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DEVELOPMENT AND TESTING OF AN INTEGRATED INS/GPS CROSS-LINKED SYSTEM FOR SUB-METER POSITIONING OF A CF-188 JET FIGHTER M.E. Cannon, G. Lachapelle, and H. Sun Department of Geomatics Engineering University of Calgary Calgary, Alberta T. Fletcher, R. Caballero and I. Hawes Aerospace Engineering Test Establishment Department of National Defence Cold Lake, Alberta

BIOGRAPHIES Dr. M.E. Cannon is a Professor in Geomatics Engineering at the University of Calgary where she conducts teaching and research related to GPS and integrated GPS/INS systems. She is a Past President of the ION. Dr. Gérard Lachapelle is Professor and Head of the Geomatics Engineering Department where he is responsible for teaching and research related to positioning, and hydrography. He has been involved with GPS development and applications since 1980. Mr. Huangqi Sun received an M.Sc. from the Department of Geomatics Engineering in 1994. He also holds a B.Sc. and M.Sc. in Geodesy from Wuhan Technical University of Surveying and Mapping. He is currently working as a consultant and is also completing the Ph.D program. Mr. Tom Fletcher is the Chief Data Engineer responsible for data acquisition and processing at the Aerospace Engineering Test Establishment (AETE) where he has been employed since 1972. He holds a BASc EE and MASc EE from the University of British Columbia. Capt. Ian Hawes is a Data Acquisition Engineer with AETE. He received a BEng Sc from the University of Western Ontario in 1990 and an MEng in 1996 from the Royal Military College specializing in microwave engineering. Capt. Ruben Caballero has been a Flight Test Instrumentation and Telemetry Engineer at AETE since 1996. He received a BEng EE in 1991 from the University of Montreal and an MSc EE in 1996 from New Mexico State University specializing in telemetry and telecommunications. ABSTRACT In order to achieve sub-meter accuracy for the positioning of a CF-188 jet fighter (Canadian version of the F-18) under 360 degree rolls, two GPS antennas mounted on top and under the aircraft fuselage are used. The two receivers are cross-linked through the use of a common oscillator and the continuous exchange of position, velocity and Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

clock information to accelerate satellite acquisition during roll overs. A gimbaled INS is used to derive the lever arm between the two antennas and to augment GPS during critical roll over periods. The GPS/INS data time synchronization and data logging are performed using a solid state data logging system developed for this purpose. GPS data is post-processed in differential carrier phase ambiguity float mode, with respect to a reference station within 60 km from the aircraft. A Kalman filter is used to enhance positioning accuracy, especially during periods of losses of carrier phase lock. The analysis of flight tests conducted under various dynamics shows that a positioning accuracy better than one meter is maintained. INTRODUCTION The Aerospace Engineering and Test Establishment (AETE) Data Acquisition and Processing Services Branch at Canadian Forces Base Cold Lake is responsible for the operation and maintenance of the cinetheodolite system which makes up the Primrose Lake Evaluation Range (PLER). PLER is the airborne weapons and equipment test site for AETE, which is the primary air test establishment for the Canadian Forces. Over the past year, the University of Calgary has been working with AETE to assess the feasibility of using a GPS-based positioning system for some of their aircraft testing. The accuracy of GPS compared to an optical system, and the flexibility it offers over a fixed test range, are some of the reasons for assessing its capability. One of the challenges in achieving the required sub-meter accuracy is maintaining accurate positions during severe dynamic maneuvers that can typically include 360 degree rolls. For this reason, a GPS cross-linked twin antenna/receiver system was utilized whereby two receivers are connected and share information such as position and clock errors. One of the antennas was mounted on the top of the fuselage, while the other was mounted on the bottom to allow for increased availability and reacquisition during dynamic maneuvers. In addition, an inertial navigation system (INS) was also integrated with the cross-linked system to further increase position availability during reduced satellite availability. 1

This paper describes the hardware, methodology, tests and results for the integrated INS/GPS cross-linked system which was installed in a CF-188 aircraft and flown under typical operating conditions. The overall project objective was to determine if the system could provide post-mission positions of less than 1 m in accuracy.

