## 4 Experiment and Analysis
### Satellite Selection Algorithm Results  
To verify the greater capability of the weighted quasi-optimal satellite selection algorithm presented in this paper for engineering applications compared to the optimal satellite selection algorithm, this experiment compared the quality of satellite selection and performance between the two algorithms. The data used in this experiment were collected in an open area with satellite signals from the GPS and BDS systems. Figure 9a shows the trajectory of the experimental carrier. Figure 9b, on the other hand, displays the number of satellites and the GDOP values for all satellites during the experiment. Before starting the comparative experiment, it was necessary to determine the number of satellites selected for our experiment. Although there are no strict requirements for the number of satellites selected, we need to follow a principle that, while ensuring the satellite navigation positioning accuracy meets requirements, the number of selected satellites should be as small as possible. The advantage of doing so lies in the fact that it can reduce the computational scale in the integrated navigation solution, thereby lowering computational complexity and minimizing the potential impact on the accuracy of error  
Figure 8: Performance comparison chart of attitude errors in horizontal directions with and without VG. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Without VG** & **With VG** \\ \hline Global & 0.149 & 0.081 \\ GNSS denial period & 0.240 & 0.098 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Horizontal attitude RMSE comparison with and without VG in different periods. estimation. Our approach is to first use the optimal satellite selection algorithm to calculate the optimal GDOP values at various times for 6 to 17 satellites. Based on these calculations, we further plot the curve of the average GDOP values under different numbers of satellites. Through a detailed analysis of this curve, we can select the optimal number of satellites. In addition, according to the satellite count graph shown in Figure 9b, we observe that the maximum number of visible satellites is 18. Therefore, when selecting the number of satellites, we limit the maximum number of considered satellites to 17. The GDOP variation curve for the optimal satellite selection algorithm under various numbers of selected satellites is shown in Figure 10a. It can be visually observed that as the number of selected satellites increases, the GDOP values at each moment do not decrease uniformly, but rather, the rate of decrease gradually slows down. To more clearly demonstrate this rate of decrease, the curve of the average best GDOP values for each number of selected satellites is displayed in Figure 10b. The results show that when the number of selected satellites is between 6 and 8, the GDOP value changes by about 0.1; between 8 and 10, the change is around 0.06; and between 10 and 12, the change is close to 0.03. Beyond 12 satellites, this change drops to about 0.01. Therefore, in order to balance the reduction in the GDOP and keep the number of selected satellites as small as possible, we selected 12 satellites for the experiment. After determining the number of selected satellites, we conducted simulation experiments for the optimal satellite selection algorithm (OSA), Q  
Figure 10: (**a**) The GDOP variation curve under various numbers of selected satellites, where the GDOP decreases as the number of selected satellites increases. (**b**) The curve showing the variation in the average best GDOP values for each number of selected satellites. Figure 9: (**a**) The vehicle’s travel trajectory and (**b**) the variation curves of observable satellites and the GDOP during the experiment. of the experiments are shown in Figure 11a, which illustrates the GDOP variation curves. The figure demonstrates that the GDOP variation curves of the QOSA and WQOSA, after satellite selection, exhibit a similar trend to those obtained by the OSA.