Figure 1. Distribution of the GPS+COMPASS tracking network established by the GNSS Research Center at Wuhan University and used as test network in this study.
Data from a tracking network with 12 stations in China, the Pacific region, Europe, and Africa demonstrates the capacity of Compass with a constellation comprising four geostationary Earth-orbit (GEO) satellites and five inclined geosynchronous orbit (IGSO) satellites in operation. The regional system will be completed around the end of 2012 with a constellation of five GEOs, five IGSOs, and four medium-Earth orbit (MEO) satellites. By 2020 it will be extended into a global system.
By Maorong Ge, Hongping Zhang, Xiaolin Jia, Shuli Song, and Jens Wickert
China’s satellite navigation system Compass, also known as BeiDou, has been in deveopment for more than a decade. According to the China National Space Administration, the development is scheduled in three steps: experimental system, regional system, and global system.
The experimental system was established as the BeiDou-1 system, with a constellation comprising three satellites in geostationary orbit (GEO), providing operational positioning and short-message communication. The follow-up BeiDou-2 system is planned to be built first as a regional system with a constellation of five GEO satellites, five in inclined geosynchronous orbit (IGSO), and four in medium-Earth orbit (MEO), and then to be extended to a global system consisting of five GEO, three IGSO, and 27 MEO satellites. The regional system is expected to provide operational service for China and its surroundings by the end of 2012, and the global system to be completed by the end of 2020.
The Compass system will provide two levels of services. The open service is free to civilian users with positioning accuracy of 10 meters, timing accuracy of 20 nanoseconds (ns) and velocity accuracy of 0.2 meters/second (m/s). The authorized service ensures more precise and reliable uses even in complex situations and probably includes short-message communications.
The fulfillment of the regional-system phase is approaching, and the scheduled constellation is nearly completed. Besides the standard services and the precise relative positioning, a detailed investigation on the real-time precise positioning service of the Compass regional system is certainly of great interest.
With data collected in May 2012 at a regional tracking network deployed by Wuhan University, we investigate the performance of precise orbit and clock determination, which is the base of all the precise positioning service, using Compass data only. We furthermore demonstrate the capability of Compass precise positioning service by means of precise point positioning (PPP) in post-processing and simulated real-time mode.
After a short description of the data set, we introduce the EPOS-RT software package, which is used for all the data processing. Then we explain the processing strategies for the various investigations, and finally present the results and discuss them in detail.
Tracking Data
The GNSS research center at Wuhan University is deploying its own global GNSS network for scientific purposes, focusing on the study of Compass, as there are already plenty of data on the GPS and GLONASS systems. At this point there are more than 15 stations in China and its neighboring regions.
Two weeks of tracking data from days 122 to 135 in 2012 is made available for the study by the GNSS Research Center at Wuhan University, with the permission of the Compass authorities. The tracking stations are equipped with UR240 dual-frequency receivers and UA240 antennas, which can receive both GPS and Compass signals, and are developed by the UNICORE company in China. For this study, 12 stations are employed. Among them are seven stations located in China: Chengdu (chdu), Harbin (hrbn), HongKong (hktu), Lhasa (lasa), Shanghai (sha1), Wuhan (cent) and Xi’an (xian); and five more in Singapore (sigp), Australia (peth), the United Arab Emirates (dhab), Europa (leid) and Africa (joha). Figure 1 shows the distribution of the stations, while Table 1 shows the data availability of each station during the selected test period.
Table 1. Data availability of the stations in the test network.
There were 11 satellites in operation: four GEOs (C01, C03, C04, C05), five IGSOs (C06, C07, C08, C09, C10), and two MEOs (C11, C12). During the test time, two maneuvers were detected, on satellite C01 on day 123 and on C06 on day 130. The two MEOs are not included in the processing because they were still in their test phase.
Software Packages
The EPOS-RT software was designed for both post-mission and real-time processing of observations from multi-techniques, such as GNSS and satellite laser ranging (SLR) and possibly very-long-baseline interferometry (VLBI), for various applications in Earth and space sciences. It has been developed at the German Research Centre for Geosciences (GFZ), primarily for real-time applications, and has been running operationally for several years for global PPP service and its augmentation. Recently the post-processing functions have been developed to support precise orbit determinations of GNSS and LEOs for several ongoing projects.
We have adapted the software package for Compass data for this study. As the Compass signal is very similar to those of GPS and Galileo, the adaption is straight-forward thanks to the new structure of the software package. The only difference to GPS and Galileo is that recently there are mainly GEOs and IGSOs in the Compass system, instead of only MEOs. Therefore, most of the satellites can only be tracked by a regional network; thus, the observation geometry for precise orbit determination and for positioning are rather different from current GPS and GLONASS.
