## 4 Simulation and Analysis
### Analysis of the Number of Satellite Switches Between Adjacent Moments  
A reduced number of satellite switches between adjacent moments allows for prolonged continuous observation of the same group of satellites, thereby enhancing the accuracy and stability of positioning. Figure 17 illustrates the number of satellite switches between adjacent moments when selecting four, five, or six satellites, along with the percentage of these switching instances relative to the total observation duration. Tables 3-5 detail the specific number of satellite switches for different algorithms when four, five, or six satellites are selected, respectively. Table 6 provides a comparison of the longest observable time across the different algorithms. Based on analysis of the data presented in Figure 17 and Tables 3-5, it is evident that the GWO algorithm exhibited a higher frequency of satellite switching between adjacent time intervals, with a larger number of satellites being switched each time. In contrast, both the SFGWO-B and MSFGWO algorithms demonstrated lower switching frequencies and fewer satellite switches between adjacent moments. This indicates that incorporating the EWM algorithm into the GWO framework effectively reduces satellite switching, thereby enhancing the continuous observation time for the same group of satellites. However, due to issues such as reduced diversity and susceptibility to local optima in the SFGWO-B algorithm, despite the reduction in satellite switching achieved through the introduction of the EWM algorithm, significant switching still occurred as the global optimal solution remained difficult to attain. Although the traversal method could identify the optimal satellite combination, it does not account for the impact of satellite switching, resulting in a high number of satellite changes between adjacent moments. Notably, when selecting five or six satellites, the MSFGWO algorithm achieved zero satellite switches between adjacent moments, meaning that no simultaneous replacement of five or six satellites occurred. Table 6 further highlights the advantage of the MSFGWO algorithm in terms of the longest continuous visible time; specifically, when selecting six satellites, it achieved a continuous observation time of 45 s, which is twice the value of 22 s observed with the traversal method. In summary, the experimental results demonstrate that the integration of the EWM algorithm into the GWO algorithm not only effectively reduces the frequency of satellite \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **4 Satellites** & **5 Satellites** & **6 Satellites** \\ \hline Traversal & 31 & 37 & 22 \\ GWO & 21 & 23 & 21 \\ SFGWO-A & 43 & 25 & 22 \\ SFGWO-B & 51 & 38 & 21 \\ MSFGWO & 48 & 54 & 45 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Longest continuous observation times under different numbers of selected satellites. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Satellite** & \multirow{2}{*}{**Traversal**} & **GWO** & **SFGWO-A** & **SFGWO-B** & **MSFGWO** \\ \hline
0 & 2778 & 899 & 2069 & 1775 & 3003 \\
1 & 292 & 1272 & 898 & 798 & 279 \\
2 & 277 & 934 & 406 & 659 & 196 \\
3 & 162 & 410 & 195 & 286 & 103 \\
4 & 74 & 70 & 43 & 78 & 16 \\
5 & 16 & 14 & 8 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The number of satellite switches in adjacent moments when selecting five satellites. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Satellite** & \multirow{2}{*}{**Traversal**} & **GWO** & **SFGWO-A** & **SFGWO-B** & **MSFGWO** \\
0 & 2771 & 883 & 1822 & 15,744 & 2819 \\
1 & 298 & 1066 & 976 & 718 & 337 \\
2 & 225 & 1021 & 530 & 792 & 309 \\
3 & 193 & 492 & 205 & 430 & 109 \\
4 & 89 & 128 & 58 & 108 & 21 \\
5 & 21 & 9 & 8 & 7 & 4 \\
6 & 2 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The number of satellite switches in adjacent moments when selecting six satellites. handovers between consecutive time intervals but also significantly prolongs the continuous observation duration for the same set of satellites.