Experiments of inverted pseudolite positioning for airship-based GPS augmentation system

Experiments of Inverted Pseudolite Positioning for Airship-Based GPS Augmentation SystemToshiaki Tsujii, Masatoshi HarigaeFlight Systems Research Center, National Aerospace Laboratory, Japan (NAL)Joel Barnes, Jinling Wang and Chris RizosSchool of Surveying & Spatial Information Systems, The University of New South Wales, Australia (UNSW)BIOGRAPHIESToshiaki Tsujii is a senior researcher at the Flight Systems Research Center, NAL, Japan, where he has been investigating aspects of satellite navigation and positioning for ten years. He holds a Ph.D. in applied mathematics and physics from Kyoto University.Masatoshi Harigae is the leader of the Navigation Systems Group, Flight Systems Research Center, NAL, and has over 15 years experience in the development of GPS/INS navigation systems for automatic landing applications. He is now engaged in the High Speed Demonstration project that is carried out in cooperation with NASDA. He has a B.S., a M.S. and a Ph.D. from the University of Tokyo in aerospace engineering.Joel Barnes holds a Ph.D. in satellite geodesy from the University of Newcastle-upon-Tyne, UK. Since December 2000 he has been a postdoctoral research fellow within the Satellite and Navigation and Positioning (SNAP) group, in the School of Surveying and Spatial Information Systems, the University of New South Wales (UNSW). His current research interests are high precision kinematic GPS positioning, pseudolites and GPS receiver firmware customization.Jinling Wang is a Lecturer in the School of Surveying & SIS, UNSW. He is Chairman of the Working Group “Pseudolite applications in Engineering Geodesy”, of the International Association of Geodesy’s (IAG) Special Commission 4.Chris Rizos is a Professor at the School of Surveying & Spatial Information Systems, UNSW, and leader of the SNAP group, which specializes in addressing precise static and kinematic applications of GPS. He is secretary of Section 1 'Positioning', of the IA G.ABSTRACTRecently some countries have begun conducting feasibility studies and R&D projects on High Altitude Platforms Systems (HAPS). Japan has been investigating the use of an airship system that will function as a stratospheric platform (altitude of about 20km) for applications such as environmental monitoring, communications and broadcasting. In addition, if pseudolites (PL) were mounted on the airships, their GPS-like signals would be stable augmentations that would improve the accuracy, availability, and integrity of GPS-based positioning systems because the airship network would cover all of Japan. The accuracy of the pseudolite positions would be a limiting factor for such a service since the PL 'ephemeris error' is more serious than GPS due to the lower height of the airship. The carrier phase-based inverted PL method is one of the positioning schemes that could provide the precise 'ephemeris' of the airship. Therefore, a preliminary ground test of the pseudolite-based inverted GPS positioning has been conducted in both static and kinematic mode, and a high positioning accuracy in both modes has been demonstrated.INTRODUCTIONThe transmitters of GPS-like signals, which are called pseudolites (PL), or "pseudo-satellites", have been widely investigated as additional ranging sources to enhance the performance of GPS (see, e.g., Cobb, 1997). Ground-based GPS augmentation systems using pseudolites have been investigated for several applications such as vehicle navigation in downtown urban canyons (Altmayer, 1998), positioning in deep open-cut pits and mines (Stone & Powell, 1999), attitude determination (Wang et al., 2000), precision landing of aircraft (Barltrop et al., 1996; Pervan& Parkinson, 1997), and integrated positioning system with GPS/INS (Wang et al, 2001). The application of airborne pseudolites was suggested by Raquet et al. (1995). However, their purpose was the positioning of mobile pseudolites installed on military aircraft (Pachter &MaKay, 1998), not the augmentation of a navigation/positioning system. Recently, some countries have begun conducting feasibility studies and R&D projects on High Altitude Platforms Systems (HAPS). Although some authors have suggested the use of HAPS as navigation aids, their main function would be providing (pseudo-range) DGPS correction data (Dovis et al., 2000), not transmitting extraranging signals.Figure 1. Conceptual image of the stratospheric airship system (Taken from http://www.nal.go.jp).Japan has been investigating an airship system, as shown in Figure 1, that will function as a stratospheric platform (SPF) at an altitude of about 20km for applications such as environmental