Figure 2 shows the structure of the software package. It includes the following basic modules: preprocessing, orbit integration, parameter estimation and data editing, and ambiguity-fixing. We have developed a least-square estimator for post-mission data processing and a square-root information filter estimator for real-time processing.
Figure 2. Structure of the EPOS-RT software.
GPS Data Processing
To assess Compass-derived products, we need their so-called true values. The simplest way is to estimate the values using the GPS data provided by the same receivers.
First of all, PPP is employed to process GPS data using International GNSS Service (IGS) final products. PPP is carried out for the stations over the test period on a daily basis, with receiver clocks, station coordinates, and zenith tropospheric delays (ZTD) as parameters. The repeatability of the daily solutions confirms a position accuracy of better than 1 centimeter (cm), which is good enough for Compass data processing. The station clock corrections and the ZTD are also obtained as by-products.
The daily solutions are combined to get the final station coordinates. These coordinates will be fixed as ground truth in Compass precise orbit and clock determination. Compass and GPS do not usually have the same antenna phase centers, and the antenna is not yet calibrated, thus the corresponding corrections are not yet available. However, this difference could be ignored in this study, as antennas of the same type are used for all the stations.
Orbit and Clock Determination
For Compass, a three-day solution is employed for precise orbit and clock estimation, to improve the solution strength because of the weak geometry of a regional tracking network. The orbits and clocks are estimated fully independent from the GPS observations and their derived results, except the station coordinates, which are used as known values.
The estimated products are validated by checking the orbit differences of the overlapped time span between two adjacent three-day solutions. As shown in Figure 3, orbit of the last day in a three-day solution is compared with that over the middle day of the next three-day solution. The root-mean-square (RMS) deviation of the orbit difference is used as index to qualify the estimated orbit.
Figure 3. Three-day solution and orbit overlap. The last day of a three-day solution is compared with the middle day of the next three-day solution.
In each three-day solution, the observation models and parameters used in the processing are listed in Table 2, which are similar to the operational IGS data processing at GFZ except that the antenna phase center offset (PCO) and phase center variation (PCV) are set to zero for both receivers and satellites because they are not yet available.
Satellite force models are also similar to those we use for GPS and GLONASS in our routine IGS data processing and are listed in Table 2. There is also no information about the attitude control of the Compass satellites. We assume that the nominal attitude is defined the same as GPS satellite of Block IIR.
Table 2. Observation and force models and parameters used in the processing.
Satellite Orbits. Figure 4 shows the statistics of the overlapped orbit comparison for each individual satellite. The averaged RMS in along- and cross-track and radial directions and 3D-RMS as well are plotted. GEOs are on the left side, and IGSOs on the right side; the averaged RMS of the two groups are indicated as (GEO) and (IGSO) respectively. The RMS values are also listed in Table 3.
As expected, GEO satellites have much larger RMS than IGSOs. On average, GEOs have an accuracy measured by 3D-RMS of 288 cm, whereas that of IGSOs is about 21 cm.
As usual, the along-track component of the estimated orbit has poorer quality than the others in precise orbit determination; this is evident from Figure 4 and Table 3. However, the large 3D-RMS of GEOs is dominated by the along-track component, which is several tens of times larger than those of the others, whereas IGSO shows only a very slight degradation in along-track against the cross-track and radial. The major reason is that IGSO has much stronger geometry due to its significant movement with respect to the regional ground-tracking network than GEO.
Figure 4. Averaged daily RMS of all 12 three-day solutions. GEOs are on the left side and IGSOs on the right. Their averages are indicated with (GEO) and (IGSO), respectively.
Table 3. RMS of overlapped orbits (unit, centimeters).
If we check the time series of the orbit differences, we notice that the large RMS in along-track direction is actually due to a constant disagreement of the two overlapped orbits. Figure 5 plots the time series of orbit differences for C05 and C06 as examples of GEO and IGSO satellites, respectively. For both satellites, the difference in along-track is almost a constant and it approaches –5 meters for C05.
Note that GEO shows a similar overlapping agreement in cross-track and radial directions as IGSO.
Figure 5. Time series of orbit differences of satellite C05 and C06 on the day 124 2012. A large constant bias is in along-track, especially for GEO C05.
Satellite Clocks. Figure 6 compares the satellite clocks derived from two adjacent three-day solutions, as was done for the satellite orbits. Satellite C10 is selected as reference for eliminating the epoch-wise systematic bias. The averaged RMS is about 0.56 ns (17 cm) and the averaged standard deviation (STD) is 0.23 ns (7 cm). Satellite C01 has a significant larger bias than any of the others, which might be correlated with its orbits.