A MiLLennium™ receiver was also used on the ground as the GPS reference receiver. Although this receiver is a dual frequency receiver, only L1 data was used in this experiment. The operational version now utilized by AETE is a twin antenna NovAtel L1 Beeline™ unit. Inertial Navigation System (INS)

Two flight tests were conducted in August, 1998. The INS/GPS data was post-processed and compared to a GPS-only solution to assess whether the filter had been properly designed and implemented. In addition, aircraft positions derived from the cinetheodolite data were also compared to the INS/GPS results to provide an independent assessment of the position accuracy. HARDWARE SYSTEMS GPS Cross-linked System and Reference Receiver The GPS system on-board the aircraft was comprised of a cross-linked receiver system consists of two NovAtel MiLLennium™ dual-frequency GPS receivers and antennas that are intended to point in opposite directions (i.e. for the current application on opposite sides of the aircraft fuselage). The two receivers pass information back and forth to keep each receiver updated in terms of position, velocity, acceleration and clock model data. The intent of this system is to allow the receivers to quickly reacquire satellites under high dynamic situations. The two receivers share a common oscillator from which the output signal is split for input to the receiver OCXO ports. Firmware required to accomplish this was provided by NovAtel. The top receiver was designated as the Primary receiver while the other acts as a Secondary. The 1 Pulseper-second (PPS) from the Primary is connected to the Secondary to maintain internal alignment. One of the communication ports is also connected to share necessary information (e.g. position and velocity). A second communication port from each receiver is output to the user for external data collection. The cross-linked system was installed on-board the CF188 aircraft which is the Canadian version of the US F18. Figure 1 shows the aircraft on the tarmac.

The aircraft INS is a Litton AN/ASN-130A navigationgrade gimbaled system with a drift rate of 1 nautical mile per hour. The civilian counterpart of the system is the Litton-38. The functionality of the INS is controlled by a mode controller whereby there are four different modes namely (1) Off, (2) Ground Alignment, (3) Navigation and (4) Inflight Alignment. The alignment procedure consists of two steps, one being coarse alignment (wide angle alignment) and another being fine alignment (small angle alignment). Fine alignment is performed either on the ground or in the air. It uses either the zero velocity update (ZUPT) or velocity and position from another source (e.g. Doppler radar) to update an internal filter to estimate the inertial error terms. Since the INS is inherently unstable in the vertical channel, barometric heights are used to stabilize the channel using a fourth-order baro-inertial loop. The loop feedback gains are a function of the square of the barovelocity. However, the gains become constant if the aircraft climb/dive critical velocity is exceeded. The positions of the aircraft antennas with respect to the on-board INS were precisely surveyed in order to determine their relative location which was required when integrating the GPS and INS data streams. Data Acquisition The GPS and INS messages were logged through the CF188 1553 Merlin data recorder. INS position and smoothed attitude parameters were recorded at a 20 Hz rate, while raw GPS pseudorange and carrier phase data was recorded at 4 Hz. The time-tagging capability between the GPS and INS systems was estimated to have an average error of 64 µs and a maximum error of 256 µs. METHODOLOGY

Figure 1: CF-188 Aircraft

Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

Raw GPS and INS data were recorded during the flight trials for post-mission processing. GPS carrier phase and pseudorange data was first processed in an unaided mode (i.e. no INS integration) to assess the quality of the GPS data and to generate a reference trajectory to compare to the integrated solution. The GPS and INS data sets were then reprocessed using a tightly coupled INS/GPS Kalman filter. The processing strategies for both the GPSonly and INS/GPS solutions are described below.

2

An independent comparison of the INS/GPS position results with cinetheodolite data was also made and will be reported in the sequel.

INS/GPS Cross-linked Processing Strategy

Carrier Phase GPS Kinematic Processing Strategy

A centralized Kalman filter was developed to integrate double difference GPS pseudorange, carrier phase and Doppler measurements with the output INS position, velocity and attitude information in an open loop design as shown in Figure 2. r, v, and ω refer to the position, velocity and attitude angle vectors, respectively.

The GPS data was processed using FLYKIN™, which is a kinematic software package that processes double differenced carrier phase, pseudorange and Doppler measurements. A Kalman filter is utilized whereby the filter states consist of position and velocity corrections as well as an ambiguity state for each of the double difference carrier phase measurements. This gives a total of 3+3+(n-1) states where n is the number of satellites tracked. The carrier phase ambiguities are estimated to be floating (i.e. real) values in the filter. Parallel to this, an integer ambiguity resolution scheme is implemented whereby a search is conducted for the correct integer ambiguity. The Fast Ambiguity Search Filter (FASF) technique is used to perform this search (Chen and Lachapelle, 1995). Since the accuracy requirements for the aircraft positions are at the sub-meter level, and also due to the fact that the aircraft was typically more than 60 km from the reference station, the ambiguities were estimated to be floating values and integer ambiguity resolution was not attempted. L1 integer ambiguity resolution is generally restricted to cases where the separation between the remote platform and the ground reference station is within ten kilometers. The accuracy of the floating ambiguities improves as more measurements are processed (i.e. time has elapsed) so that the filter converges towards the true integer values. During this convergence period (typically a few minutes), the position estimates will also not be as accurate. Since the estimation of the floating ambiguity must be reset on a particular satellite pair after a cycle slip occurs, frequent cycle slips will degrade the overall position accuracy. The FLYKIN™ program has been used to assess numerous receiver technologies and GPS missions (e.g. Cannon et al., 1997). The most important task of the filter to achieve accurate position solutions is the estimation of the doubledifference phase ambiguities, but ambiguity estimation is highly dependent on the characteristics of the data at the time the filter is initialized after acquisition and cycle slips. For forward time processing, initialization data is at the beginning of the data set, while the data at the end of the mission initializes the reverse filter processing. If widely spaced starting times are used to initialize the filter (i.e. longer than the correlation time of code multipath), two or more output solution sets can be compared to estimate the accuracy of the filter on the given data set. In the present case, the forward and reverse time kinematic GPS solutions were combined into a weighted solution which was then used to compare with the INS/GPS solution (Stephen et al., 1997). Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

