PhD in Geodetic and Topographical Sciences at Università degli studi di Napoli Parthenope
Outline Background Estimation
Multi-constellation Opportunity RAIM Concepts/Algorithms Urban and Indoor Navigation Conclusions and Outlook
Background and Motivation (1/2)
GNSS provides 3-D PVT GNSS positioning is based on the one-way ranging technique and on trilateration.
Mode of operation: Single Point Positioning or Relative Observables: Pseudorange, Doppler Shift, Carrier Phase
Background and Motivation (2/2)
Satellite navigation critical in signaldegraded scenarios;
GPS alone cannot provide accurate and continuous positioning.
Estimation (1/4) Estimation is the process of obtaining a set of unknowns from a set of noisy
measurements, according to a definite optimization criterion. Measurement model, relationship between the measurements and the states 𝑧 =𝐻∙𝑥+𝜂 Process model is a set of equations representing the system state dynamics 𝑥 =𝐹∙𝑥+𝐺∙𝑤
Estimation (2/4) 𝜌𝐺𝑃𝑆 = 𝑑 − 𝑐𝑑𝑡𝑠 + 𝑐𝑑𝑡𝑟 + 𝐼 + 𝑇 + 𝜀𝜌
Pseudorange Measurement Model
𝜌𝐺𝑁𝑆𝑆,2 = 𝑑 − 𝑐𝑑𝑡𝑠 + 𝑐𝑑𝑡𝑟 + 𝐼 + 𝑇 + 𝑐𝑑𝑡𝑠𝑦𝑠 + 𝜀𝜌 Inter-system Bias
Pseudorange-rate Measurement Model
𝜌𝐺𝑃𝑆 = 𝑑 − 𝑐𝑑𝑡𝑠 + 𝑐𝑑𝑡𝑟 + 𝜀𝜌 𝜌𝐺𝑁𝑆𝑆,2 = 𝑑 − 𝑐𝑑𝑡𝑠 + 𝑐𝑑𝑡𝑟 + 𝑐𝑑𝑡𝑠𝑦𝑠 + 𝜀𝜌 Inter-system Drift
Linearization
∆𝜌 = 𝐻 ∙ ∆𝑥 State vector
∆𝑥 = ∆𝐸 ∆𝑣 = 𝑉𝐸
∆𝑁 𝑉𝑁
∆𝑈 𝑉𝑈
∆𝑐𝑑𝑡𝑟 𝑐𝑑𝑡𝑟
∆𝑐𝑑𝑡𝑠𝑦𝑠 𝑐𝑑𝑡𝑠𝑦𝑠
Estimation (3/4) Least Squares (LS) only the measurements model:
𝑧𝑘 = 𝐻𝑘 ∙ 𝑥𝑘 + 𝜂𝑘
Time discrete version
LS minimizes the sum of the squares of the residuals defined as:
𝑟𝑘 = 𝑧𝑘 − 𝐻𝑘 ∙ 𝑥𝑘
Predicted measurements
Current measurements Cost function to minimize
𝐽1 = 𝑟 𝑇 ∙ 𝑟
LS solution and associated Variance-Covariance (VC) matrix: 𝑥 = 𝐻𝑇 𝐻
−1
𝐻𝑇 ∙ 𝑧
𝐶𝑥 = 𝜎 2 𝐻 𝑇 𝐻
−1
Estimation (4/4) 𝐽2 = 𝑟 𝑇 ∙ 𝑊 ∙ 𝑟
Cost function to minimize:
Weighted Least Squares (WLS) :
𝐶𝑥 = 𝐻 𝑇 𝑊𝐻 −1 𝑥 = 𝐻 𝑇 𝑊𝐻 −1 𝐻 𝑇 𝑊 ∙ 𝑧 Weighting matrix as the inverse of measurement accuracy matrix: 𝑊 = 𝑅−1 Residuals are useful for monitoring the quality of the estimated state 𝑟 = 𝑧 − 𝐻 ∙ 𝑥 = 𝐼 − 𝐻 𝐻 𝑇 𝑊𝐻
−1 𝐻 𝑇 𝑊
𝜂 Measurements errors
𝑒 =𝑥−𝑥 =
𝐻 𝑇 𝑊𝐻
−1
𝐻𝑇 𝑊 ∙ 𝜂
∙𝜂
Multi-constellation Opportunity Multi-constellation system uses together measurements provided by different GNSSs. Different time scales: GPS Time and GST Connection GGTO= 𝑡𝐺𝑎𝑙 − 𝑡𝐺𝑃𝑆