monitoring, communications and broadcasting (Yokomaku, 2000). Because of the airship’s station-keeping characteristics, the SPF can be considered as a signal source for a navigation/positioning service (Figure 2). If pseudolites were mounted on the airships, their GPS-like signals would be stable augmentations that would improve the accuracy, availability, and integrity of GPS-based positioning systems across all of Japan.The concept of an innovative GPS navigation/positioning system augmented by SPF-based pseudolites, which is referred to as GPS/PL system hereafter, was introduced by Tsujii et al. (2001). Also, some tests of PL positioning based on the 'inverted-GPS' concept were conducted in April 2001, because the precision of the PL position ('PL ephemeris') would be a limiting factor for such a service. The static test of the inverted GPS positioning, where a GPS satellite was used as a reference transmitter, showed excellent positioning accuracy. In a following test in December 2001, the the pseudolite-based inverted GPS configuration (Dai et al., 2001; Barnes et al., 2002), where another ground pseudolite was used as a reference transmitter, was tested and a similar positioning accuracy was obtained in the static mode (Tsujii et al., 2002). However, in both tests, the carrier phase ambiguities were not able to be resolved in the kinematic mode due to severe multipath error. In this paper, the results of inverted GPSusing multipath resistant antennas are presented.Figure 2. Navigation/positioning service using pseudolites on stratospheric platforms.INVERTED GPS POSITIONINGThe advantages of the GPS/PL system were discussed and the results of a feasibility study was presented in an earlier paper (Tsujii et al., 2001). Since the precise positioning of the PL antenna to provide the ‘PL ephemeris’ is one of the most important challenges, some schemes for estimating the PL position were described. Although the transceiver-based method seems to be the best, the inverted-GPS experiment was conducted as a preliminary test to identify potential problems of the proposed GPS/PL system, because an off-the-shelf transceiver is currently notavailable.Figure 3. Inverted GPS method.The system configuration of the inverted-GPS is shown in Figure 3. The position of a PL antenna underneath a SPF can be estimated directly by the inverted-GPS method (Raquet et al., 1995), where the ranging information is obtained by a receiver on the ground. In order to perform the double-differenced processing for the inverted-GPS approach an additional transmitter, such as a GPS satellite or ground-based PL, is required. The use of a GPS satellite would affect the positioning accuracy because ionospheric delay exists only in the GPS signal (not in the PL signal). If a ground-based PL is used as a reference transmitter, this system is referred to as ‘pseudolite-based inverted GPS’because the satellite ranging data are not required to obtain the position of the rover PL. In this system, the reference transmitter should be located on a high mountain or a tower to ensure line-of-sight from all ground receivers.The measurement equation for the carrier double-differenced observable for the 1st/i-th receivers and the airborne/base transmitters of the GPS/PL system can be written as follows:∇∆ab1i Φ=X 1−X a (t a1)−X i−X a (t ai )−X 1−X b (t b1)+X i−X b (t bi )+∇∆N ab 1i+∇∆d ion +∇∆d trop +∇∆d multi +∇∆ε, (i=1,2, …,n)(1)where b a i X X X ,,denote the position vectors of the i-th receiver on the ground, which are static, the airborne transmitter, and the base transmitter respectively. The i b i a t t ,represent the signal transmitting time to the i-th receiver from the airborne/base transmitters, referred to each of the transmitter clocks. With GPS positioning, the signal reception time for all the observed satellites is the same.However, in the case of inverted-GPS, the signal transmitting time to the receivers, which is analogous with the reception time in conventional GPS, may differ depending on the clock biases of the receivers and the distances between the transmitter and the receivers. These time differences may degrade the PL positioning accuracy because the motion of a PL on a SPF is difficult to predict (in contrast to GPS satellites). The GPS receivers normally synchronize to GPS time to within 1msec. Assuming that the motion of a SPF is less than 1m/sec, the position change of a PL is less than 1mm (=1m /sec ×1m sec). Since the distance difference between the PL and the receivers is less than 150km, in the example of the proposed Japanese configuration of SPFs (Tsujii et al., 2001), the PL position change is less than 0.5mm (=1m /sec ×150km /speed of light ).This effect would