# Real-Time Phase Bias Estimation for BeiDou Satellites Based on Consideration of Orbit Errors
## 4 Results
### PPP-IAR Performance Analysis  
We performed kinematic PPP-IAR for all hourly observations from the 20 rover stations using three models: GPS-only, GPS + BDS without consideration of the orbit error, and GPS + BDS with consideration of the orbit error. The fixing percentages at the different observation durations are shown in Figure 8, while typical values for observation durations of 5, 10, and 20 min are given in Table 4. When compared with the GPS-only solution, addition of BDS without consideration of the orbit corrections causes the fixing percentage to be severely degraded from 46.25 to 4.77% at the observation duration of 20 min. When the orbit corrections are considered, the fixing percentage improves significantly from 4.27 to 64.56% at an observation duration of 5 min, and from 46.25 to 91.73% at an observation duration of 20 min. Figure 8: Fixing percentages for various observation durations for kinematic PPP when using different strategies. Figure 7: Distributions of the a posteriori residuals of the NL ambiguities when considering the orbit errors. The fixing percentages in static PPP-IAR at different observation durations are shown in Figure 9, while typical values for the observation durations of 5, 10 and 20 min are given in Table 5. When compared with the kinematic solution, the fixing percentage of the GPS-only solution improves significantly, i.e., from 46.25 to 77.29% for an observation duration of 20 min. However, for the GPS + BDS approach when considering the orbit corrections, the improvement from the static to the kinematic solution is less than 4% for the different observation durations. It should be noted that if we do not consider the orbit corrections, then the fixing percentage for GPS + BDS is also very small in the static solution. For further assessment of the performance of the proposed method, we calculated the fixing percentages for an observation duration of 20 min for each station, where the results are shown in Figure 10 for the kinematic solution and in Figure 11 for the static solution. The stations are arranged in terms of the distance from each station to the central station (HALN). The fixing percentages for GPS-only are between 33% and 60% for each station in kinematic PPP and improved to percentages of between 67% and 90%. If we add BDS without the orbit corrections, the percentages are severely degraded to less than 12% for all stations. After use of the orbit corrections, the fixing percentages of GPS + BDS exceed 79% for all stations and average 92.2% in the kinematic solution, while they exceed 84% for all stations and average 94.1% in the static solution. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Time (min)**} & \multirow{2}{*}{**GPS Only (\%)**} & **GPS + BDS** & **GPS + BDS** \\ \cline{3-4}  & & **NoOrb (\%)** & **HaveOrb (\%)** \\ \hline
05 & 4.27 & 0.78 & 64.56 \\
10 & 18.33 & 1.78 & 81.53 \\
20 & 46.25 & 4.77 & 91.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fixing percentages for various observation durations for kinematic PPP when using different strategies. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Time (min)**} & \multirow{2}{*}{**GPS Only (\%)**} & **GPS + BDS** & **GPS + BDS** \\ \cline{3-4}  & & **NoOrb (\%)** & **HaveOrb (\%)** \\ \hline
05 & 10.33 & 0.91 & 68.17 \\
10 & 42.44 & 2.49 & 84.01 \\
20 & 77.29 & 6.05 & 93.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fixing percentages for various observation durations for static PPP when using different strategies. Figure 9: Fixing percentages for various observation durations for static PPP when using different strategies. station. For the IGSO and MEO satellites, however, for which the NL residuals are not as large as those of the GEO satellites, the residuals gradually increase with increasing distance to the central station. For comparison to Figure 12, Figure 13 gives the results when the orbit errors were considered.