GPS and GLONASS Time Connection 𝑡𝐺𝑃𝑆 = 𝑡𝐺𝐿𝑂 + 𝜏𝑔 + 𝜏𝑢 + 𝜏𝑟
Different weights for the measurements of the considered systems
Multi-constellation Opportunity
Multi-constellation receivers connected to the same rooftop antenna Galileo observables accuracy
Galileo vs GPS
Multi-constellation Opportunity GPS\Galileo
First Galileo-Only PVT
Velocity
Multi-constellation Opportunity GPS\Galileo
Geometry improvements
Benefits of the combined Galileo+GPS PVT solution, with
respect to the GPS only case
Multi-constellation Opportunity GPS\GLONASS
Availability: percentage of time that the services are usable.
Accuracy: degree of conformance of an estimated position with respect to the true position
Multi-constellation Opportunity Psuedo-measurements
Pseudo-measurements definition ℎ𝑎𝑖𝑑 − ℎ0 = 01×2
1
01×
𝑛−2
𝑑𝑡_𝑖𝑛𝑡𝑎𝑖𝑑 − 𝑑𝑡_𝑖𝑛𝑡0 = 01×4
∙ ∆𝑥
Altitude
1 ∙ ∆𝑥
Inter-system Bias
Pseudo-measurements improvements Configuration
RMS [m]
Max [m]
SA [%]
H
V
H
V
GG
6.8
4.7
39.0
29.5
84
GG aid H
5.6
3.2
31.0
6.8
88
GG aid cdt
6.8
4.7
39.0
29.5
86
GG aid H+cdt
5.6
3.2
31.0
6.8
89
Multi-constellation Opportunity Pros and Cons
• More satellites available (DOP improvement) • Necessity to determine inter-system biases (one satellite per additional GNSS may be “sacrificed”)
• Inter-system bias problem: potentially alleviated by broadcast parameters • Increased receiver complexity • Improved continuity and integrity
RAIM Concepts (1/2) Integrity ability to provide timely warnings to users when the system should not be used Integrity information to users into the navigation message
GBAS SBAS techniques Receiver Autonomous Integrity Monitoring (RAIM) based on selfconsistency check on redundant measurements and so it is able to detect user-level errors as multipath or local interference
RAIM Concepts (2/2) Several RAIM schemes based on the analysis of the residuals 𝑟 : 𝑟 =𝑧−𝐻∙𝑥 The detection of blunders is based on statistical hypothesis testing
The presence of outliers is detected if the test statistic exceeds a threshold Global Test (GT) and Local Test (LT)
RAIM Algorithms Snapshot Approaches Preliminary Check
Global Test Local Test Separability Check
Rejection
Are the measurements consistent? Who is the Outlier?
