The Performance of a Pseudolite-Based Positioning System for Deformation Monitoring Joel Barnes, Jinling Wang, Chris Rizos School of Surveying and Spatial Information Systems University of New South Wales Sydney, NSW 2052, Australia, email:
[email protected]
Toshiaki Tsujii Flight Systems Research Center, National Aerospace Laboratory, 6-13-1 Osawa Mitaka, Tokyo 182-0015, Japan
Abstract. There are three general scenarios for the use of pseudolites in deformation monitoring systems; namely GPS augmented with pseudolites, pseudolite-only and pseudolite ‘inverted’ positioning. This paper focuses on the results and analysis of experimental data collected for these three pseudolite scenarios. The results suggest that the use of helical antennas can reduce pseudolite multipath error. The performance of pseudolite-GPS and pseudolite-only systems are evaluated and shown to be suitable for precise (cm-level) positioning. Keywords: Pseudolite, Inverted GPS, Deformation monitoring
1
Introduction
The Global Positioning System (GPS) has proven an invaluable tool for precision deformation monitoring, utilising the carrier phase measurement. It has been widely used for measuring crustal motion, ground subsidence and volcanic activity monitoring (Page, 2000; Roberts & Rizos, 2001), and more recently for the monitoring of bridges (Roberts et al., 2001), dams, buildings, and other structures. When using GPS the accuracy, availability, reliability and integrity of the position solution is very dependent on the number and geometric distribution of the available satellites. In some situations, such as the monitoring of structures in built up urban environments, the availability of GPS satellites may be insufficient for positioning requirements. Ground-based transmitters of GPS-like signals (called “pseudolites” or PLs) can be used to improve satellite geometry and, with enough devices, could replace the GPS constellation entirely. There are three general scenarios for the use of pseudolites in deformation monitoring systems: i. The first case is GPS augmentation with pseudolite(s), which is suitable where the geometry of the existing GPS constellation is insufficient for positioning requirements. Common applications include precision approach aircraft landing (Cobb, 1997) and positioning in deep open-cut mines (Stone & Powell, 1999). ii. In the second case a pseudolite-only system replaces the GPS constellation entirely. This could extend satellite-based deformation monitoring applications indoors, into tunnels or
underground, where GPS signals cannot be tracked. Laboratory test results of such an indoor navigation system are presented in Kee et al. (2000). iii. The final case is an inverted pseudolite-based deformation monitoring system, where a ‘constellation’ of GPS receivers tracks a mobile pseudolite. The system consists of an array of GPS receivers, a base reference pseudolite (or base GPS satellite) and a mobile pseudolite. The idea behind inverted pseudolite positioning was first introduced by Raquet et al. (1995). The purpose of the system was for precise positioning of military aircraft, and the proof-of-concept was demonstrated using a ground-based vehicle. More recent investigations into inverted positioning using pseudolites have been conducted at The University of New South Wales (Dai et al., 2001, and Tsujii et al., 2001). The decision of whether to use a reference pseudolite or a GPS satellite results in two basic configurations for an inverted positioning system. This paper will concentrate on analysis of experimental data collected in the three above mentioned scenarios.
2
Experimental studies
The performance of the pseudolite-based scenarios described in §1 were investigated through three static experiments, conducted in December 2001, at The University of New South Wales (UNSW). IntegriNautics IN200C (IN200) and Global Simulation Systems GSS4100 (GSS) pseudolites were used, together with NovAtel Millennium (NovAtel) and Canadian Marconi Corp. Allstar (Allstar) GPS receivers. The IN200 pseudolite was operated in a pulsed mode with a 10% duty cycle, to reduces interference and near-far problems. For each experiment its output power was adjusted to have good signal-to-noise ratio, but not jam GPS signals. The GSS pseudolite had no pulsing or power attenuation options, and when necessary its power was boosted using an inline amplifier. Both the NovAtel and Allstar GPS receivers allow individual channels to be assigned to track particular PRN codes, and this is an essential requirement when using pseudolites. 2.1 GPS augmented with pseudolites The experiment was carried out on the roof of the Electrical Engineering (EE) building at the UNSW. One IN200 and one GSS pseudolite were setup on permanent poles at known locations on the roof. These two pseudolites were connected to passive patch antennas and setup to transmit on PRN codes 12 and 32. These antennas were mounted on their side vertically with the antenna pointing in the direction of the test area. Two NovAtel receivers were used to collect GPS and pseudolite data. The base receiver was setup on a permanent pole and the rover receiver on a tripod, with a separation of approximately 11.4m. Figure 1 shows the relative location of the pseudolites and receivers, and Table 1 details the approximate elevation angle and distance of the two pseudolites from the rover GPS receiver. PL Elevation Distance to Bias Stdev PL/Ant. PRN (Degrees) Rover (m) (mm) (mm) 32 IN200/patch 34.0 38.5 -7.9 2.7 12 GSS/patch 31.5 41.5 1.8 2.4 Table 1. Test 1, PL details: elev. angle, dist. to rover, computed bias and standard deviation.