Kalman Filter Design

INS

NAV

GPS

GPS carrier phase and phase rate

uncorrected r,v, ω

GPS/INS Kalman

corrected r,v, ω , biases

Figure 2: Open Loop GPS/INS Integration Scheme Fifteen error states were estimated by the Kalman filter, namely three position error states, three velocity error states, three misalignment states, three gyro drifts and three accelerometer biases (Cannon, 1991). They are expressed as the following state vector, x: x=

{ εn, εe, εh, δφ, δλ, δh, δvn, δve, δvh, dn, de, dh, bn, be, bh }T

(1)

where εn, εe, εh

are the three misalignments in north, east and vertical directions, respectively (rad) δφ, δλ, δh are the three position errors components in latitude, longitude and height, respectively (m) δvn, δve, δvh are the three velocity error components in north, east and upward directions respectively (m/s), dn, de, dh are the three gyro drift components (rad/h), and bn, be, bh are the three accelerometer biases (m/s2). Gyro drifts and accelerometer biases are modeled as firstorder Gauss-Markov processes. INS prediction is performed until the INS time tag and GPS time tag match, then the GPS double difference carrier phase is computed. The double difference carrier phase is compared with the predicted values based on the INS predicted position. If the difference is larger than a preset threshold, then a cycle slip is detected and is subsequently corrected. After correcting the double difference carrier phase observables, these are used to update the INS in the filter. Position, velocity and attitude 3

information output from the update are the final GPS/INS integration results. This process is repeated until the end of the GPS or INS data files. Figure 3 gives an overview of the system. Further details can be found in Cannon (1991) and Sun (1994).

IN S d ata

Kalm an filter p red iction equ ation

between the INS and the antennas as determined from drawings, was used to calculate the lever arm vector between the GPS antennas and the INS. The integration of the INS with the cross-linked system is given in Figure 4.

IN S d ata

GPS d ata

N u m ber of SVs Observed

Kalm an Filter Pred iction Equ ations

Com p u te d ou ble d ifference phase and phase rate

Antenna 2

Antenna 1

Ad d itional SVs

Com p u te d ou ble d ifference carrier p hase

Check for cycle slip

IN S-GPS tim e tag?

No

IN S-GPS Tim e tag ?

Kalm an Filter Up d ate Equ ations

Kalm an filter u p d ate equ ation

Figure 4: Integration of INS with multiple GPS antennas

Figure 3: GPS/INS integration

A software program called FLYKINS™ was designed to integrate the INS data with the GPS cross-linked system. The integration software was designed to take advantage of GPS measurements from both antennas of the crosslinked system (Lachapelle et al., 1998). There are several scenarios that may be encountered in flight testing, namely (1) the top antenna always maintains at least four satellites in good geometry, (2) the top antenna tracks less than four satellites but there are additional satellites from the bottom antenna, and (3) there are no satellites from the top antenna while there are satellites tracked on the bottom antenna. In the first case, only the GPS measurements from the top antenna are used to update the filter. In the second case, GPS measurements from both antennas are used to update the filter, while in the third case, only measurements from the bottom antenna are used. When measurements are combined from the two antennas, double differencing is first performed on satellites at the top antenna. The INS position is first translated to this antenna and a filter update is performed using these double differences. This updated position is then translated to the bottom antenna where double difference carrier phase measurements are formed and used to update the filter. This two-step procedure is needed since it is virtually impossible to accurately translate carrier phase measurements from antenna to another. The INS attitude data, along with the distances Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

FLIGHT TEST DESCRIPTION Two flight tests were performed on August 13, 1998. One flight under mild maneuvers was conducted during the morning and a second flight with sharp maneuvers was conducted during the afternoon (hereby designated AM and PM flights). Each flight lasted for about 1.5 hours. The trajectory for the AM flight is shown in Figure 5 while the trajectory for PM flight is shown in Figure 6 (from the INS). The aircraft speed was typically 500 kts. 55

54.9

Trajectory From INS (Aug 13, AM)

54.8

Latitude (deg)

