## 3 Tests, Results, and Discussion
### Performance of BSSD PPP/INS TCI  
In comparison with BSSD PPP, position errors can be reduced visibly by the addition of INS in all three components (shown in Figure 7). The average improvements provided by BSSD PPP/INS TCI are 31.24%, 23.35%, and 27.38% in the three directions (Table 3).  
Figure 8 shows the position differences between BSSD PPP and BSSD PPP/INS TCI. Significantly, the accuracy of PPP is similar to that of PPP/INS TCI when there are sufficient satellites. That is because the absolute position accuracy mainly depends on PPP. However, such differences are significant during the periods with frequent GNSS outages, primarily from the 1500 s to 2500 s and 6500 s to 7500 s. That is because PPP/INS TCI can still provide high-accuracy position results when the number of satellites is less than 4, even if there is  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{3}{c}{**BSSD PPP**} & \multicolumn{3}{c}{**Undifferenced PPP**} \\ \cline{2-6}  & **North (cm)** & **East (cm)** & **Down (cm)** & **North (cm)** & **East (cm)** & **Down (cm)** \\ \hline GPS & 69.68 & 75.25 & 218.18 & 95.65 & 76.73 & 218.77 \\ BDS-3 & 62.67 & 47.91 & 162.23 & 63.89 & 49.97 & 186.07 \\ BDS-3/GPS & 60.64 & 37.25 & 81.93 & 62.73 & 38.05 & 103.12 \\ \hline \end{tabular}
\end{table}
Table 2: Positioning errors of undifferenced PPP and BSSD PPP with different GNSS.  
Figure 6: Positioning errors of undifferenced PPP (**left**) and BSSD PPP (**right**) with different GNSS.  
Figure 7: Positioning errors of BSSD PPP/INS TCI with different GNSS.  
no available satellite in short-term time. The frequent GNSS outages between the 1500 s and 2500 s are displayed in Figure 9, from which we can see about ten partial and complete outages with the time last 1 s to 32 s happened. The details about the outage time and the average number of available satellites during these periods are listed in Table 4. As is shown, the maximum outage time for BDS-3, GPS, and BDS-3+GPS are 28 s, 32 s, and 26 s, respectively. During these periods, although a few satellites are still available, the number does not meet the minimum requirement of positioning both for single and dual systems PPP calculation. However, these available satellites can be used in BSSD PPP/INS TCI mode. The corresponding position differences of PPP and PPP/INS TCI during the 1500 s to 2500 s are shown in Figure 10. Visibly, BSSD PPP cannot provide position results, but BSSD PPP/INS TCI can work in partial outage periods. The divergence of position error can also be restrained in short-term outages. The average maximum drifts of position decreased from 107.96 cm, 59.90 cm, and 78.22 cm to 88.52 cm, 54.54 cm, and 62.00 cm after integrating with INS. Therefore, PPP/INS TCI can provide the position result with better continuity and accuracy. Nevertheless, in cases where the duration of complete outages is too long, such as outages 7 and 8, a divergence of the position results still can be found because INS would drift rapidly along with time.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Outages Scenes**} & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \multirow{3}{*}{Outages time(s)} & GPS & 16 & 4 & 2 & 9 & 14 & 3 & 32 & 26 & 8 & 1 \\ \cline{2-10}  & BDS-3 & 19 & 1 & 2 & 7 & 11 & 2 & 28 & 22 & 3 & 1 \\ \cline{2-10}  & GPS/BDS-3 & 17 & 1 & 2 & 6 & 11 & 2 & 26 & 22 & 2 & 1 \\ \hline \multirow{3}{*}{Satellite number} & GPS & 0.6 & 2.3 & 0.5 & 1.4 & 0.9 & 1 & 0.4 & 0.3 & 1.3 & 3 \\ \cline{2-10}  & BDS-3 & 0.3 & 2 & 1.5 & 1.3 & 0.9 & 0.5 & 0.2 & 2.4 & 1.7 & 1 \\ \cline{2-10}  & GPS/BDS-3 & 0.5 & 4 & 2 & 2.5 & 1.2 & 0.5 & 0.5 & 2.5 & 1.5 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The number of available satellites and the GNSS outages time.  
Figure 8: Positioning differences between BSSD PPP and BSSD PPP/INS TCI with different GNSS.  
Figure 9: Satellite numbers and outages time between the 1500 s and 2500 s.