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Approximately 1 hour of GPS and pseudolite data were collected at 1Hz, and during this period six GPS satellites were tracked. To investigate the effect of using different pseudolite antennas, the IN200 patch antenna was replaced with a 10 inch helical antenna and an additional 20 minutes of data were recorded. Lastly, a further 30 minutes of data were collected without any pseudolites transmitting. This was to allow the precise determination of the rover coordinate without any possible pseudolite interference. The pseudolite and GPS data were processed using the baseline software developed at the UNSW.
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that the two pseudolite residuals are offset from zero and have significant biases. Visually the biases appear constant, and the residual time series mean values for PL12 (GSS) and PL32 (IN200) are –7.0 and –42.3mm respectively. These bias values were used in the following data processing to correct the pseudolite data. Carrier phase double-differenced residuals were also computed for the data recorded using a helical antenna with the IN200 pseudolite. Helical antennas have a more directional gain pattern than patch antennas. Figure 2d shows the double-differenced residuals for PL32 (IN200) using reference GPS satellite 14. The residual time series has a mean bias of –9.7mm. This is much less than the bias using a patch antenna of –42.3mm. This suggests that the directional beam of the helical antenna can help reduce pseudolite multipath. The standard deviations of time series in Figures 2b & d are not directly comparable because the data was collected at different times, and the reference satellite was different; they are however similar. To assess the performance of GPS-only and GPS-PL positioning, single-epoch L1 carrier phase solutions were computed. Figures 3 and 4 show the horizontal and vertical error position time series for GPS-only and GPS-PL solutions. Table 2 summarises, for the horizontal and vertical components, the positional standard deviations and dilution of precision values. It is clear that the precision of the vertical component has been improved to a level where it is almost the same as the horizontal. The additional low elevation pseudolite measurements have dramatically improved the vertical geometry, indicated by smaller VDOP values (Table 2). It is interesting that the horizontal precision of the GPS-pseudolite solution is marginally worse than the GPSonly, despite a marginal improvement in geometry for the horizontal. On closer inspection of the horizontal time series of the two solutions, those for GPS-pseudolite has a slight downward Horizontal 0.05
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trend. The reason for this trend is unknown and currently under investigation. Horizontal Vertical stdev (mm) stdev (mm) GPS-only (6 SVs) 1.8-1.5 5.6-3.9 2.9 8.6 GPS-pseudolite (6 SVs & 2 PLs) 1.1-1.2 1.2-1.5 2.3 3.8 Table 2. Test 1: horizontal & vertical positional standard deviation and DOP values. L1 single epoch solution type
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In GPS-based deformation monitoring systems, especially where high accuracy height component is needed, the use of pseudolites can provide extremely valuable additional ranging information.