Integration with GPS Cross-Linked System

Check cycle slip s in p hase d ata

Yes

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Figure 5: AM flight trajectory from the INS output 4

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Numbe r of SVs Observed During PM Flight for Top and Bottom Antennas (Cutoff Angle = 5 Deg)

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Trajectory From INS (Aug 13, PM)

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Figure 8: Number of satellites observed - PM flight

Longitude (deg) 10

Figure 6: PM flight trajectory from the INS output

No. of SVs

No. of SVs

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0


-2 421815 14:53:35

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Figure 9: Number of satellites observed above 5 degrees during sharp maneuvers – PM flight

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Rolls During the Three 360-degree Roll 100

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-200 421815 14:53:35

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GPS Tim e (s)/Local Time (h)

Figure 10: INS Rolls during sharp maneuvers – PM flight

12

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6

Pitch (deg)

The antenna on top of the fuselage observed five or more satellites during the entire AM flight. During the afternoon flight, there were periods of less than four satellites from both antennas during sharp maneuvers which combined with the finite reacquisition time of the receivers, limited the tracking capability in some instances. The number of satellites observed for by antennas during the AM flight is shown in Figure 7 while Figure 8 shows the number of satellites during the afternoon flight. Figure 9 shows the availability during the PM flight section when the aircraft made three consecutive 360 degrees rolls (Figure 10 shows the roll angles). No satellites above 5 degrees were available for up to 7 seconds during the rolls. Figure 11 shows all satellites tracked during these three consecutive rolls (i.e. 0 degree cutoff angle). From this figure it can be seen that when the aircraft started to roll at GPS time 421830 s, the number of satellites observed by the top antenna started to decrease while the number of satellites observed by the bottom antenna started to increase, which is expected from the cross-link system. At GPS time 421832.5 s, however, the number of satellites from both antennas are decreasing together which may be due to roll angle of the aircraft (145 degrees) and the reacquisition time required.

Num ber of SVs Observed During the Three 360-Degree Rolls for Top and Bottom Antennas (Cutoff Angle = 5 Deg)

8

Num ber of SVs Observed During AM Flight for Top and Bottom Antennas (Cutoff Angle = 5 Deg)

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No. of SVs Obs erved During the 360-Degree s Rolls 10

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Figure 7: Number of satellites observed - AM flight Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

Figure 11: Number of satellites observed above 0 degrees during sharp maneuvers – PM flight 5

GPS Reference Trajectory Generation – AM Flight In order to generate a reference trajectory which could be compared to the INS/GPS cross-linked system to determine if the integration filter was properly designed and implemented, data collected by the top aircraft antenna was processed using FLYKIN™, which was previously described. Results for the PM flight are not included but are similar. Processing was done in forward and reverse time directions and the results were then combined in an optimal Kalman filter weighting scheme (Stephen et al., 1997). The difference between the forward and reverse processing solutions was used as an indicator of the quality of the solution. For this case, only L1 data was processed since the final system to be deployed by AETE is a single frequency system. The overall unaided DGPS results were assessed through two approaches namely, (1) an evaluation of the double difference measurement residuals and, (2) a comparison between the trajectories estimated from the forward- and reverse-time solutions. Measurement residuals are valuable for analysis, since any unmodelled errors will be absorbed by the filter estimates (i.e. position, velocity and ambiguities) as well as residuals. If the magnitude of the residuals is small, this is a good indicator that the overall filter results are also accurate. For the present case, carrier phase residuals should be within 10-20 cm to ensure that position estimates are within 1 m. A comparison of the forward- and reverse-time trajectories is the second way to evaluate the quality of the results. Since these two trajectories are initialized using different segments of data (forward using the front end of the data and reverse using the back end of the data), then if the floating ambiguities are estimated incorrectly in one case, the two trajectories will not agree. If there is strong consistency between the two solutions, this is a good indicator that the position results are reliable and accurate within the agreement range. The double differenced carrier phase residuals for satellite pairs 17-3 and 17-6 are shown in Figures 12 and 13. The forward residuals are shown in black while the reverse residuals are given in gray. Carrier phase residuals are on Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

Statistics for the all of the carrier phase residuals for the forward and reverse runs are summarized in Tables 1 and 2, respectively. RMS values for the carrier phase are generally less than 1 cm, as expected, and the maximum phase residuals do not exceed ±4.4 cm in either the forward and reverse runs which shows that the accuracy is highly consistent throughout the entire test and that no gross errors occurred. RMS values for the code residuals are not shown, but are about 1 m. 0.05 Phase Residuals 0.025

M etres

Aircraft position results are presented for two cases, namely (i) a comparison of the INS/GPS cross-linked system versus a GPS-only solution, and (ii) a comparison of the INS/GPS cross-linked system versus cinetheodolite-derived positions. The first comparison was done to determine if the integration filter was properly designed and implemented, while the second is used for an independent assessment of position accuracy. The generation of the GPS-only reference trajectory is first presented (AM flight only), followed by the results from the above two comparisons.

the order of several millimeters. Overall the residuals are correlated between the forward and reverse filter runs, as expected. They also show a cyclical effect which is typical of multipath. Residuals for the remaining satellites are similar.

