## 4 Experiment and Analysis
### Satellite Selection Algorithm Results
However, overall, the GDOP values of the WQOSA and QOSA are slightly higher than those of the OSA. The GDOP values of the WQOSA range from 1.5 to 2.5, with occasional values close to 3, but they still fall within the range of excellent positioning accuracy. Through calculations, we obtained average GDOP values of approximately 1.628 for the OSA, 1.785 for the QOSA, and 1.809 for the WQOSA. We also analyzed the differences among the three methods and plotted two GDOP difference curves. From these curves, it can be observed that the difference between the WQOSA and OSA fluctuates between 0 and 0.5, with an average difference of approximately 0.1815. The average difference between the QOSA and WQOSA is 0.0424. Although the WQOA's GDOP is slightly higher than that of the QOSA, the difference is relatively small. The above analysis shows that the difference in satellite selection results between the WQOSA and OSA is very small, and the quality of satellite selection is very close. To further evaluate the performance of the two, we also compared the time consumption during the execution process. We analyzed the running times of the two algorithms within each time element and plotted the running time comparison chart between the OSA and WQOSA, as shown in Figure 11b. From the chart, it can be clearly observed that there is a significant difference in the order of magnitude of time consumption between the two algorithms. After calculation, we found that the average running time of the OSA is 0.1057 s, while the average running time of the WQOSA is only 0.0002723 s, which is about a 388 times difference. Considering the 200 Hz sampling frequency of the IMU, our system must complete one round of correction calculation within 5 ms to meet real-time requirements. Obviously, the running time of the OSA is far beyond this limit. On the contrary, the running time of the WQOSA, which is 0.27 ms, not only is far below the threshold of 5 ms but also meets this condition even in the worst case in this set of data. Therefore, the WQOSA not only has comparable satellite selection quality to the OSA but also has a clear advantage in running time, which can fully meet our requirements for high-performance integrated navigation systems. To verify the improvement of the WQOSA over the QOSA in satellite selection quality, we conducted a comparative experiment between the two algorithms. Following Equation (17), we used the standard deviation of pseudo-range measurement errors as a substitute for UREE [30] and analyzed the average pseudo-range error standard deviation of the satellite selection results for both algorithms. A comparison graph, as shown in Figure 12a, was plotted accordingly. The results in Table 6 show that the WQOSA outperforms the QOSA in this metric, with specific average values of 1.787 (WQOSA) and 2.237  
Figure 11: (**a**) The GDOP curves for the OSA and WQOSA satellite selection, along with the GDOP difference curve. (**b**) The variation curves of the satellite selection time consumption for the OSA and WQOSA using the experimental data. (QQSA). This aligns with our expectations, as the WQOSA considers additional influencing factors beyond the satellite distribution during the satellite selection process. Finally, we comprehensively evaluated the satellite selection quality of both algorithms by considering both the GDOP and UERE. The average pseudo-range error standard deviation at each time point was multiplied by the GDOP, and the results are shown in Figure 12b. This yielded the navigation error standard deviation curves for both algorithms. It is evident that in certain time intervals, the satellites selected by both algorithms completely overlap, resulting in consistent curves during that period. However, for the majority of the time, the WQOSA exhibits a significantly smaller error standard deviation compared to the QQSA. Specifically, the average values of the two curves are 3.241 (WQOSA) and 3.941 (QQSA). In conclusion, the WQOSA demonstrates superior satellite selection quality over the QQSA.