2.2 Pseudolite-based positioning The objective of the experiment was to study the performance of a pseudolite-only positioning system, which could potentially be used for deformation monitoring. Four pseudolites were used in this test (two IN200 and two GSS), the minimum number required for 3D positioning, together with two NovAtel receivers. In a pseudolite-based positioning system, the installation of pseudolites in locations that ensure good geometry is the key to good positional precision. Unfortunately this can often be difficult to achieve logistically. In particular, pseudolite positions at high elevation angles are usually the most problematic. For this reason the walkway outside the EE building (with roof access) was a logical choice for the test area (see Figure 5). Two GSS pseudolites (assigned PRNs 12 & 32) were set up on permanent poles on the roof of the EE building, approximately 30m above ground level, and connected to two helical antennas of lengths 8 and 10 inches. These were directed to beam the pseudolite signals down to the test area on the ground. Additionally, two IN200 pseudolites (assigned PRNs 2 & 4) were setup on tripods at ground level to patch antennas. These were mounted on their side vertically with the antenna pointing in the direction of the test area. Two NovAtel GPS receivers were used to collect GPS and pseudolite data, with both antennas setup on tripods. The distance between the GPS receivers was approximately 2.5m and Table 3 summarises the approximate elevation angles and distances of the four pseudolites from the ‘rover’ GPS receiver. Figure 5. Test 2: configuration of pseudolite-based positioning.
PL Elevation Distance to Bias Stdev PL/Ant. PRN (Degrees) Rover (m) (mm) (mm) 32 GSS/helical 34.0 38.5 -7.9 2.7 12 GSS/helical 31.5 41.5 1.8 2.4 2 IN200/patch 5.6 7.8 -11.2 2.8 4 IN200/patch 0.0 28.1 7.6 4.2 Table 3. Test 2, PL details: elev. angle, dist. to rover, computed bias and standard deviation. Approximately 30 minutes of GPS and pseudolite data was collected at a 1Hz rate, and during this period five GPS satellites were tracked. After the experiment an hour of GPS data was collected using Leica System 500 GPS receivers at the ground-based receiver and pseudolite locations, and at a reference point on the roof of the EE building.
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The Leica data was used to determine the precise pseudolite and GPS receiver coordinates. Then, as discussed in §2.1, it was necessary to compute any multipath biases associated with the pseudolite data. Using the processed coordinates, carrier phase double-differenced residuals were computed for the pseudolite data using GPS SV23 as the reference satellite. Doubledifferenced residual time series plots for the four pseudolites are given in Figure 6. The residual time series have a constant offset from zero, and this bias is probably due to multipath. Table 3 summaries the mean values (bias) for each of the residual times series and its standard deviation. It is interesting to note that the smallest bias value (1.8mm) is for PL12 with a helical antenna, while PL2 using a patch antenna has the largest bias value (–11.2mm). Also, the roof top PL12 has the lowest standard deviation, while the ground-based PL4 has the greatest. During the experiment people sometimes walked through the Double difference residuals, Ref. SV23 line-of-sight between the PL4 and the GPS 0.02 0.01 receivers. This could account for the data spikes 0 and generally less random appearance in −0.01 comparison to the other pseudolite residuals. −0.02 mean −11.2 mm
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To assess the performance of the pseudolite-only positioning, single-epoch carrier phase solutions were computed using the four pseudolites, with PL12 selected as the reference PL. With both the GPS receivers and pseudolites stationary, carrier phase ambiguity resolution could not be performed using a normal procedure. Therefore the initial double-differenced carrier phase ambiguities were determined using the known coordinates of the base and rover receiver. Figure 7 shows the pseudolite– only horizontal and vertical error time series of the L1 carrier phase single epoch position solution. Table 4 summarises, for horizontal and vertical components, the positional standard deviations and dilution of precision values. The worse precision in the vertical is entirely due to the poor geometry. If the pseudolites were placed in the optimum
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Figure 7. PL-only L1 single epoch solution: horz. (top) and vert. (bottom) error. configuration (Dai et al., 2001) then even better precision could be obtained. It is clear to see that the data spikes present in the residuals for PL4 propagate into both the horizontal and vertical positions. Using the GPS data for the five available satellites, GPS-only and GPS-PL position solutions were also computed. Figures 8 & 9 show the horizontal and vertical position error time series, and Table 4 summarises the standard deviations and dilution of precision values. The HDOP values for the GPS-only solution are high (5) at the beginning of the test, and this is due to tall buildings near the test area blocking satellites. The high HDOP causes poor horizontal precision in the results with a standard deviation of 11.5 mm, which is slightly worse than the vertical precision. The precision of the GPS-PL results are the best and similar in both horizontal and vertical, due to additional pseudolite signals improving the geometry.
