# A Parallel Approach for Multi-GNSS Ultra-Rapid Orbit Determination
## 3 Computation and Comparison
### Analysis of the Accuracy of Parallel Ultra-Rapid POD
#### 3.3.2 Evaluation of Predicted Orbit Accuracy of Ultra-Rapid POD by Parallel Approach  
In order to further analyze the performance of the parallel approach, the accuracy of the ultra-rapid predicted orbit is evaluated. The GPS/GLONASS precise orbit of IGS and the Galileo/BDS precise orbit of CODE are selected as reference values. The experiment includes three groups. The first one uses the proposed parallel POD approach with a 1-h updated result (denoted as SDU-1h). The second one uses the non-parallel POD approach with a 6-h updated result (denoted as SDU-6h), and the third one is the 1-h updated result of Wuhan University analysis center (denoted as WHU-1h). The statistical results of accuracy are shown in Figure 11.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & R (cm) & A (cm) & C (cm) & 1D RMS (cm) &
\begin{tabular}{c} **Improvement of** \\ **Accuracy** \\ \end{tabular} \\ \hline GPS\_6 & 2.3 & 6.8 & 2.7 & 4.8 & \\ GPS\_1 & 2.3 & 3.9 & 2.2 & 3.2 & 33.4\% \\ GLO\_6 & 3.2 & 10.4 & 4.4 & 7.4 & \\ GLO\_1 & 3.1 & 6.4 & 3.6 & 5.1 & 31.4\% \\ Gal\_6 & 6.3 & 12.4 & 4.4 & 9.3 & \\ Gal\_1 & 5.8 & 5.2 & 3.6 & 5.6 & 40.1\% \\ BDS\_6 & 14.3 & 21.0 & 6.9 & 16.9 & \\ BDS\_1 & 12.2 & 12.0 & 5.6 & 11.3 & 32.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Accuracy of ultra-rapid predicted Multi-GNSS orbit updated per 6 h.  
Figure 10: Accuracy of BDS ultra-rapid predicted orbit updated per 6 h and BDS ultra-rapid predicted orbit updated per 1 h.  
From Figure 11, it can be seen that as the extrapolation time increases, the orbit accuracy of SDU-6h decreases in the orbit sequence. The phenomenon that the orbit accuracy fluctuates with extrapolation time does not exist in WUH-1h and SDU-1h. The accuracy of WUH-1h is better than that of SDU-6h result, and it is relatively stable except for occasionally large outliers. The predicted orbits of GPS, GLONASS, Galileo, and BDS of SDU-1h have the highest accuracy and the most stable performance. Combined with the statistical results in Table 8, the 1D mean RMS of the ultra-rapid predicted orbit with the proposed parallel approach is 3.2 cm, 5.1 cm, 5.6 cm and 11.8 cm, respectively.  
The accuracy of the predicted orbit of each satellite from GPS/GLONASS/Galileo/BDS are plotted in Figure 12, and BDS-2 MEO and BDS-2 IGSO of the BDS system are used in this processing. It can be seen from these figures that the predicted orbits of GPS, GLONASS, Galileo and BDS determined by the parallel approach with 1-h update frequency have the highest accuracy. The accuracies of GPS, GLONASS, Galileo and BDS predicted orbit are  
Figure 11: RMS of GPS, GLONASS, Galileo and BDS (from top to bottom) orbit of SDU-1h, SDU-6h and WHU-1h compared with CODE precise orbit.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellite System** & **Scheme 1** & **Scheme 2** & **Scheme 3** \\ \hline GPS & 3.2 & 4.8 & 4.3 \\ GLONASS & 5.1 & 7.3 & 6.5 \\ Galileo & 5.6 & 9.2 & 11.2 \\ BDS & 11.8 & 16.9 & 16.4 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Statistics of the accuracy of ultra-rapid predicted orbit (cm).  
mostly better than 3 cm, 5 cm, 6 cm, and 12 cm, respectively. One of the GPS satellites, G18, has poor accuracy, which may be due to its large orbit error during the shadow period. In general, the accuracy of the ultra-rapid predicted orbit of each GNSS satellite with the parallel approach and 1-h updated frequency have greatly improved.  
Figure 12: RMS of predicted orbit of each satellite from GPS, GLONASS, Galileo and BDS (from top to bottom) using SDU-1h, SDU-6h and WUH-1h strategy.