0

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Figure 12: PRN 3 double difference carrier phase residuals – AM flight 0.05 Phase Residuals 0.025

M etres

RESULTS AND ANALYSIS

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Figure 13: PRN 6 double difference carrier phase residuals – AM flight Table 1: Statistics for GPS double differenced carrier phase residuals – forward run (cm) PRN Std Dev 3 -0.2 6 -0.2 10 0.0 13 -0.1 17 -0.3 21 -0.3 22 -0.2 26 -0.1

RMS 0.5 0.6 0.5 0.7 0.7 0.8 0.8 0.5

Max 2.1 2.1 3.6 1.3 1.6 2.3 2.8 2.2

Min -2.5 -3.4 -1.7 -2.4 -2.7 -2.8 -4.4 -2.2 6

PRN 3 6 10 13 17 21 22 26

Std Dev -0.2 -0.4 -0.4 -0.1 -0.3 0.0 -0.5 -0.1

RMS 0.5 0.8 0.7 0.7 0.7 0.8 1.1 0.6

Max 2.4 2.3 3.1 1.3 1.7 3.6 3.3 2.4

Min -2.3 -3.5 -2.1 -3.1 -2.4 -2.7 -4.3 -2.1

Figure 14 shows the difference between the forward and reverse solutions. The consistency of the two solutions is at the sub-meter level, except during filter stabilization at the beginning of the data sequences and after cycle slips. Table 3 gives the statistics of the differences between the forward and reverse runs in the position domain, and show RMS values ranging between 29 and 72 cm for the three position components. The smoothed solution obtained by combining the forward and reverse solutions eliminates most of the position errors that occur after initialization or cycle slips. The accuracy of such a solution is expected to be similar to that of the longitude results shown in the table, namely about 25 cm RMS in each of the horizontal components and 40 to 50 cm in the height component. The smoothed GPS kinematic solution from the AM and PM flights were used as references in the following section.

GPS Versus INS/GPS Cross-linked System Results Figure 15 gives the differences between the positions from the GPS-only smoothed solution and those from FLYKINS™ for the AM flight. Figure 16 gives similar values for the PM flight. The discontinuities in both plots are during the times when there are severe roll maneuvers. The PM flight results are poorer especially during maneuvers. Since GPS updates are given at a consistent rate, the integrated trajectory is heavily weighted towards the GPS-only solution (i.e. the INS has limited impact on position when regular GPS updates are available). Statistics of the differences are given in Table 4 and show that the GPS-smoothed and INS/GPS results are consistent to within 0.5 m for the AM flight and 0.9 m for the PM flight which is an indicator that the integration algorithm has been properly designed and implemented for this data set. These results are also consistent with GPS/INS results achieved in previous airborne experiments (e.g. Sun et al., 1994). 2 1.5 1 Diff. (m)

Table 2: Statistics for GPS double differenced carrier phase residuals – reverse run (cm)

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Figure 15: Differences between the GPS-only smoothed and the GPS/INS solutions - AM flight

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Figure 14: Difference between forward and reverse GPS solutions

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Table 3: Difference statistics between forward and reverse GPS processing (m) Component Std Dev 0.63 Latitude -0.25 Longitude 0.38 Height

RMS 0.72 0.29 0.62

Max 1.23 0.26 3.07

Min -2.07 -0.68 -1.97

Figure 16: Differences between the GPS-only smoothed and the GPS/INS solutions - PM flight Table 4: Difference statistics between the GPS smoothed and GPS/INS solutions (m) Component Latitude Longitude Height


AM Flight Mean RMS 0.05 0.14 -0.17 0.19 -0.46 0.52

PM Flight Mean RMS -0.49 0.73 0.16 0.31 0.80 0.90 7

INS Performance During GPS Outages

1 0.8

Drift of Position During Simulated GPS Outages

0.6 0.4 D iff. (m )

In order to test the capability of the INS to bridge GPS outages, 15-second outages were introduced at different times in the raw AM GPS data prior to processing. It is expected that during an outage, the position accuracy will deteriorate due to the drift characteristics of the INS. The magnitude of the deterioration will generally be correlated to the time elapsed and to the aircraft dynamics since this will impact the behavior of the INS.