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Horizontal Vertical stdev (mm) stdev (mm) Pseudolite-only (4 PLs) 2.4 4.3 5.1 12.0 GPS-only (5 SVs) 5.1-2.8 3.0-4.1 11.5 10.9 GPS-pseudolite 1.3-1.2 1.3-1.5 3.0 4.3 Table 4. Test 2: horizontal & vertical positional standard deviation and DOP values. L1 single epoch solution type
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In this experiment cm-level pseudolite-only positioning has been demonstrated with just four pseudolites. Of course, pseudolite-only positioning allows for a wide variety of indoor-based deformation applications such as mining and tunnelling. In order to conduct the experiment described above in an indoor scenario then the time-tag error must be addressed. The time-tag error arises because the pseudolites that are used are not synchronised, unlike GPS satellites. Therefore, in order for the GPS receivers to record measurements at the same time, the receivers must adjust the sample time to the data message of one master pseudolite. This requires a firmware modification to the GPS receiver.
2.3 Pseudolite ‘inverted’ positioning The purpose of the experiment was to assess the performance of a low-cost inverted positioning system using pseudolites. In a previous experiment conducted at the UNSW (Tsujii et al., 2001) six dual-frequency NovAtel receivers were used. For this study six L1-only lowcost CMC Allstar receivers were used together with two IN200 pseudolites. The use of two pseudolites in this test allowed both PL-only and GPS-PL inverted positioning scenarios, whereas only the latter case was investigated previously. The experiment was carried out on the roof of the EE building at the UNSW. For the reference pseudolite a 10 inch helical beam antenna was mounted on a permanent pillar. This was situated on a secondary auxiliary building roof top, approximately 4m above the main roof. This location had a clear line-of-sight to the test area, approximately 61m away. The configuration of the test area is illustrated in Figure 10. For the rover-pseudolite, a patch antenna was mounted 3 metres above the main roof on a wooden rail attached to two staffs. The PL patch antenna faced directly down on the roof, and a GPS receiver antenna was mounted directly above the PL antenna pointing upwards. This would provide a reference position for the rover PL antenna. Six GPS antennas for the Allstar receivers were mounted on tripods around the rover PL antenna. To ensure good positioning geometry, five of the GPS antennas were approximately spaced equally around a circle, with the last antenna at the centre directly beneath the rover PL antenna. The reference and rover PLs were assigned PRN numbers of 32 and 12 respectively. Approximately one hour of pseudolite and GPS data were collected at a 1Hz rate using the Allstar receivers. Unfortunately, due to logging problems, the data for Allstar receiver No. 6 was lost, and so the following results are based on five receivers. GPS data was also collected at the network of receiver locations and the rover GPS antenna using Leica system 500 GPS receivers. The Leica data was used to determine the precise pseudolite and GPS coordinates. As described in §1, there are two particular cases for pseudolite-inverted positioning, characterised by the
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Figure 10. Test 3: configuration of inverted-pseudolite positioning. choice of reference pseudolite or GPS satellite used in the double-differencing. The data collected in this experiment was processed for both cases. First any multipath biases associated with the pseudolite data were determined. Using the coordinates computed from the Leica data, four carrier phase double-differenced residuals were computed, using receiver No. 1 as the reference receiver, for both inverted positioning cases. The residuals for GPS-PL inverted positioning (using SV21 and PL12) are given in Figure 11, while those for the PL-only inverted position (using PL32 and PL12) are given in Figure 12. It should be noted that although the minimum and maximum y-axis values are sometimes different the range is always 5cm. Mean (bias) values and standard deviations for the double-differenced residuals are given in Table 5. In both figures the double-differenced residuals visually have constant biases, probably caused by PL multipath. In the GPS-PL case for receivers 2 and 3 it is clear to see sinusoidal fluctuations. This is probably multipath from the GPS SV21, since there are no such fluctuations in the PL-only case (these