## 4 Analysis and Evaluation of the PPP-B2b and Broadcast Ephemeris Performance
### Comparision of the Globally Averaged Signal in Space Range Error of PPP-B2b and Broadcast Empeheris  
The signal in space in space range errors are more effective to characterize the common orbit and clock errors in the satellite-user directions. This article takes the signal in space range error (SISRE) as the key performance indicator of the system. According to [PERSON] and [PERSON] (2021) [27; 28], the combined error of the radial orbit error and clock error \(\Delta RT\) can roughly characterize the globally averaged signal in space range error. The \(\Delta RT\), SISRE, and SISRE (ORB) are calculated as follows:  
\[\Delta RT=W_{R}\cdot\Delta X_{radial}-c\cdot\Delta t^{s} \tag{20}\]  
\[SISRE_{orb}=\sqrt{\left[RMS(W_{R}\cdot\Delta X_{radial})\right]^{2}+W_{A,C}^ {2}\cdot(A^{2}+C^{2})} \tag{21}\]  
\[SISRE=\sqrt{\left[RMS(W_{R}\cdot\Delta X_{radial}-c\cdot\Delta t^{s})\right]^ {2}+W_{A,C}^{2}\cdot(A^{2}+C^{2})} \tag{22}\]  
where \(W_{R}\) and \(W_{A,C}^{2}\) are the weight factors for the statistical contribution of radial (R), along-track (A), and cross-track (C) errors to the line-of-sight ranging error. \(\Delta X_{radial}\) is the orbit error in the radial direction; \(c\) represents the light speed in a vacuum; and \(\Delta t^{s}\) represents the clock offset error. A and C are the RMS of the orbit errors in the along and cross directions, respectively. The weight factors used for calculating the SISRE are shown in Table 6.  
Figure 8: STDs of GPS and BDS-3 satellite clock offset errors with and without PPP B2b correction.  
The GPS and BDS-3 PPP-B2b and broadcast ephemeris \(\Delta RT\) time series are shown in Figure 9. The RT series values of GPS PPP-B2b are larger than those of the broadcast ephemeris value, because there is a larger system bias in the GPS PPP-B2b clock offset error. After correction, the \(\Delta RT\) time series of the PPP-B2b and broadcast ephemeris are smoother than the broadcast ephemeris. Just like the clock offset series curve and orbit error series curve, the \(\Delta RT\) series also indicate that the PPP-B2b can reduce the effect caused by error jumps compared to the broadcast ephemeris.  
The SISRE and SISRE (ORB) of the PPP-B2b and broadcast ephemeris are shown in Table 7. Compared to the GPS broadcast ephemeris, the SISRE (ORB) of GPS PPP-B2b has increased by 37.5% and the SISRE of GPS PPP-B2b has increased by 141.7%. Compared to the BDS-3 broadcast ephemeris, the SISRE (ORB) of BDS-3 PPP-B2b has increased by 29.8% and the SISRE of BDS-3 PPP-B2b has increased by 10.3%. It can be seen from Table 7 and the statistical data calculated above that after PPP-B2b correction, the accuracy of the GPS broadcast ephemeris and BDS-3 broadcast ephemeris have been improved significantly.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Ephemeris** & **Type** & \(W_{\mathbf{R}}\) & \(W_{A,C}^{2}\) \\ \hline GPS & 0.98 & 1/49 \\ BDS-3 MEO & 0.98 & 1/54 \\ BDS-3 IGSO & 0.98 & 1/126 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The weight factors used for SISRE computation.  
Figure 9: Time series of ART for PPP-B2b and broadcast ephemeris.