RAIM: Preliminary Check (1/2) The Preliminary Check is performed, before RAIM application, to screening out bad geometries, which could imply erroneous detections. Based on WARP (Weighted Approximate Radial-error Protected), generalization of the classical ARP
WARP ARP Slope The Slope parameter is the ratio between the Horizontal Position Error (HPE) and 𝑟 𝐻𝑃𝐸 𝑠𝑙𝑜𝑝𝑒 = =𝑓 𝐻 𝑟 𝑊𝑠𝑙𝑜𝑝𝑒 =
𝐻𝑃𝐸 𝑟 𝑇 𝑊𝑟
= 𝑓 𝐻, 𝑊
RAIM: Preliminary Check (2/2) ARP has a direct relationship to the position error that can be protected (direct geometric interpretation) 𝐴𝑅𝑃 = 𝑠𝑙𝑜𝑝𝑒𝑚𝑎𝑥 ∙ 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 WARP is a generalization of the classical ARP, considering different weights for each measurement 𝑊𝐴𝑅𝑃 = 𝑊𝑠𝑙𝑜𝑝𝑒𝑚𝑎𝑥 ∙ 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑊𝐴𝑅𝑃 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑𝑊𝐴𝑅𝑃
Solution Impossible to Check
RAIM: Global Test GT performs the self-consistency check of a measurement set
Measurement errors are assumed to be zero-mean Gaussian and uncorrelated The decision variable is quadratic form of the residuals 𝐷 = 𝑟 𝑡 𝑊𝑟
fixed
Measurement Set inconsistent, LT to Perform
Solution Realiable
PFA = 0.1%
RAIM: Local Test (1/2) LT is performed in the case of a GT failure Measurements are tested individually The decision variables are the normalized residuals, assumed as normally distributed
fixed
PFA = 0.1%
RAIM: Local Test (2/2)
Threshold
Ok
Outlier
Decision Variable is compared with threshold 𝒎𝒂𝒙 𝑤𝑖 suspected as blunder Separability Check has to be performed
Solution Unreliable GT and LT inconsistent!
RAIM: Separability Check Separability is the ability to separate measurements from each other; The decision variables: correlation coefficients of standardized residuals 𝐶𝑟 𝑖𝑗 𝑗 ∈ 1, … . , 𝑚 − 𝑖 & 𝑤𝑗 > 𝑇𝐿 𝛾𝑖𝑗 = 𝐶𝑟 𝑖𝑖 ∙ 𝐶𝑟 𝑗𝑗 𝑖 ∈ 1, … . , 𝑚 & 𝑤𝑖 = 𝑚𝑎𝑥 𝑤
𝑇𝑆 = 0.9
Performed only for normalized residuals exciding 𝑇𝐿 ith-measurement Rejected Solution Unreliable
Forward-Backward
Forward uses all the tests shown before and is repeated until: no additional outliers are identified (solution reliable) solution is declared unreliable impossible to check (ARP limit overpassed or lack of redundancy)
If more than one measurement is excluded, the Backward phase is performed, only GT
Subset
Subset test: use only GT If a measurements set is declared inconsistent, all the possible combinations of measurements are checked The subset that passes the GT is used to compute the navigation solution
The set with the minimum test variable and the largest number of measurements is chosen.
Danish
Iteratively reweighted
Used to achieve consistency between the measurements by modifying the a priori weights
This technique involves the use of the GT, LT, and Separability Check to identify and de-weight the outliers.
Urban Navigation Static test (1/2)
Reliable Availability is the percentage of time when the solution is declared reliable by the RAIM schemes adopted.
Multiple Rejections
Configuration
Availability [%]
Reliable Availability [%]
GPS Subset
98.1
76.2
GG Subset
100
96.5
GPS FB
98.1
43.6
GG FB
100
74.0
GPS Danish
98.1
49.0
GG Danish
100
75.8
Urban Navigation Static test (2/2)
RAIM Comparison
Configutation
RMS [m]
Max [m]
H
V
H
V
GPS no RAIM
54.9
85.6
1265
1686
GG no RAIM
34.8
65.4
246
372
GPS Subset
27.5
56.4
299
327
GG Subset
15.1
36.1
322
399
GPS FB
17.9
44.5
160
286
GG FB
13.4
31.3
160
284
GPS Danish
23.2
56.1
160
343
GG Danish
16.0
38.1
160
284
Forward-Backward and Danish similar performance (smallest errors) Usefulness of Separability check (not applied to Subset) Subset highest value of reliable availability but largest errors Usefulness of Backward
Urban Navigation Pedestrian test (1/2)
GPS GPS aid
GG GG aid
No RAIM RAIM No RAIM RAIM No RAIM RAIM No RAIM RAIM
RMS (m) H U 5.1 4.2 4.1 2.7 5.7 3.7 4.1 0.6 4.2 3.9 3.7 3.2 4.5 3.9 3.3 0.7
Max (m) H U 43.9 50.1 17.5 14.7 57.8 7.9 15.2 1.3 44.0 49.9 16.7 30.7 54.9 8.3 17.6 1.5
RA [%] 19 31 38 62
Urban Navigation Pedestrian test (2/2)
High Sensitivity Solution
RMS (m)
GPS GPS aid
Max (m)
H
U
H
U
noRAIM
47.1
56.2
157.3
217.3
RAIM
23.2
19.2
153.9
125.7
noRAIM
48.5
58.2
150.4
111.8
RAIM
25.3
1.3
282.7
4.8
RA [%] 70 82
Indoor Navigation GNSS solution
GNSS HS Solution (red and black markers)
Indoor GNSS positioning unfeasible Architecture of by PSEUDOLITE system.
