# Assessment of Different Stochastic Models for Inter-System Bias between GPS and BDS
## 4 Results and Discussion
### Convergence Time and Positioning Accuracy
#### The Case with WUM Precise Products  
The analysis of the convergence time and positioning accuracy in GPS/BDS combined kinematic PPP using WUM precise products is shown in Figure 10. Meanwhile, Table 6 presents the statistics of convergence time and positioning accuracy. The ISB stochastic model applied in AC Wuhan University is considered it as an arc-dependent constant [14]. From the figure and the table, we can see that different from the tests with the GBM products, the performance using the WUM products have similar accuracy level whether considering the ISB parameter or not. The possible reason is that ISB estimation strategy used in WUM products is the same as the ambiguity processing strategy, and both are estimated as a constant each arc window. Thus, the ISB is highly correlative with the ambiguity; in this case, if the ISB is not introduced, the impact of its error will be absorbed by ambiguity. This finding corresponds with the statements from Figure 7. For the convergence time, in N component the improvements are small (6.7% from 7.5 min to 7.0 min) at the 95% quantile, and at 68% quantile, it is on average 19.2%, from 6.5 min to 5.25 min. For the E component, the schemes ISB-PW and ISB-AD perform better than ISB-OFF, and ISB-RW is worse than ISB-OFF, while ISB-WN performs worst. Compared with ISB-WN, the convergence time of ISB-PW and ISB-AD can be improved by 40.4% from 23.5 min to 14.0 min, and 34.2% from 19.0 min to 12.5 min at 95% quantile and 68% quantile, respectively. Similar to N component, the improvements of convergence time in U component considering ISB are low, which can on average reach 16.2%, and 5.8% at 95% quantile, and 68% quantile, respectively.  
\begin{table}
\begin{tabular}{c 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 & 9.5 & 31.9 & 23.6 & 1.3 & 9.3 & 4.3 & 14.6 & 34.6 & 31.8 & 4.6 & 12.7 & 10.7 \\ PW & 1.4 & 3.6 & 3.9 & 0.7 & 1.6 & 1.8 & 2.9 & 6.7 & 8.6 & 1.4 & 3.0 & 3.8 \\ RW & 1.2 & 1.6 & 2.7 & 0.7 & 0.7 & 1.3 & 2.0 & 3.0 & 5.8 & 0.8 & 1.3 & 2.6 \\ AD & 12.0 & 36.3 & 34.3 & 3.6 & 18.9 & 12.8 & 19.1 & 50.6 & 43.8 & 7.9 & 24.8 & 19.8 \\ WN & 1.2 & 1.6 & 2.8 & 0.7 & 0.7 & 1.3 & 2.0 & 3.0 & 5.8 & 0.8 & 1.3 & 2.6 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Positioning accuracy of GPS/BDS combined static and kinematic PPP with five different schemes (unit: cm).  
From these two cases with GBM and WUM precise products, we can conclude that GPS/BDS combined PPP processing with orbit and clock products from different ACs can get a completely different result, because during the generations of multi-GNSS orbit and satellite clock products, different ISB resolution strategies (stochastic model) are applied in different ACs, and if the users use the same ISB strategies as the ACs (GBM and WUM) during the PPP performance, a better result can be obtained. So, based on the tests in this study, we recommend users consider the ISB parameter as random-walk processing, or white noise if the GBM products are used; however, when the _WUM_ products are applied, it is better to consider the ISB as a piece-wise constant, or an arc-dependent constant.