## 4 Result and Analysis
### The Performance of BDS-2 and BDS-3 Combined SPP  
As mentioned earlier, the datum of broadcast clock offsets for BDS-2 and BDS-3 is inconsistent. From Equations (13) and (14), the ISB contains the inconsistency of the datum of satellite clock offsets and receiver pseudorange bias. In order to research the performance of BDS-2 and BDS-3 combined SPP, the selected observations are divided into seven categories according to the receiver type. According to Equation (13), the selected data is used to calculate the ISB between BDS-2 and BDS-3. Figure 14  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Agency** & \multicolumn{2}{c}{**Items**} & **BDS-2** & **BDS-3** & **Improvement Rate** \\ \hline \multirow{4}{*}{GFZ} & \multirow{2}{*}{RMS} & SISRE & 2.06 m & 0.47 m & 77.18\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 1.98 m & 0.16 m & 91.92\% \\ \cline{2-6}  & \multirow{2}{*}{STD} & SISRE & 0.41 m & 0.14 m & 66.85\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 0.36 m & 0.03 m & 91.67\% \\ \hline \multirow{4}{*}{WHU} & \multirow{2}{*}{RMS} & SISRE & 2.02 m & 0.52 m & 74.25\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 1.97 m & 0.16 m & 91.88\% \\ \cline{2-6}  & \multirow{2}{*}{STD} & SISRE & 0.44 m & 0.14 m & 68.18\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 0.34 m & 0.04 m & 88.24\% \\ \hline \multirow{4}{*}{SHA} & \multirow{2}{*}{RMS} & SISRE & 1.26 m & 0.52 m & 58.73\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 1.23 m & 0.17 m & 86.18\% \\ \cline{2-6}  & \multirow{2}{*}{STD} & SISRE & 0.36 m & 0.14 m & 61.11\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 0.36 m & 0.05 m & 86.11\% \\ \hline \multirow{4}{*}{Average} & \multirow{2}{*}{RMS} & SISRE & 1.78 m & 0.50 m & 71.91\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 1.72 m & 0.17 m & 90.12\% \\ \cline{2-6}  & \multirow{2}{*}{STD} & SISRE & 0.40 m & 0.14 m & 65.00\% \\  & & SISRE\({}_{\text{ORBIT}}\) & 0.34 m & 0.04 m & 88.24\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The mean RMS and STD statistical results of SISRE and orbit-only SISRE and the improvement rate of BDS-3 compared to BDS-2 in terms of RMS and STD (DOY 089-123, 2020).  
Figure 13: The STD and RMS of SISRE and orbit-only SISRE of broadcast ephemeris relative to precise ephemeris provided by GFZ, WHU and SHA.  
illustrates the 35-day time series of ISB for seven types of receivers. In the seven types of receivers described above, the ISBs of JAVAD TRE_3 are smaller than other receivers, and its average and STD are \(-0.75\) m and \(0.79\) m, respectively.  
Now turn to the performances of BDS-2 and BDS-3 combined SPP, Figure 15 depicts SPP positioning errors of the selected stations for two different processing cases. Setting ISB parameters to estimate ISB will make the positioning accuracy worse for the tracking stations with JAVAD TRE_3 receiver (POTS, SGOC, ULAB, URUM and WUH2). Combining Figures 14 and 15, we can conclude that when the ISB is relatively minor, setting the parameter to estimate ISB will reduce the stability of the SPP model and make the positioning accuracy of the SPP worse. However, the positioning accuracy of the receivers with relatively large ISB will be improved by setting parameters to estimate ISB. As Table 7 indicates, setting parameters to estimate ISB can improve the positioning accuracy by 20.15%, 19.81% and 12.76% compared to ordinary BDS SPP models in north, east and up directions, respectively.  
Figure 14: The time series of inter-system bias (ISB) between BDS-2 and BDS-3 for JAVAD TRE_3, TRIMBLE ALLOY, SEPT POLARX5, CETC-54-GMR-4016, CETC-54-GMR-4011, GNSS-GGR and UB4B0-13478 from DOY 089 to 123.