# Assessment of Different Stochastic Models for Inter-System Bias between GPS and BDS
## 5 Conclusions  
To study the effect of stochastic models for the ISB estimation and the importance of considering ISB, five different ISB processing strategies are proposed. From the comparison of pseudorange observation residuals between five strategies, it can be found that the ISB-OFF strategy has the largest residuals, and the other four schemes have much lower results. Compared to ISB-OFF, the RMS of pseudorange residuals in ISB-PW, ISB-RW, ISB-AD, and ISB-WN can reduce by 21.3 m (improvement rate is 95.9%) both in static mode and kinematic mode. That is to say, it is quite necessary to consider the effect of ISB parameter in multi-GNSS combined positioning. As for the analyses on the convergence time and positioning accuracy, the cases with GBM and WUM precise products are carried out to reveal the potential impact on ISB caused by the different solution strategies in the analysis center. The result of the GBM case shows that ISB-RW and ISB-WN strategies have a similar processing accuracy, and perform best, while ISB-AD performs worst, even worse than the ISB-OFF, which is against the conclusion of pseudorange observation residuals results, the most probable reason being that the ISB stochastic model during GBM precise product generation is not set as an arc-dependent constant. The result of the WUM case is opposite; the schemes ISB-PW and ISB-AD perform best, and ISB-RW is worse than ISB-OFF, while ISB-WN performs worst. Based on the above findings, it can be concluded that the ISB processing strategies of GBM and WUM products are quite different. Thus, the recommendation of the ISB stochastic model selection can summarized as follows: it is better to consider the ISB parameter as random walk, 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. The test of accuracy improvement during the convergence period is performed as well. From the results, the conclusion can be drawn that just as after a converged period, considering ISB or not also has a strong impact on PPP positioning accuracy during the convergence period. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**8 min (95\%)**} & \multicolumn{3}{c}{**16 min (95\%)**} & \multicolumn{3}{c}{**8 min (68\%)**} & \multicolumn{3}{c}{**16 min (68\%)**} \\ \cline{2-13}  & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** \\ \hline OFF & 71.4 & 78.4 & 191.8 & 76.1 & 94.7 & 178.7 & 49.3 & 57.9 & 106.1 & 35.6 & 45.5 & 76.4 \\ PW & 58.2 & 69.3 & 135.6 & 43.3 & 58.8 & 100.0 & 24.6 & 31.4 & 58.1 & 18.1 & 27.1 & 42.7 \\ RW & 58.7 & 71.2 & 135.9 & 42.9 & 53.1 & 99.0 & 24.3 & 30.6 & 57.4 & 17.6 & 23.7 & 41.5 \\ AD & 58.2 & 69.3 & 135.6 & 43.4 & 58.8 & 100.0 & 24.6 & 31.4 & 58.1 & 18.1 & 27.1 & 42.7 \\ WN & 60.5 & 69.9 & 137.1 & 43.8 & 54.3 & 99.2 & 24.6 & 31.1 & 57.5 & 17.8 & 24.3 & 41.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Positioning accuracy of GPS/BDS combined kinematic PPP during the convergence period (8 min and 16 min) in five different schemes with GBM precise products (unit: cm).