visually appear more random). Also, the residuals when only using pseudolites have better precision than the GPS-PL case, with standard deviations values approximately half. Receiver SV21 & SV12 PL32 & PL12 SV21 & PL12 Elevation Bias Stdev Bias Stdev Bias Stdev No. (Degrees) (mm) (mm) (mm) (mm) (mm) (mm) 2 26.4 45.0 5.2 28.1 2.2 16.8 5.1 3 21.1 -56.3 5.0 -76.1 2.6 19.7 5.1 4 23.5 -55.3 4.4 -42.0 2.5 -13.4 4.1 5 25.6 -18.8 4.3 -23.9 2.3 5.0 4.1 6 23.9 No data 1 75.0 Reference receiver Table 5. Test 3, receiver DD details: elev. angle, computed bias and standard deviation. To investigate multipath characteristics further, carrier phase double-differenced residuals were computed using the reference SV21 and reference PL32. These double-differenced residuals are plotted in Figure 13. As expected, visually the sinusoidal fluctuations are almost identical to those in Figure 11, (SV21 & PL12), and this confirms the presence of GPS multipath on SV21. Also, bias values given in Table 5 suggest less pseudolite multipath from the reference PL32
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(with a helical antenna) in comparison to rover PL12 (with a patch antenna). To assess the performance of the two inverted positioning cases, single epoch carrier phase solutions were computed, for the GPS-PL case (using SV21 and PL12) and PL-only case (using PL32 & PL12). Initial double-differenced carrier phase ambiguities were determined using known coordinates. Figures 14 and 15 show the horizontal and vertical error time series of the GPS-PL and PL–only inverted positioning scenarios. Standard deviations for position components in both cases are given in Table 6. The precision of the PL-only is better than the GPS-PL case, especially in the height component. The worse precision in the GPSPL case is purely due to the time-varying GPS multipath on the reference GPS satellite, since the dilution of precision in both cases is identical. Visually, the PL-only position time series are mostly random, and the standard deviations are 2.3 and 3.8mm in the horizontal and vertical respectively. It should also be
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Figure 15. Inverted PL-only L1 single epoch solution: horz. (top) & vert. (bottom) error.
noted that the wooden bar used to mount the rover pseudolite was not structurally rigid. Some of the very small fluctuations in the position time series could be due to movement of wooden bar in strong gusts of wind. Very high precision positioning has been demonstrated for both GPS-PL and PL-only inverted positioning cases, using cheap L1-only OEM style receivers. For the PL-only inverted case positioning indoor deformation applications are possible, but time-tag error issues would need to be addressed, as mentioned in §2.2. Horizontal Vertical stdev (mm) stdev (mm) GPS-pseudolite (SV21 & PL12) 2.9 8.6 Pseudolite-only (PL32 & PL12) 2.3 3.8 Table 6. Test 3: horizontal & vertical positional standard deviation (HDOP=2.0, VDOP=2.2). Single epoch solution type
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Concluding remarks
The paper has presented the results and analysis of three different scenarios for the use of pseudolites in deformation monitoring applications (namely GPS-PL integration, PL-only and PL-based inverted positioning). In each case the static nature of the experiment allowed the calibration of constant pseudolite biases, probably due to multipath. Although further investigations are necessary, constant biases due to pseudolite multipath were reduced by the use of helical beam antennas.
When GPS is augmented with pseudolites the vertical precision can be improved to a level that is similar to that of the horizontal. In a pseudolite-only position system with four satellites, cmlevel 3D positioning has been demonstrated. In this case even better precision could be obtained with optimal pseudolite geometry. A low-cost pseudolite-based inverted positioning system, using one or two pseudolites and five cheap L1-only CMC Allstar receivers, gave positional standard deviations in both horizontal and vertical of less than 9mm (one PL) and 4mm (two PLs). The researchers are currently working with the Mitel GPS Architect development kit, which allows complete control over the GPS receiver firmware. Such control will allow the development of indoor applications and better tracking of pseudolite signals. Overall, the great potential of pseudolites for use in deformation monitoring systems has been demonstrated.
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