Modeling and Performance Analysis of GPS/GLONASS/BDS Precise Point Positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain a centimeter level accuracy. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. Along with the competition of the first phase of the Beidou Navigation Satellite System (BDS) which comprising 5 satellites in Geostationary Orbit (GEO), 5 in Inclined Geosynchronous Orbit (IGSO) and 4 in Medium Earth Orbit (MEO) by the end of 2012, the regional navigation capabilities has been formed and the visibility and availability have been significantly improved for users in the Asia-Pacific regional area. Attention has been paid to improve the performance of PPP by combining BDS and other navigation satellite system (GPS/GLONASS). This study introduces a single-differenced (SD) between-satellite PPP model which can process any single-system or multi-system GNSS (GPS/GLONASS/BDS) raw dual-frequency carrier phase measurements. In this model, the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. Thus the GPS receiver clock offset is canceled and only a system time offset between GPS and other GNSS system is estimated for the observations of GLONASS or BDS. In the proposed model, noisy pseudorange measurements are ignored thus modeling the pseudorange stochastic model is not required. The stochastic model for SD measurements and states can be easily realized by mapping that for undifferenced measurements and states. Also the correlation of the SD measurements is considered. Using a 7-day data set from 10 multiple system GNSS stations, we have investigated the performance of single-system PPP, GPS/GLONASS PPP and GPS/GLONASS/BDS PPP, including convergence speed and positioning accuracy. The contribution of BDS observation to the performance of multi-GNSS PPP is analyzed and assessed with special concern. Numerous experimental results indicate that after adding BDS observations, the convergence time can be reduced by 10-12 % for GPS PPP, and reduced by about 5-7 % for GPS/GLONASS PPP further. Besides, BDS observations can contribute to improving the accuracy of kinematic PPP with 3 h observations. After adding BDS observations, the RMS in kinematic mode is improved by 14.3, 7.1 and 7.5 % for GPS PPP while 11.1, 16.7 and 6.5 % for GPS/GLONASS PPP, in the east, north and up directions, respectively. For GPS/GLONASS/BDS PPP, an accuracy of 1-2 cm in horizontal and 2-3 cm in vertical directions can be achieved in kinematic mode while an accuracy of less than 1 cm in horizontal and 1-2 cm in vertical directions can be achieved in static mode.