## 3 Experiments and Discussions
### Assessments of BDS-3 Real-Time Orbits and Clock Products  
To evaluate the accuracies of PPP-B2b BDS-3 real-time orbits and clocks from CAS, DLR, GFZ, and WHU, as well as the broadcast ephemeris objectively, this study uses the final precision product from WHU as the reference. The B2b corrected GPS orbit and clock are also studied as a comparison. The time series of the orbit errors in radial, along-track, and cross-track directions, as well as the clock errors, are depicted in Figure 3. The corresponding statistics in terms of RMSE and STD are shown in Figures 4 and 5. In Figure 3, the orbit errors of different real-time products of BDS are within 20 cm, 60 cm, and 60 cm in radial, along-track, and cross-track directions. The BDS B2b corrected and broadcast orbit error in radial and along-track directions are similar to those of other real-time products; in the cross-track direction, however, the fluctuations of B2b-corrected and BDS broadcast orbit errors are more significant than those of other real-time products. The B2b corrected GPS orbit error is similar to that of the B2b corrected BDS orbit. As plotted in Figure 4, the statistic orbit accuracies of the IGSO satellites, C38-C40, are much lower than those of MEO satellites, especially while using the SSR corrections from GFZ. Generally, the orbit RMSE values of the real-time products from CAS, DLR, GFZ, WHU, and WHU_U (ultra-precise products) are within 10 cm in the radial, along-track, and cross-track components for MEO satellites. The RMSE of BRDC, PPP-B2b for BDS-3, are about 20 cm in the radial component and 50 cm in the along-track and cross-track components; the B2b corrected orbit for GPS has a similar performance as those for BDS in three directions. According to earlier studies, the higher accuracy in the radial direction is related to the high-quality satellite hydrogen and rubidium clocks [37]. In Figure 3, it is noted that systematic biases existed among different real-time clock products, especially the B2b corrected BDS and GPS clocks. This systematic clock bias is caused by pseudorange observation and can be absorbed by ambiguities [24; 38]. In Figure 5, The clock STD of the real-time products from CAS, DLR, GFZ, WHU, and WHU_U are within 0.4 ns for BDS MEO satellites. In contrast, the STD of PPP-B2b is within 0.2 ns, and the STD of BRDC is within 1.0 ns. The STD of the B2b corrected GPS clock is 0.3 ns.  
track and cross-track components. The RMSE of the BDS-3 PPP-B2b orbits in the radial, along-track, and cross-track components are 9.42 cm, 21.26 cm, and 28.65 cm, respectively. The accuracy of BDS-3 PPP-B2b orbits in terms of RMSE is lower than that of IGS centers products due to the distribution and number of the monitoring stations. Compared to the broadcast orbit, the IGS real-time products provide about 30.62-54.95% improvements in the radial component, and the improvement provided by BDS PPP-B2b is 2.89%. The STD of PPP-B2b clocks is 0.18 ns, which has the highest accuracy among these real-time products of BDS-3. The improvements of the BDS-3 real-time clock provided by PPP-B2b is 79.87% compared to broadcast ephemeris. For the GPS correction, the B2b corrected orbit RMSE in radial, along-track, and cross-track directions are 13.73 cm, 23.83 cm, and 17.96 cm, respectively, and the clock STD is 0.25 ns. For the user side, the positioning accuracy is mainly affected by the orbit in radial and the clock. Therefore, the PPP-B2b SSR products theoretically can provide precise positioning solutions.  
Figure 3: Time series of the orbit radial and clock errors of C32 and G20.  
Figure 4: RMS of real-time orbit errors.  
Figure 5: STD of real-time orbit clock errors.