From the orbit and clock comparison, both orbit and clock can hardly fulfill the requirement of PPP of cm-level accuracy. However, the biases in orbit and clock are usually compensatable to each other in observation modeling. Moreover, the constant along-track biases produce an almost constant bias in observation modeling because of the slightly changed geometry for GEOs. This constant bias will not affect the phase observations due to the estimation of ambiguity parameters. Its effect on ranges can be reduced by down-weighting them properly. Therefore, instead of comparing orbit and clock separately, user range accuracy should be investigated as usual. In this study, the quality of the estimated orbits and clocks is assessed by the repeatability of the station coordinates derived by PPP using those products.
Figure 6. Statistics of the overlap differences of the estimated receiver and satellite clocks. Satellite C10 is selected as the reference clock.
Precise Point Positioning
With these estimates of satellite orbits and clocks, PPP in static and kinematic mode are carried out for a user station that is not involved in the orbit and clock estimation, to demonstrate the accuracy of the Compass PPP service.
In the PPP processing, ionosphere-free phase and range are used with proper weight. Satellite orbits and clocks are fixed to the abovementioned estimates. Receiver clock is estimated epoch-wise, remaining tropospheric delay after an a priori model correction is parameterized with a random-walk process. Carrier-phase ambiguities are estimated but not fixed to integer. Station coordinates are estimated according to the positioning mode: as determined parameters for static mode or as epoch-wise independent parameters for kinematic mode.
Data from days 123 to 135 at station CHDU in Chengdu, which is not involved in the orbit and clock determination, is selected as user station in the PPP processing. The estimated station coordinates and ZTD are compared to those estimated with GPS data, respectively.
Static PPP. In the static test, PPP is performed with session length of 2 hours, 6 hours, 12 hours, and 24 hours. Figure 7 and Table 4 show the statistics of the position differences of the static solutions with various session lengths over days 123 to 125.
The accuracy of the PPP-derived positions with 2 hours data is about 5 cm, 3 cm, and 10 cm in east, north, and vertical, compared to the GPS daily solution. Accuracy improves with session lengths. If data of 6 hours or longer are involved in the processing, position accuracy is about 1 cm in east and north and 4 cm in vertical. From Table 4, the accuracy is improved to a few millimeters in horizontal and 2 cm in vertical with observations of 12 to 24 hours. The larger RMS in vertical might be caused by the different PCO and PCV of the receiver antenna for GPS and Compass, which is not yet available.
Figure 7. Position differences of static PPP solutions with session length of 2 hours, 6 hours, 12 hours, and 24 hours compared to the estimates using daily GPS data for station CHDU.
Table 4. RMS of PPP position with different session length.
Kinematic PPP. Kinematic PPP is applied to the CHDU station using the same orbit and clock products as for the static positioning for days 123 to 125 in 2012.
The result of day 125 is presented here as example. The positions are estimated by means of the sequential least-squares adjustment with a very loose constraint of 1 meter to positions at two adjacent epochs. The result estimated with backward smoothing is shown in Figure 8. The differences are related to the daily Compass static solution. The bias and STD of the differences in east, north, and vertical are listed in Table 5. The bias is about 16 mm, 13 mm, and 1 mm, and the STD is 10 mm, 14 mm and 55 mm, in east, north, and vertical, respectively.
Figure 8. Position differences of the kinematic PPP and the daily static solution, and number of satellites observed.
Table 5. Statistics of the position differences of the kinematic PPP in post-processing mode and the daily solution. (m)
Compass-Derived ZTD. ZTD is a very important product that can be derived from GNSS observations besides the precise orbits and clocks and positions. It plays a crucial role in meteorological study and weather forecasting.
ZTD at the CHDU station is estimated as a stochastic process with a power density of 5 mm √hour by fixing satellite orbits, clocks, and station coordinates to their precisely estimated values, as is usually done for GPS data.
The same processing procedure is also applied to the GPS data collected at the station, but with IGS final orbits and clocks. The ZTD time series derived independently from Compass and GPS observations over days 123 to 125 in 2012 and their differences are shown on Figure 9.
Figure 9. Comparison of ZTD derived independently from GPS and COMPASS observations. The offset of the two time series is about -14 mm (GPS – COMPASS) and the STD is about 5 mm.
Obviously, the disagreement is mainly caused by Compass, because GPS-derived ZTD is confirmed of a much better quality by observations from other techniques. However, this disagreement could be reduced by applying corrected PCO and PCV corrections of the receiver antennas, and of course it will be significantly improved with more satellites in operation.
Simulated Real-Time PPP Service
Global real-time PPP service promises to be a very precise positioning service system. Hence we tried to investigate the capability of a Compass real-time PPP service by implementing a simulated real-time service system and testing with the available data set.