0.2 0 -0.2 -0.4 -0.6

Latitude Height

-0.8 -1 409200 11:40:00

The first GPS outage was simulated at time 409200 s when the aircraft was stationary. Figure 17 gives the position accuracy as a function of time during this outage as well as the 2x3D error envelope, as estimated by the FLYKINS™ filter as:

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11:40:02 11:40:04 11:40:06 11:40:08 11:40:10 11:40:12 GPS Time (s)/Local Time (h)

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Figure 17: INS drift after GPS outage – Test A 4

2x3D error = 2 x [σ2φ + σ2λ + σ2h]1/2

Drift of Position During Simulated GPS Outages

3

Subsequent outages were simulated at 500 s intervals. A outage was also simulated at GPS time 410700 s when the aircraft was at flight level (roll is within ±10 degrees). The INS performance during the 15 second outage period is given in Figure 18 and shows that the error degradation was significantly faster than for the static case (note that the vertical scale is changed). Errors in the height component exceed 1 m after about 3 seconds, while the latitude and longitude stay within 30 cm during the outage. The 2x3D error envelope estimated by the FLYKINS™ filter is also shown. It generally agrees well with the actual errors. This level of agreement means that the FLYKINS™ filter is generally well tuned for the application at hand. Results from the remaining tests are not shown, but in general, the INS performance is correlated to aircraft dynamics and has a drift rate of about 20 cm/s.


Diff. (m )

2

The aircraft is static in this test. It can be seen that the error growth is relatively low and does not exceed ±0.1 m after the 15-second period. This means that the system should be able to detect and correct any GPS carrier phase cycle slips at the 1 cycle level if the GPS outage is less than 15 seconds and the platform is stationary (since 10 cm is about one half of the L1 wavelength of 19 cm). The estimated 2x3D errors appear to be conservative in this case as the envelope grows faster than the actual errors. However, the actual errors can be interpreted as RMS or 1σ errors in each of the three coordinate components. In order to compare these with the 3D errors estimated by the filter, one has to apply the above formula. The agreement will be better, although the 3D errors estimated by the filter would still be conservative in this case, which is more desirable to maintain a conservative safety margin.

1 0 -1 -2 -3

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410716

12:05:14 12:05:16

Figure 18: INS drift after GPS outage - Test B Effect of Using Two Aircraft Antennas In order to test the effectiveness of the cross-link twin antenna system, a test was performed using data from both antennas simultaneously. When measurements are combined from the two antennas, double differencing is first performed on satellites from the top antenna, after which the updated position is translated to the bottom antenna where double difference carrier phase measurements are formed and used to update the filter. The time period chosen for the test was at 410700 s when the aircraft was in a normal flight mode. The concept of using carrier phase data from two antennas to integrate with an INS was discussed previously and is further described in Sun (1994). The FLYKINS™ program was first run with GPS updates from two satellites from the first aircraft antenna (i.e. one double difference using PRNs 6 and 17, with 17 as the base satellite). Figure 19 gives the drift with only these two satellites, compared to the complete outage case which is shown in Figure 18. For the two satellite case, the maximum error in height reaches 2.3 m (not shown on the figure) while the maximum error for the no satellite case is 3.3 m. As can be seen from the latitude and longitude errors in Figures 18 and 19, the errors actually 8

The two satellites from the top antenna were then used along with the six satellites tracked by the bottom antenna for a total of eight satellites. Results from this test are shown in Figure 20. When both sets of measurements are used as updates, the position agreement is at the several decimeter level compared to the FLYKIN™ smoothed solution and no large drift effects are present. This shows the effectiveness of the cross-link system. 2 Drift of Position With 2 Satellites

1.5

Diff. (m )

Overall, the performance with the bottom antenna is only slightly degraded compared to the case when satellites from the top antenna are used. 2 1.5

Drift of Position w ith Bottom Antenna Only

1 0.5 0 -0.5 -1 -1.5 -2 410700 12:05:00

Latitude

Longitude

Height

2 3D Sigma

410702 12:05:02

410704 410706 12:05:04 12:05:06

410708 410710 410712 12:05:08 12:05:10 12:05:12

410714 410716 12:05:14 12:05:16


1

Figure 21: Test using bottom aircraft antenna satellites

0.5 0 -0.5 -1 -1.5 -2 410700 12:05:00

Latitude

Longitude

Height

2 3D Sigma

410702 410704 410706 12:05:02 12:05:04 12:05:06

410708 410710 410712 410714 410716 12:05:08 12:05:10 12:05:12 12:05:14 12:05:16


Figure 19: Drift test using two satellites from top antenna 2 1.5

Drift of Position With 2 Satellites from First Antenna and All Satellites from Second Antenna

1 D iff . (m )

There are some drifts in the solution which are most likely due to the quality of estimation of the floating ambiguities when using only the bottom antenna satellites.

Diff. (m)

increase when the two satellites from the top antenna are used. This shows that in some cases, a limited number of satellites may not actually improve the achievable accuracy depending on the geometry and filter estimates at the time of signal shading. In other test cases, the errors did decrease.