the
SSF
Synchronization problems due to multipath and fading
Relative positioning to overcome synchronization problem
Indoor Navigation Asynchrnous approach (1/3)
RSS is the voltage measured by a receiver's RSSI circuit and corresponds to the measured power in logarithmic scale. RSS measurements can be obtained from the AGC levels or from C N0
𝐶 𝑁0 Proximity User position is determined as that of the transmitter associated to the strongest received pseudolite signal
𝑖
= 𝑘𝑖 − 𝛼10𝑙𝑜𝑔10 𝑑𝑖
Indoor Navigation Asynchrnous approach (2/3)
Meeting room test Equipment
4 pseudolites Calibration Ublox 6T Android phone
Indoor Navigation Asynchrnous approach (3/3)
Filtering Effect Unfiltered measurements
Filtered measurements
Repeatability
Loss
of lock
Conclusions Open-sky
Performance assessment of different GNSS configurations: GPS, GPS/GLONASS, GPS/Galileo
standard, high sensitivity receivers;
different operational scenarios (static and Kinematic test);
pseudo-measurement inclusion;
Pseudolites for indoor navigation.
From the analysis: Galileo observable errors reduced by approx 50% with respect to GPS Position and velocity domains: potential of Galileo Use of multi-constellation GSP/Galileo: maximum positioning error only slightly reduced with respect to the GPS-only case
Conclusions
Urban Navigation (1/2)
GPS/GLONASS improves solution availability (of almost 10%) and accuracy (RMS values reduced of 1 m, maximum error reduced of 8 m in the horizontal plane) Use of pseudo-measurements (altitude and intersystem bias) without RAIM: improves the solution availability (doubled with respect to the base-line configuration); it can degrade the navigation solution with respect to various aspects. Application of RAIM necessary to identify and reject gross errors.
The RAIM algorithms (Forward-Backward, Danish and Subset methods): analyzed in terms of reliable availability, RMS and maximum errors.
Conclusions
Urban Navigation (2/2)
Subset method: highest reliable availability but with the largest errors
Forward-Backward and Danish methods: similar performance and smallest errors RAIM methods: comparable robustness.
GLONASS measurements: benefits in terms of reliable availability, accuracy and integrity. Aid on the altitude along with RAIM, improved performance on the vertical component (RMS and maximum strongly reduced). Standard vs. HS: accuracy vs. availability trade-off The use of HS for urban scenarios: justified only when RAIM is implemented.
Conclusions Indoor navigation
GNSS indoor navigation unfeasible Alternative solutions required: synchronous and asynchronous pseudolites Limitations of synchronous pseudolite systems analyzed: not suitable for deep indoor navigation. Solution based on differential positioning not effective: impossibility to achieve reliable solution. Asynchronous pseudolites: indoor navigation with meter level accuracy demonstrated Simplified system design and use of different frequencies for asynchronous pseudolites Impact of pre-filtering and geometry Possible integration between GNSS and asynchronous pseudolites
Thanks to everyone
[email protected] [email protected]