We used estimates of a three-day solution as a basis to predict the orbits of the next 12 hours. The predicted orbits are compared with the estimated ones from the three-day solution. The statistics of the predicted orbit differences for the first 12 hours on day 125 in 2012 are shown on Figure 10.
From Figure 10, GEOs and IGSOs have very similar STDs of about 30 cm on average. Thus, the significantly large RMS, up to 6 meters for C04 and C05, implies large constant difference in this direction. The large constant shift in the along-track direction is a major problem of the current Compass precise orbit determination. Fortunately, this constant bias does not affect the positioning quality very much, because in a regional system the effects of such bias on observations are very similar.
Figure 10. RMS (left) and STD (right) of the differences between predicted and estimated orbits.
With the predicted orbit hold fixed, satellite clocks are estimated epoch-by-epoch with fixed station coordinates. The estimated clocks are compared with the clocks of the three-day solution, and they agree within 0.5 ns in STD. As the separated comparison of orbits and clocks usually does not tell the truth of the accuracy of the real-time positioning service, simulated real-time positioning using the estimated orbits and clocks is performed to reveal the capability of Compass real-time positioning service.
Figure 11 presents the position differences of the simulated real-time PPP service and the ground truth from the static daily solution. Comparing the real-time PPP result in Figure 11 and the post-processing result in Figure 8, a convergence time of about a half-hour is needed for real-time PPP to get positions of 10-cm accuracy. Afterward, the accuracy stays within ±20 cm and gets better with time. The performance is very similar to that of GPS because at least six satellites were observed and on average seven satellites are involved in the positioning. No predicted orbit for C01 is available due to its maneuver on the day before. Comparing the constellation in the study and that planned for the regional system, there are still one GEO and four MEOs to be deployed in the operational regional system. Therefore, with the full constellation, accuracy of 1 decimeter or even of cm-level is achievable for the real-time precise positioning service using Compass only.
Figure 11. Position differences of the simulated real-time PPP and the static daily PPP. The number of observed satellites is also plotted.
Summary
The three-day precise orbit and clock estimation shows an orbit accuracy, measured by overlap 3D-RMS, of better than 288 cm for GEOs and 21 cm for IGSOs, and the accuracy of satellite clocks of 0.23 ns in STD and 0.56 in RMS. The largest orbit difference occurs in along-track direction which is almost a constant shift, while differences in the others are rather small.
The static PPP shows an accuracy of about 5 cm, 3 cm, and 10 cm in east, north, and vertical with two hours observations. With six hours or longer data, accuracy can reach to 1 cm in horizontal and better than 4 cm in vertical. The post-mission kinematic PPP can provide position accuracy of 2 cm, 2 cm, and 5 cm in east, north, and vertical. The high quality of PPP results suggests that the orbit biases, especially the large constant bias in along-track, can be compensated by the estimated satellite clocks and/or absorbed by ambiguity parameters due to the almost unchanged geometry for GEOs.
The simulated real-time PPP service also confirms that real-time positioning services of accuracy at 1 decimeter-level and even cm–level is achievable with the Compass constellation of only nine satellites. The accuracy will improve with completion of the regional system.
This is a preliminary achievement, accomplished in a short time. We look forward to results from other colleagues for comparison. Further studies will be conducted to validate new strategies for improving accuracy, reliability, and availability. We are also working on the integrated processing of data from Compass and other GNSSs. We expect that more Compass data, especially real-time data, can be made available for future investigation.
UA240 OEM card made by Unicore company and used in Compass reference stations.
Acknowledgments
We thank the GNSS research center at Wuhan University and the Compass authorities for making the data available for this study.
The material in this article was first presented at the ION-GNSS 2012 conference.
Maorong Ge received his Ph.D. in geodesy at Wuhan University, China. He is now a senior scientist and head of the GNSS real-time software group at the German Research Centre for Geosciences (GFZ Potsdam).
Hongping Zhang is an associate professor of the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing at Wuhan University, and holds a Ph.D. in GNSS applications from Shanghai Astronomical Observatory. He designed the processing system of ionospheric modeling and prediction for the Compass system.
Xiaolin Jia is a senior engineer at Xian Research Institute of Surveying and Mapping. He received his Ph.D. from the Surveying and Mapping College of Zhengzhou Information Engineering University.
Shuli Song is an associate research fellow. She obtained her Ph.D. from the Shanghai Astronomical Observatory, Chinese Academy of sciences.
Jens Wickert obtained his doctor’s degree from Karl-Franzens-University Graz in geophysics/meteorology. He is acting head of the GPS/Galileo Earth Observation section at the German Research Center for Geosciences GFZ at Potsdam.
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