BDS-3 and GPS/Galileo integrated PPP using broadcast ephemerides

Improved broadcast ephemerides of BDS-3 and Galileo systems provide new opportunities for precise point positioning with broadcast ephemerides (BE-PPP) instead of using precise ephemeris products. We propose an approach of BDS-3 and GPS/Galileo integrated BE-PPP, emphasizing modeling and mitigating specific errors of broadcast ephemerides. First, the standard precise point positioning (PPP) model is extended by considering systematic rotation errors implied in BDS-3 broadcast orbits. For each station, a comprehensive bias is then considered to account for the known signal-in-space error (SISE) bias and the satellite/receiver hardware delay unavailable for some observations before the positioning. Besides, an explicit parameter is included in the PPP model to compensate for the remaining errors of SISE for each satellite. Considering that the SISE discontinuity of BDS-3 is larger than that of Galileo, the SISE parameters for BDS-3 satellites are reset in all the BE-PPP solutions except the BDS-3 only kinematic positioning when broadcast ephemerides are updated. Tests performed with 64 global stations demonstrate that the three-dimensional (3D) position errors of BDS-3/GPS/Galileo integrated PPP can be 8.6 cm in static mode and 23.4 cm in simulated kinematic mode. Although suffering from fewer BDS-3 observations tracked by ground stations, triple-constellation solutions with BDS-3 still offer a 9% performance improvement for static mode and 20% for simulated kinematic mode compared to GPS/Galileo solutions. On the other hand, the orientation errors in BDS-3 broadcast orbits have been successfully mitigated by explicit estimations of rotation parameters in the integrated BE-PPP. The averaged rotation estimates derived from BDS-3/Galileo solutions agree well with those from orbit comparisons, and correlations of 0.79, 0.88 and 0.94 are obtained for x-, y- and z-rotations, respectively. With considering orientation and translation errors of BDS-3 orbits in integrated solutions, improvements of 3D position accuracy up to 1.7 cm (static) and 0.9 cm (kinematic) can be achieved, where the horizontals offer the dominating improvements.