# Assessment of Different Stochastic Models for Inter-System Bias between GPS and BDS
## 4 Results and Discussion
### Pseudorange and Carrier-Phase Observation Residuals  
As is already known, the remaining measurement noises and other unmodeled errors will be assimilated by the observation residuals, which is a very important indicator to assess the accuracy of the positioning model. Thus, here the pseudorange and carrier-phase observation residuals will be assessed and compared in the five different schemes. The pseudorange residuals at station STR1 (with the GBM products as an example) of each satellite with different colors in GPS and BDS system, respectively, are shown in Figures 2 and 3. Figure 2 is the result of static mode, while Figure 3 is the kinematic mode. From the figures, we can see that both in the static and kinematic modes, compared to considering ISB, neglecting ISB (ISB-OFF) will lead to a higher pseudorange residual. After introducing the ISB parameter (ISB-PW, ISB-RW, ISB-AD, and ISB-WN), the ionospheric-free pseudorange (PC) residuals in GPS system will on average improve 4.8 cm (i.e., 5.4%) in static mode, and 5.1 cm (i.e., 5.7%) in kinematic mode. The improvement is not obvious, which is in accordance with the ISB processing strategy that the GPS receiver clock error is considered to be the reference clock error, and ISB covers the biases between BDS and GPS. Thus, the ISB has no effect on the pseudorange residuals in GPS system. As for the BDS system, the PC residual of ISB-OFF is largest; because the remaining errors and difference are not absorbed by ISB, they go into the residuals. The statistical results of the other four schemes are similar, and compared to ISB-OFF, the RMS of pseudorange residuals for ISB-PW, ISB-RW, ISB-AD, and ISB-WN can reduce by 21.3 m (95.9%) both in static mode and kinematic mode. Hence, we can conclude that it is necessary to consider the ISB parameter in multi-GNSS combined positioning. In addition, the carrier-phase observation residuals of GPS and BDS satellites in station STR1 with the GBM products are also taken as an example, the results of static and kinematic modes are displayed in Figures 4 and 5, respectively. It can be noted from Figures 4 and 5 that the RMS of carrier-phase observation residuals is two orders of magnitude lower than that of the pseudorange residuals, which is caused by the different measurement accuracy levels of pseudorange and carrier-phase observations. Compared with neglecting ISB, the RMS of carrier-phase residuals considering ISB has no significant improvement regarding the pseudorange residuals. That is because in the carrier-phase PPP performance except ISB, the ambiguity is also an unknown parameter. If the ISB is neglected, the impact of unmodeled ISB will be partly or even totally assimilated by the ambiguity, which means the effect of considering ISB or not will not obviously reflect in the carrier-phase residuals. Besides, we can see that when using \(GBM\) products, the RMS of carrier-phase residuals in ISB-RW and ISB-WN are the best. Compared with the residuals in ISB-OFF and ISB-AD, the RMS can on average improve by 25.5% and 33.8% in GPS and BDS satellites in the static mode, and for the kinematic mode the improvement rate is 20.2% and 36.3% in GPS and BDS satellites. The carrier-phase observation residuals mainly reflected the accuracy of PPP performance, so we can conclude that the ISB stochastic models impact the carrier-phase observation residuals, and will have a further influence on the PPP performance. In the following parts, the impact of ISB stochastic models on the ISB estimation and PPP performance will be studied in detail. Figure 2: Ionospheric-free pseudorange observation residuals of GPS and BDS systems at STR1 station as an example on DOY 251, 2017, here is the results of the first 3h period with static PPP mode, left column is the GPS system, the right one denotes the BDS system, from top to bottom represents different schemes.