# 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
However, similar to the static PPP, both at 95% and 68% quantile, ISB-AD performs worst in the convergence performance, while ISB-RW and ISB-WN perform best. PPP performance cannot be converged in E and U components for ISB-OFF, and ISB-AD at 95% quantile. For the 68% quantile, there are no convergence time values in E component. Compared with ISB-PW, the convergence time of ISB-RW at 95% quantile can be improved by 71.7% from 72.5 min to 20.5 min in E component, and 47.8% from 34.5 min to 18.0 min in U component, respectively. As for the 68% quantile, the improvement can reach 74.8% from 63.5 min to 16.0 min in E component, and 45.1% from 25.5 min to 14.0 min. ISB-WN has a similar convergence time as ISB-RW. It can also be noted that the convergence time in U component is less than that in E component in ISB-PW, ISB-RW, and ISB-WN. The first reason may be the phase ambiguities are more correlative with the E component than U component. Thus, in some cases, the convergence time of E component will be enlarged because of their correlation with phase ambiguities [35]. The second reason may be caused by the GPS and BDS satellites with north-south ground tracking in the earth-fixed reference frame [27]. GPS/BDS combined positioning accuracy in static and kinematic modes for five different schemes is listed in Table 5. In static PPP, we make the statistics using the results in the last epoch. As for the kinematic mode, since PPP performance cannot converge in some schemes, we make statistics with the same processing period, here using two hours later for each test. We can see, from the table, ISB-RW and ISB-WN have a similar processing accuracy, and perform best, while ISB-AD performs worst. Compared with ISB-AD, in static PPP at 95% quantile, the accuracy of ISB-RW and ISB-WN are improved by 90% from 12.0 cm to 1.2 cm, 95.6% from 36.3 cm to 1.6 cm, and 91.8% from 34.3 cm to  
Figure 9: GPS/BDS combined kinematic PPP convergence performance with five different schemes. 2.8 cm in N, E, and U components, respectively. At 68% quantile, the remarkable improvement can also be achieved with 80.6%, 96.3%, and 89.8% in three components. For kinematic mode at 95% quantile, the accuracy improvements are 89.5% from 19.1 cm to 2.0 cm, 94.1% from 50.6 cm to 3.0 cm, and 86.8% from 43.8 cm to 5.8 cm in N, E, and U components, respectively, while at 68% quantile, 89.9%, 94.8%, and 86.9% accuracy increment in three components can be acquired. Compared to ISB-OFF, schemes with the ISB parameter (i.e., ISB-PW, ISB-RW, and ISB-WN) can get an obvious accuracy improvement, which indicates the importance of considering ISB. Therefore, we conclude that from the validation of convergence time and performance accuracy using the GBM precise products, it is necessary to introduce the ISB parameter, and estimate it as a random-walk processing, or white noise, if you want to get a higher processing precision in a short time period (e.g., 3 h in this study). The scheme of ISB estimated as an arc-dependent constant (ISB-AD) is not recommended, because of its longest convergence time and worst positioning accuracy.