## 5 Conclusions  
This study introduced a satellite selection method utilizing the proposed MSFGWO, which is specifically tailored to address the unique characteristics of LEO satellites, including their high velocity and brief visibility periods. Through a series of simulation experiments, we evaluated the performance of various algorithms with respect to their DGDOP values, computational time consumption, and times of satellite switching at adjacent moments when selecting different numbers of satellites. The experimental results demonstrated that the perturbation mechanism of the VNS algorithm and the mutation strategy of the GA can substantially enhance the global search capability of the GWO algorithm, thereby leading to a significant reduction in the DGDOP value. Furthermore, through an analysis of the times of satellite switching at adjacent time intervals, it was confirmed that \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**4 Satellites**} & \multicolumn{2}{c}{**5 Satellites**} & \multicolumn{2}{c}{**6 Satellites**} \\ \hline  & 2D (m) & 3D (m) & 2D (m) & 3D (m) & 2D (m) & 3D (m) \\ Traversal & 152.05 & 239.93 & 132.88 & 209.91 & 119.82 & 189.36 \\ GWO & 156.51 & 253.12 & 135.19 & 216.77 & 120.87 & 195.79 \\ SFGWO-A & 152.92 & 239.89 & 131.68 & 211.46 & 119.46 & 189.73 \\ SFGWO-B & 157.95 & 261.86 & 138.32 & 222.21 & 123.31 & 196.42 \\ MSFGWO & 151.94 & 240.97 & 132.08 & 210.23 & 121.43 & 192.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The 2D and 3D position accuracy values under different numbers of selected satellites. the integration of the EWM algorithm into the GWO algorithm can substantially reduce the frequency of satellite switching and extend the continuous observation duration for the same group of satellites. Specifically, when selecting six satellites, the MSFGWO algorithm yielded an average DGDOP value of 222.08. Compared with the DGDOP ratio of the traversal method, it is 1.03. The 3D positioning accuracy is 192.86 m, and the positioning error is improved by 54.43% compared with the positioning accuracy of the traditional GWO algorithm. Furthermore, the system achieved a continuous observation duration of up to 45 s, with zero instances of switching between the six satellites at adjacent time points. This significantly enhances the stability and reliability of the positioning solution. Despite having the shortest computational time, the GWO algorithm exhibited relatively inferior satellite selection performance. Conversely, although the introduction of multiple strategies into the MSFGWO algorithm led to a slight increase in its computational time, it remained significantly lower than that of the exhaustive search method; for example, when selecting six satellites, the MSFGWO algorithm consumed only 0.0174 s, and the calculation efficiency is increased by 93.43% when compared to the traversal method. In summary, the MSFGWO algorithm introduced in this paper not only achieves an optimal balance between the DGDOP value and the satellite switching times between adjacent moments but also significantly enhances the satellite selection efficiency. This algorithm significantly enhances the overall optimization capabilities of the GWO algorithm, thus effectively reducing the DGDOP value, improving positioning accuracy, minimizing the satellite handover times between adjacent time intervals, and substantially extending the continuous observation duration for the same set of satellites. Consequently, the proposed method contributes to improvements in the stability and accuracy of positioning solutions. Conceptualization, W.L. ([PERSON]) and M.C. ; methodology, W.L. ([PERSON]), M.C. and Y.L. ; software, W.L. ([PERSON]), X.S., Y.L. and Y.S. ; resources, W.L. ([PERSON]) and S.T. ; writing, W.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research was funded by the Key Laboratory of Smart Earth Independent Research Fund, grant number SYS-ZX02-2024-01.