## 4 Analysis and Evaluation of the PPP-B2b and Broadcast Ephemeris Performance
### Evaluation of the PPP-B2b and Broadcast Orbit Accuracy  
The final precision German Research Centre for Geosciences (GFZ) products are a reference for evaluating the accuracy of RT orbit determination [26]. The broadcast orbit reference point is the antenna phase center of the navigation satellite as for the PPP-B2b orbit whereas the GFZ precise orbit reference point is the centroid of the navigation satellite. Therefore, the IGS satellite antenna phase center offset correction file is used for eliminating the reference difference among the broadcast, PPP-B2b, and precise orbit. Figure 3 shows the GPS PPP-B2b and broadcast ephemeris orbit error series for a period of 3 days. The graph shows that after correction, the GPS satellite orbit errors in all three directions are not only smaller but also smoother, and the errors due to broadcast ephemeris update jumps are thus well compensated. The orbit errors in the along direction are the largest, and correspondingly, the correction in the along direction is the most obvious. Figure 4 shows the PPP-B2b and broadcast ephemeris orbit error series for the BDS-3 MEO satellites. Overall, the PPP-B2b orbit errors of the BDS-3 MEO satellites are slightly smaller than the errors in the broadcast ephemeris. However, it is possible that the BDS-3 MEO PPP-B2b orbit precision is a little worse than the BDS-3 MEO broadcast ephemeris (BDS-3 CNAV1 broadcast ephemeris) orbit precision in some cases. It is thus possible to sacrifice some orbital numerical accuracy to make the orbit smoother and more continuous. Figure 3: GPS orbit error series after PPP-B2b correction (**left**) and with the GPS broadcast ephemeris (**right**). Therefore, the BDS-3 PPP-B2b orbit corrections not only slightly reduce the broadcast ephemeris orbit errors but also affect their discontinuity due to data updates. Figure 5 shows the BDS-3 IGSO satellite broadcast ephemeris orbit error series with and without PPP-B2b correction. Similar to the case for the BDS-3 MEO satellites, after correction, the BDS-3 IDSO satellite broadcast ephemeris orbit errors are only slightly less but they are smoother. Figures 4 and 5 together reveal that the numerical precision of the broadcast orbit and PPP-B2b orbit of the BDS-3 IGSO satellite is much worse than that of the corresponding BDS-3 MEO satellite. This is due to only a few monitoring stations in specific areas receiving signals from the IGSO satellites, resulting in a poor geometric configuration when calculating the IGSO satellite broadcast ephemeris. The orbit accuracy of the IGSO satellites is thus lower than that of the MEO satellites. To make an in-depth comparison of the orbit numerical precision between the PPP-B2b and broadcast ephemeris, the RMS errors of the PPP-B2b and broadcast ephemeris orbit are calculated for 9 days of data. The obtained orbit precisions are presented in Figure 6 and Table 5. The RMS errors of the GPS PPP-B2b orbit in the three axial directions of the centroid orbit coordinate system are 0.12 (radial), 0.34 (along), and 0.26 (cross) m, respectively. These values are much smaller than those of the GPS broadcast ephemeris, which are 0.17, 0.92, and 0.49 m in the corresponding directions. In summary, the GPS PPP-B2b clearly improves the GPS broadcast orbits. The same is observed for the BDS-3 satellites. The BDS-3 MEO satellite broadcast orbit is more accurate than that of the GPS satellite broadcast ephemeris  
Figure 4: Orbit error series of BDS-3 MEO satellites after PPP-B2b correction (**left**) and with the original broadcast ephemeris (**right**). as inter-satellite link observations are involved in the generation of the BDS-3 MEO satellite broadcast orbit [12]. It has been reported that the numerical precision of the BDS-3 satellite broadcast ephemeris orbit is currently much higher than that of 1 year ago, as the orbit accuracy is improving every 6 months.