Abstract
In this contribution, we present a GPS+GLONASS+BeiDou+Galileo four-system model to fully exploit the observations of all these four navigation satellite systems for real-time precise orbit determination, clock estimation and positioning. A rigorous multi-GNSS analysis is performed to achieve the best possible consistency by processing the observations from different GNSS together in one common parameter estimation procedure. Meanwhile, an efficient multi-GNSS real-time precise positioning service system is designed and demonstrated by using the multi-GNSS Experiment, BeiDou Experimental Tracking Network, and International GNSS Service networks including stations all over the world. The statistical analysis of the 6-h predicted orbits show that the radial and cross root mean square (RMS) values are smaller than 10 cm for BeiDou and Galileo, and smaller than 5 cm for both GLONASS and GPS satellites, respectively. The RMS values of the clock differences between real-time and batch-processed solutions for GPS satellites are about 0.10 ns, while the RMS values for BeiDou, Galileo and GLONASS are 0.13, 0.13 and 0.14 ns, respectively. The addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing, reduces the convergence time almost by 70 %, while the positioning accuracy is improved by about 25 %. Some outliers in the GPS-only solutions vanish when multi-GNSS observations are processed simultaneous. The availability and reliability of GPS precise positioning decrease dramatically as the elevation cutoff increases. However, the accuracy of multi-GNSS precise point positioning (PPP) is hardly decreased and few centimeter are still achievable in the horizontal components even with 40\(^{\circ }\) elevation cutoff. At 30\(^{\circ }\) and 40\(^{\circ }\) elevation cutoffs, the availability rates of GPS-only solution drop significantly to only around 70 and 40 %, respectively. However, multi-GNSS PPP can provide precise position estimates continuously (availability rate is more than 99.5 %) even up to 40\(^{\circ }\) elevation cutoff (e.g., in urban canyons).
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Acknowledgments
We are very grateful to IGS, MGEX, WHU and HuBei CORS for providing multi-GNSS data.
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Appendices
Appendix A
Figure 16 shows the kinematic PPP results for another four-system station GMSD, which is located in Japan. The PPP solutions related to GPS, GLONASS and BeiDou have similar performance compared to the results of CUT0 station. As shown in Fig. 16d, Galileo-only PPP is achievable for few hours even with four satellites. The accuracy of several centimeters can be obtained for about 2–3 h, although currently it is not possible to use Galileo as a stand-alone system for continuous positioning. Meanwhile, as shown in Fig. 16h, Galileo also provides a contribution to some extent for PPP solutions when used together with, e.g., GPS. The sky plots (azimuth vs. elevation) of four systems for GMSD are shown in Fig. 17.
Kinematic PPP solutions of single-system, dual-system and four-system modes at station GMSD (latitude 30.55\(^{\circ }\), longitude 131.01\(^{\circ }\), Japan, Asia), on September 1, 2013
Sky plots (azimuth vs. elevation) of four GNSS (BeiDou in pink, Galileo in red, GPS in blue and GLONASS in green) at GMSD on September 1, 2013
Kinematic PPP solutions of single-system, dual-system and four-system modes at station LMMF (latitude 14.59\(^{\circ }\), longitude \(-\)60.99\(^{\circ }\), Martinique, Latin America), on September 1, 2013
Figure 18 shows the kinematic PPP results for another four-system station LMMF located in Latin America with latitude of –14.59\(^{\circ }\) and longitude of –60.99\(^{\circ }\). At this location, both Beidou and Galileo cannot provide continuous positioning as a stand-alone system and only few hours of Beidou-only and Galileo-only PPP are obtainable, as shown in Fig. 18c, d. However, the PPP solutions can converges faster and achieve more accurate position series when Beidou or Galileo are combined together with GPS, as demonstrated in Fig. 18g, h.
The PPP accuracy with different observational lengths (e.g., 0.25, 0.5, 1, and 2 h) is compared in Fig. 19. The accuracy of single-system PPP is improved along with the observational lengths. If data of 2 h or longer are involved in the processing, position accuracy of few centimeters can be achieved. For multi-GNSS PPP, the accuracy of few centimeters is already available in all the three components with observational length of 0.25 h and then stays on cm-level.
Position errors of kinematic PPP solutions at station LMMF with different observational lengths of 0.25, 0.5, 1, and 2 h in single-system and multi-GNSS modes
Appendix B
Figure 20 shows the PPP results, satellite numbers, and PDOP values under different elevation cutoffs for another four-system station GMSD. It has similar performance as the station CUT0: PDOP gets larger as the elevation cutoff gets larger. The availability and reliability of GPS precise positioning decrease dramatically as the elevation cutoff increases. Importantly though, the PDOP of the multi-GNSS remains small for large elevation cutoffs. Furthermore, the positioning accuracy of multi-PPP is nearly not decreased and few centimeters are still achievable in horizontal components even with 40\(^{\circ }\) elevation cutoff. The vertical accuracy decreases gradually as the elevation cutoff increases.
Comparisons of PPP results in single- and multi-system modes under different elevation cutoffs (from 10\(^{\circ }\) to 40\(^{\circ }\)) at station GMSD. The corresponding satellite numbers and PDOP values are also shown
Comparisons of PPP results in single- and dual-system modes under different elevation cutoffs (from 10\(^{\circ }\) to 40\(^{\circ }\)) at station CENT. The corresponding satellite numbers and PDOP values are also shown
We also present the PPP results under different elevation cutoffs for the dual-system station CENT in Fig. 21. With elevation cutoff of 20\(^{\circ }\), there is a obvious spike in the north components of GPS PPP due to the reduction of observable satellites to only four, while GPS+BeiDou PPP does not present any decrease in accuracy. When the elevation cutoff is increased to 30\(^{\circ }\) or 40\(^{\circ }\), reliable GPS PPP is not achievable. The position series of combined PPP are only a little nosier for 30\(^{\circ }\) elevation cutoff. They are much nosier at 40\(^{\circ }\), but the accuracy of centimeter lever can still be obtained in horizontal components. Compared with the Fig. 20, although the dual-system PPP solutions are not as stable and robust as the four-system PPP, the convergence time, PNT accuracy and reliability benefits from adding BeiDou.
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Li, X., Ge, M., Dai, X. et al. Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J Geod 89, 607–635 (2015). https://doi.org/10.1007/s00190-015-0802-8
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DOI: https://doi.org/10.1007/s00190-015-0802-8