have to be investigated further if the station-keeping performance of SPFs were found to be worse. The ionospheric delay term can be neglected if the reference PL is used instead of a GPS satellite, or if GPS transceivers were used.For the test configuration, described below, both the ionospheric and tropospheric delay term s were neglectedbecause of the close proximity of the receivers. Also, the effect of non-simultaneous transmitting time can be neglected due to the close proximity of the PL and receivers, and the slow motion of the rover PL. The measurement equation can be simplified as:∇∆ab 1iΦ=X 1−X a (t)−X i −X a (t)−X 1−X b (t b1)+X i −X b (t b i )+∇∆N ab1i+∇∆d multi +∇∆ε , (i=1,2,…,n)(2)where t is the signal transmitting time from the PL,referred to the PL clock. The position of the receivers, X i ,and the base transmitter, X b , are precisely determined before the test if a PL is used as the base transmitter. If a GPS satellite is used as the base, the ephemeris error can be neglected because the receivers and the rover PL are close to each other relative to their distance from the satellite (Raquet et al., 1995).All data processing were performed using a modified version of the KINGS software developed at NAL (Tsujii et al., 1998).GROUND TEST CONFIGURATIONA miniature configuration of the GPS/PL system was constructed as shown in Figures 4 and 5, and the inverted-GPS experiment in static/kinematic modes was conducted on 30 August 2002. Six single-frequency GPS/PL receivers (Furuno PL-10) were placed on the ground in the Chofu Airfield Branch, NAL. The test ground is expected to be a multipath-rich area since it is surrounded by buildings onall sides and there are some tall trees.Figure 4. Miniature configuration of the GPS/PL system at NAL.The Furuno PL-10 receiver has sixteen channels , of which five channels are programmed to track the PL signal (PRN33-37). An antenna connected to an IntegriNautics IN400 PL was set on a wooden mount which can be rotated by a motor as shown in Figure 4. The radius of the rotation can be set to be 19cm, 24cm, and 35cm. The PRN number 36 was assigned to this rover PL, and therefore this PL is referred to as PL36 hereafter. The motion of the PL36 is controlled by a controller on the ground as shown in Figure 6. The data from six GPS/PL receivers were recorded at 5Hz rate by two laptop computers which were connected to a LAN. In order to enable the kinematic positioning, the multipath resistant antennas were used. The antennas No. 1,2, and 3 were Ashtech choke-ring antennas, while the No.4, 5, and 6 were the Ashtech Geodetic IV antennas. In addition, the grand plane was attached to the rover PL antenna to suppress the signal from the back of the PL antenna.Figure 5. Coordinates of PL (PRN35&36) and GPS receivers.Figure 6. GPS/PL receiver system and PL motion controller.Another IntegriNautics IN400 PL was used as a referencetransmitter in order to conduct the ‘pseudolite-based’inverted GPS positioning. The PRN number 35 was assigned to this reference PL, and this PL is referred to here as PL35.EXPERIMENTS AND RESULTSIn these tests two kinds of positioning modes were used.The first one is the ‘mixed mode’ where a GPS satellite was used as the reference transmitter. The second mode is the ‘PL-based mode’ where a PL was used as the reference and no ranging information from a GPS satellite was used.Although the measurement data suffered from severe multipath error, this error should be constant in the static test and therefore can be removed by pre-processing. The static tests in both modes showed excellent positioning stability, with standard deviations less than 1cm. However,in the kinematic mode, the multipath error varied drastically due to the motion of the rover PL, and the ambiguity could not be resolved. Therefore, the main purpose of this experiment is to mitigate the multipath error, and to simultaneously estimate the ambiguities and position parameters.Table 1. Summary of the experimental casesCase Diameter (cm)124Low speed CW&CCW Medium CW&CCWHighCW&CCWLow speed CW&CCW Stop&Go at 10degree intervals,CW Stop&Go at 45degree intervals,CCW&CW 224Low speed CCW&CW Medium CCW&CW HighCCW&CW 335Low speed CCW&CW Medium CCW&CW HighCCW&CW 419Low speed CCW&CWMedium CCW&CW HighCCW&CWTable 1 summarizes the characteristics of this experiment.Three levels of rotation speed were tested in order to study the tracking performance of the Furuno PL-10 receiver, as this kind of receiver had difficulty tracking the moving PL in the previous test (Tsujii et al., 2001). These speeds are approximately 3.1 (low), 3.6 (miedium), and 4.9degrees/second (high), respectively. As an example, the trajectory of the rover PL in Case 2 