0.5 0

INS/GPS Cross-linked System Versus Cinetheodolite – AM and PM Flights To facilitate the data gathering of Time Space and Position Information (TSPI), the PLER Optical/Maintenance is equipped with nine Model F Cinetheodolites that record time, azimuth, elevation and event. The surveyed sites are located around the panhandle of Primrose Lake approximately 10 to 15 km apart. The cinetheodolites are a single operator system and are capable of 5, 10, 20 or 30 frames per second using 35mm/400ft roll film and have the potential to measure TSPI within a +/- 90 cm accuracy at 12,000 m. The sites are capable of tracking targets up to 50 km away. For the present tests, cinetheodolite positions were available at 20 Hz.

-0.5 -1 -1.5 -2 410700 12:05:00

Latitude

Longitude

Height

2 3D Sigma

410702 410704 410706 410708 410710 410712 410714 410716 12:05:02 12:05:04 12:05:06 12:05:08 12:05:10 12:05:12 12:05:14 12:05:16 GPS Time (s)/Local Time (h)

Figure 20: Drift test using both aircraft antennas Performance with Bottom Antenna Satellites In order to assess the performance with only the bottom antenna, two tests were conducted using the satellites from this antenna only. The same time period as used above was selected, namely GPS time 410700 s. As mentioned previously, there were six satellites available from the bottom antenna during this period. Figure 21 gives the differences between the FLYKINS™ positions compared to the GPS-only smoothed solution. The agreement between the two solutions is within 0.7 m. Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

The INS/GPS cross-linked positions were compared to the cinetheodolite positions in order to provide an independent accuracy assessment. Since the cinetheodolite positions were referenced to the aircraft nosecone, a translation of the INS/GPS positions (referenced to the GPS antenna) was done using the presurveyed distance between the antenna and nosecone, as well as the INS attitude angles. A transformation of the cinetheodolite-derived positions to WGS-84 was also done using transformation parameters determined from a prior ground survey. A total of 14 runs were conducted through the cinetheodolite range (each lasting about 25 s) and two representative runs from the AM flight (Runs 2 and 3) and one from the PM flight (Run 8) are presented. Both the cinetheodolite and INS/GPS solutions were available at 20 Hz, although some small interpolations had to be performed in order to match the respective time tags. Figure 22 shows the differences between the INS/GPS 9

4 3 2 1

Diff. (m)

cross-linked and cinetheodolite solutions for Run 2 during the AM flight. As can be seen, the differences are generally within ±1.5 m which is expected given that the accuracy of the cinetheodolite is about ±90 cm which is about the same as the INS/GPS solution. Differences between the two solutions should therefore be within √2 of this, or about 1.3 m. Results for Run 3 are shown in Figure 23 and are similar to those discussed above.

0 -1 X

-2

Y

-3

Z -4 14:07:20

2.5 2 1.5

Diff. Betw een GPS/INS Solution and Cine-T Solution (Run 2, AM Flight)

14:07:40

14:07:50

Local Time (h)

1

Figure 24: Position differences between GPS-only and cinetheodolite – Run 8, PM flight

0.5 0 -0.5 -1

X

-1.5

Y

-2

Z

-2.5 11:07:17

11:07:37

11:07:47

Figure 22: Position differences between INS/GPS and cinetheodolite – Run 2, AM flight Diff. Betw een GPS/INS Solution and Cine-T Solution (Run 3, AM Flight)

0 -1 X

-2

Y -3

Z 14:07:30

14:07:40

14:07:50

Local Tim e (h)

1 D if f. (m )

1

-4 14:07:20

2.5 1.5

3 2

11:07:27 Local Tim e (h)

2

4

D if f. (m )

D iff. (m )

14:07:30

Figure 25: Position differences between INS/GPS and cinetheodolite – Run 8, PM flight

0.5 0 -0.5 -1

X

-1.5

Y

-2

Z

-2.5 11:11:50

11:12:00

11:12:10

11:12:20

Table 5: Differences between the INS/GPS and cinetheodolite solutions (m) Comp.

