## 3 Tests, Results, and Discussion
### BSSD PPP/INS/ODO TCI Positioning  
In the case of a complete outage for a long time, position errors of PPP/INS TCI could accumulate rapidly. Therefore, constraint information is helpful. An odometer can measure the forward velocity of the vehicle. Based on such velocity and motion constraints, the problem above can be restrained by Equation (23). Figure 11 depicts the position errors of BSSD PPP/INS/ODO TCI with different GNSS, and the corresponding RMS for the common periods with BSSD PPP/INS TCI are calculated in Table 5. Accordingly, the position improvements caused by the addition of an odometer on average are 1.34%, 1.41%, and 1.73%. Such invisible enhancements are because the impact of the odometer on PPP/INS integration mainly affects these periods with poor or without GNSS observability. While there are enough satellites, the weight of the odometer observation function is much smaller than that of GNSS observations which can be obtained by making a comparison between Equations (14) and (23). The corresponding position differences between BSSD PPP/INS TCI and PPP/INS/ODO TCI are plotted in Figure 12. Significantly, the periods with sufficient satellites have small differences, and significant differences emerge along with long-term outages. Figure 13 depicts the position difference of BSSD PPP/INS/ODO TCI from 1500 s to 2500 s. Accordingly, the average position RMSs from 1500 s to 2500 s is reduced from 50.00 cm, 27.08 cm, and 37.42 cm to 44.40 cm, 26.85 cm, and 34.96 cm. The average of maximum positioning drifts with different GNSS during a satellite outage are plotted in Figure 14. The averages of maximum positioning drifts are reduced from 88.52 cm, 54.54 cm, and 62.00 cm to 66.29 cm, 45.84 cm, and 49.17 cm, with a maximum diminution of 74.94%, 33.0%, and 51.56%. Hence, the position performance of BSSD PPP/INS TCI can be further enhanced, especially in challenging environments, by using an odometer. Figure 11: Positioning errors of BSSD PPP/INS/ODO TCI with different GNSS by using PPP-B2b corrections. Figure 10: Positioning errors of BSSD PPP (**left**) and BSSD PPP/INS TCI (**right**) between the 1500 s and 2500 s.  
In addition, to analyze the impact of the BSSD model on PPP/INS integration, the time series of position errors of undifferenced PPP/INS/ODO TCI is shown in Figure 15. In contrast, the BSSD model provided about 7.71%, 3.09%, and 0.27% in the three directions on average, according to RMSs listed in Table 5. It can be seen that the position accuracy of the BSSD model-based integration mode is close to the undifferenced model-based integration mode. Figure 14: Average maximum position drifts of different GNSS for BSSD PPP/INS TCI (**left**) and PPP/INS/ODO TCI (**right**) on different GNSS outage scenes. Figure 12: Positioning differences between BSSD PPP/INS TCI and BSSD PPP/INS/ODO TCI with different GNSS. Figure 13: Positioning errors of BSSD PPP/INS/ODO TCI with frequent GNSS outages. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**BSSD PPP/INS/ODO TCI**} & \multicolumn{3}{c}{**Undifferenced PPP/INS/ODO**} \\ \hline  & **North (cm)** & **East (cm)** & **Down (cm)** & **North (cm)** & **East (cm)** & **Down (cm)** \\ \hline GPS & 55.23 & 60.29 & 202.20 & 55.69 & 61.92 & 207.96 \\ BDS-3 & 41.78 & 33.47 & 113.43 & 44.50 & 34.38 & 108.16 \\ GPS/BDS-3 & 35.02 & 28.63 & 40.86 & 42.90 & 29.98 & 41.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Position RMS of BSSD PPP/INS/ODO TCI with different GNSS. in the time series in general but is slightly higher in position statistics. It is due to the reason that the BSSD model can remove the receiver-depended errors (i.e., receiver clock offset, receiver time delays on pseudorange and carrier-phase, unmodelled receiver errors, etc.) that impact initial convergence or re-convergence of PPP after satellite signal outages. Such a character is illustrated in Figure 16, which depicts the differences between the BSSD-based solutions and the undifferenced PPP-based solutions.