is shown in the top of Figure 7. The rotation angle is measured counterclockwise from the east. The middle figure shows the velocity in degrees/second, while the bottom figure shows the total number of receivers which track the rover PL. Some data loss is seen in the figure due to the error of data transfer (not the loss of tracking). There seems to have been no cycle slips in the data. As indicated, the PL-10 barely lost tracking of the moving PL , and the tracking performance would therefore be sufficient for such an application.Figure 7. Motion of the PL (top & middle), and the number of PL-10 receivers which track the PL (bottom).Prior to the kinematic positioning of the rover PL, the magnitude of the multipath error was estimated. Figure 8 shows the residuals of the double-differenced L1 carrier phase in Case2 where the transmitters are GPS satellites (PRN18&5). The positions of the six antennas of the PL-10 receivers were surveyed by GPS beforehand. As seen in Table 2, which summarizes the mean values and the standard deviations, the multipath error was mitigated by using the multipath resistant antennas.Figure 8. DD residuals of L1 carrier phase (cycles) in Case 2 where the transmitters are GPS satellites (PRN18&5).On the other hand, there can be seen some biases in the combination of GPS satellite (PRN18) and static PL (PRN35). The approximate physical center of the PL35 antenna was estimated by the GPS survey and a ruler measurement, since the antenna face was directed to the receive antennas. These biases may be attributed to the unknown phase center of the reference PL35 antenna, and the mean values shown in Table 2 were used for calibration purposes in the kinematic positioning.Figure 9. DD residuals of L1 carrier phase (cycles) in Case 2 where the transmitters are GPS satellite (PRN18) and static PL (PRN35).Then the kinematic positioning of the PL36, as well as the ambiguity resolution, was carried out using the PL35 as the reference transmitter. The biases related to the PL35 were subtracted from the DD carrier phase beforehand. The DD residuals after the kinematic processing are shown in Figure 10, and the statistical values are summarized in Table 2. Since the residuals were nearly zero during the whole session, the estimated ambiguities can be considered to be the correct ones. Some structure in the residuals can be seen, and they seem to be related to the motion of PL36 (see Figure 7). These fluctuations may be the remnant multipath error related to the PL36.Figure 10. DD residuals of L1 carrier phase (cycles) in Case 2 where the transmitters are static PL (PRN35) and rover PL (PRN36).Table 2. Mean and standard deviation of DD residuals ofL1 carrier pahse. (Unit: cycles)*Biases related to the PL35 were subtracted from DD transmitter Receiver pair 121-21-31-41-51-6mean 0.003-0.007-0.010-0.003-0.007GPS 18GPS 5std 0.0280.0320.0400.0320.031mean 0.1990.1470.1030.1070.112GPS 18PL 35std 0.0380.0360.0400.0450.036mean 0.012-0.0130.0080.001-0.003*PL 35PL 36std 0.0270.0230.0250.0200.025The estimated trajectory of the PL36 in Case 2 is shown inFigure 11. This trajectory is the superposition of the 11revolutions of the PL36. Since each trajectory seems to trace the same pass, the kinematic positioning/AR can be considered to be correct. However, the shape of the circle is distorted in some parts. These distortions may be due to the small amount of multipath which is seen in Figure 11 as well. The estimated trajectories of Case 1, 3, and 4 are shown in Figure 12, 13, and 14, respectively.Figure 11. Horizontal trajectory of the rover PL (PRN36)in Case 2.Figure 12. Horizontal trajectory of the rover PL (PRN36)in Case 1.Figure 13. Horizontal trajectory of the rover PL (PRN36)in Case 3.Figure 14. Horizontal trajectory of the rover PL (PRN36)in Case 3.A true evaluation of the positioning accuracy cannot be performed because the reference position of the rover PL was not measured. Therefore, the distance from the center of circle to the estimated horizontal position of PL36 was compared to the known radius at each epoch. As shown in Table 3, the standard deviations are about five millimeters,and therefore it can be concluded that the PL-based inverted GPS positioning was possible in the kinematic mode.Table 3. Standard deviations of the estimated radiusCase Radius(cm)Numberof dataStandarddeviation (cm)1247630.5222432170.4833511590.4641914720.41 CONCLUSIONSThe PL-based inverted-GPS positioning experiments were conducted in kinematic mode. By using the multipath resistant antennas for the receivers and the rover pseudolite, kinematic positioning and ambiguity resolution was performed successfully. 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