Local Time (h)

X Figure 23: Position differences between INS/GPS and cinetheodolite – Run 3, AM flight Figure 24 shows a comparison between the GPS-only smoothed solution for Run 8 during the PM flight and the cinetheodolite solution. Although the agreement is within 1 m, there is an outage of about 10 seconds due to a loss of satellites caused by a rollover. Figure 25 shows the differences between the INS/GPS and the cinetheodolite solutions whereby the outage has been bridged with the INS. The accuracy is slightly lower than the GPS-only solution since the GPS-only solution was a combination of forward and reverse runs and hence had a better accuracy. Table 5 gives a summary of the statistics of the differences between the INS/GPS cross-linked and the cinetheodolite solutions. The RMS of the differences is within 1.3 m which is expected given the accuracy of the two systems being compared. This demonstrates that the overall accuracy of the cross-linked system is within 1 m. Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

Y Z

Flight Run Mean (m) RMS (m) Mean (m) RMS (m) Mean (m) RMS (m)

AM 2 -1.31 1.34 -0.85 0.91 -0.24 0.35

3 -1.09 1.15 -0.48 0.54 -0.10 0.23

PM 8 0.07 0.70 0.07 1.38 0.83 1.11

CONCLUSIONS The project objective of establishing the capability of providing post-mission positions of less than 1 m in uncertainty for the CF-188 aircraft under typical mission conditions was achieved using a two-antenna/receiver cross-link GPS system mounted in the aircraft along with the CF-188 aircraft multiplex (MUX) bus INS data. Two flight tests of the CF-188 were conducted to determine the performance of the positioning system. The L1 GPS-only data was processed using FLYKIN™, which estimates position, velocity and carrier phase floating ambiguities. Data from the top antenna of the AM flight 10

was selected to generate a precise trajectory for the analysis of the GPS/INS results. Through an analysis of the carrier phase residuals, and the computation of the differences between the forward- and reverse-time trajectories, it was determined that the accuracy of the smoothed DGPS solution (i.e. a combination of the forward and reverse runs) is at the level of a few decimeters. The software FLYKINS™, developed previously for the integration of DGPS and INS data, was used to analyse the flight data. Comparisons between the GPS-only smoothed and integrated solutions yielded a consistency of 0.5 m or better for the three coordinate components for the AM flight and less than 0.9 m for the PM flight which shows that the integration approach used in FLYKINS™ is sound. GPS outages showed that the INS position drift is a function of aircraft dynamics and has a maximum value of 20 cm/s. Further tests of including two satellites from the top antenna, or alternatively two satellites from the top antenna and all visible satellites from the bottom antenna, showed that the position drift is either greatly reduced or eliminated. Finally, when only satellites from the bottom antenna are used, the agreement between the INS/GPS positions and the GPS-only smoothed positions are within 0.5 m for the two cases tested. The 2x3D error envelopes estimated by the FLYKINS™ agree well with the actual position errors.

Lachapelle, G., M.E. Cannon and H. Sun (1998), Design of a GPS/INS Precise Positioning and Attitude Determination System for the CF-188 Aircraft, Contract Report, Aeronautical Engineering Test Establishment, CFB Cold Lake, 13 pp. O’Keefe, K., J. Stephen, D. Tuck, G. Lachapelle and M.E. Cannon (1998), June 1998 PLER and CF-18 Surveys, Contract Report for Aerospace Engineering Test Establishment (AETE), CFB Cold Lake, Alberta, 22 pp. Ray, J.K. and M.E. Cannon (1999), Characteristics of Carrier Phase Multipath, Proceedings of ION National Technical Meeting, San Diego, January 2224, pp. 343-352. Stephen, J., M.E. Cannon and G. Lachapelle (1997), Smoothing Algorithm and Cross-Linked Receiver System, Contract Report for Aerospace Engineering Test Establishment (AETE), CFB Cold Lake, Alberta. Sun, H. (1994), GPS/INS Integration for Airborne Applications, Report No. 20069, Geomatics Engineering, University of Calgary. Sun, H., M.E. Cannon, T. Owen and M. Meindl (1994), An Investigation of Airborne GPS/INS for High Accuracy Position and Velocity Determination, Proceedings of ION NTM, San Diego, January 2426, pp. 801-809.

The agreement between the INS/GPS and cinetheodolite solutions are within an RMS of 1.3 m which is expected given the ±0.9m accuracy of the cinetheodolite. ACKNOWLEDGEMENTS D. Swigart, D. Culshaw and I. Thaleshvar from AETE are thanked for the excellent data processing support they provided. J. Stephen and K. O’Keefe from the University of Calgary are also acknowledged for their assistance in conducting the ground surveys at AETE. REFERENCES Cannon, M.E. (1991), Airborne GPS/INS with an Application to Aerotriangulation, Report No. 20040, Geomatics Engineering, University of Calgary. Cannon, M.E., G. Lachapelle, M. Szarmes, J. Hebert, J. Keith, and S. Jokerst (1997), DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Velocity and Position Determination. Navigation, Journal of The Institute of Navigation, Vol. 44, No. 2, pp. 231-245. Chen, D., and G. Lachapelle (1995), A Comparison of the FASF and Least-Squares Search Algorithms for Ambiguity Resolution On The Fly. Navigation, Journal of The Institute of Navigation, Vol. 42, No. 2, Alexandria, VA, pp 371-390. Institute of Navigation Annual Meeting/Cambridge/June 28-30, 1999

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