# Assessment of Different Stochastic Models for Inter-System Bias between GPS and BDS
## 4 Results and Discussion
### Convergence Time and Positioning Accuracy
#### 4.3.1 The Case with GBM Precise Products  
Figure 8 presents the errors in North (N), East (E), and UP (U) components of GPS/BDS combined static PPP in different schemes. Meanwhile, Table 4 shows the convergence time derived in the N, E, and U components, based on the statistics over all the tests. Figure 7: The estimated ISBs using the _WUIM_ products in the kinematic mode. Different ISBs derived from the different schemes with considering ISB are shown in different colors. From Figure 8 and Table 4, it can be noticed that PPP performance at some components in ISB-OFF, and ISB-AD schemes cannot converge in one 3-h processing-arc window. It also can be seen that using the GBM products, the convergence time of ISB-OFF is 8.5 min and 20.0 min in N, and U components at 95% quantile. It takes 7.5 min, 74.5 min and 16.0 min to converge into the 68% quantile in three components. As for the N component, the convergence time of four schemes with ISB (ISB-PW, ISB-RW, ISB-AD, and ISB-WN) is on average improved by 41.2% from 8.5 min to 5.0 min, and 41.7% from 7.5 min to 4.4 min at 95% and 68% quantile, respectively. That means after considering the ISB, the convergence rate speeds up, compared to ISB-OFF. The convergence time of ISB-PW at the U component is longer than ISB-OFF, this may be caused by the stochastic model of ISB-PW here being inconsistent with the model of ISB estimation applied by GFZ for precise product generation, which is not mentioned in any reference, but we have confirmed with the colleagues responsible for the matter in GFZ. From the results, this inconsistency will slow down the ISB convergence rate, and PPP performance time will be increased. This finding corresponds with the results in Figure 6. At E component, ISB-PW performs faster than ISB-OFF. It also can be seen that ISB-RW and ISB-WN have similar results and perform best among the proposed schemes. ISB-PW performs better than ISB-AD, and at the end of the 3-h period, its accuracy can reach closer to ISB-RW, and ISB-WN. It is quite incredible that compared with ISB-OFF, ISB-AD has a poorer result. In other words, GPS/BDS combined PPP considering the ISB with \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Static (95\%)**} & \multicolumn{3}{c}{**Static (68\%)**} & \multicolumn{3}{c}{**Kinematic (95\%)**} & \multicolumn{3}{c}{**Kinematic (68\%)**} \\ \cline{2-13}  & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** \\ \hline OFF & 8.5 & - & 20.0 & 7.5 & 74.5 & 16.0 & 14.5 & - & - & 11.5 & - & 25.0 \\ PW & 5.0 & 63.0 & 31.0 & 4.5 & 45.5 & 31.0 & 7.5 & 72.5 & 34.5 & 6.0 & 63.5 & 25.5 \\ RW & 5.0 & 13.0 & 13.5 & 4.0 & 11.5 & 12.0 & 7.0 & 20.5 & 18.0 & 5.5 & 16.0 & 14.0 \\ AD & 5.0 & - & - & 4.5 & - & - & 7.5 & - & - & 6.0 & - & 25.5 \\ WN & 5.0 & 13.5 & 14.0 & 4.5 & 11.5 & 12.0 & 7.5 & 19.5 & 17.5 & 5.5 & 17.5 & 13.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Convergence times of GPS and BDS combined static and kinematic PPP in five different schemes (unit: min). Figure 8: GPS/BDS combined static PPP convergence performance in five different schemes with GBM precise products, each scheme uses a different color, left side is the errors of 95% quantile, while the right side is the errors of 68% quantile. GBM products performs worse than neglecting the ISB, which is largely due to the inconsistency of ISB stochastic model applied in PPP processing on the user side and the precise products generation in GFZ. Therefore, we recommend PPP users adopt the same stochastic model of ISB estimation as the analysis center. Figure 9 indicates the errors in N, E, and U components of kinematic PPP with different schemes, and Table 4 also shows the convergence time of kinematic PPP at the 95% and 68% quantile in three different components. It can be seen that the convergence times of all schemes in kinematic mode are longer than the static mode, because of different coordinate estimation strategies.