## 4 Results
### Regional Deployment Optimization  
In the case of the regional distribution of GSs, the criterion for optimal deployment is the SPDOP. The SPDOP is an indicator used to evaluate the dilution of precision of satellite positions relative to GSs [23]. Using the method detailed for the three scenarios studied according to the number of GSs used, the optimization of regional deployment is performed. Remember that the objective of optimization is the minimization of the SPDOP, which is calculated only with the GSs. The regional area used for the local deployment of GSs is shown in Figure 10, where it is delimited by a red rectangle. The regional area selected for GS deployment in the second scheme is Pacific East Asia. Table 3 shows the coordinates of this area. The optimization process is performed using the method of regional deployment shown in Figure 4. The evolutionary algorithm parameters used in this optimization problem are shown in Table 2. The number of populations used is 150, and the number of generations (iterations) is set to 30. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Coordinates** & **Longitude [\({}^{\circ}\)]** & **Latitude [\({}^{\circ}\)]** \\ \hline Value & 75E–135E & 17N–55N \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geographic limits of the selected area. Figure 9: Satellite position dilution of precision distribution (SPDOP) of 3-HC deployment. According to the number of GSs used, three cases are simulated for the optimization of the regional distribution of GSs, as shown in Table 4, where the number of GSs is fixed at 15, 20 and 25. Using the optimization method detailed in the previous sub-section, the optimization results of the two objectives (i.e., the SPDOP and the sub-objective of the maximization of the minimum distance between the two nearest GSs) are shown in Figure 11.  
The solution shows, for each scenario (i.e., 15, 20 and 25 GSs), a Pareto front of the two objectives: the SPDOP and \(1/\mathrm{d_{min}}\) (refers to the inverse of the minimum distance between the two nearest GSs in the same deployment). As the optimization is a two-objective problem with one objective and one sub-objective, the choice of the best solution is set according to the first objective (the minimum \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario Case** & **1** & **2** & **3** \\ \hline Number of GSs used & 15 & 20 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of GSs used for regional deployment. Figure 11: Pareto front solution of regional GS deployment optimization: (**a**) 15 GSs, (**b**) 20 GSs and (c) 25 GSs. The term \(1/\mathrm{d_{min}}\) refers to the inverse of the minimum distance (expressed in degree units) between the two nearest GSs in the same deployment. Figure 10: Location of the selected area for regional GS deployment. mean SPDOP). As the SPDOP is considered dominant in this optimization problem, only the solution with the minimum mean SPDOP value is considered as the final solution. Therefore, the optimal solutions for 15, 20 and 25 GSs present mean SPDOPs of 2.0544, 1.339 and 1.3301, respectively (See Figure 11). The optimal solutions correspond to minimum distances between the two nearest GSs in each deployment of 5.65\({}^{\circ}\), 4.91\({}^{\circ}\) and 2.48\({}^{\circ}\), respectively. The optimal deployment of GSs for each scenario (15, 20 and 25 GSs) and the distribution of the SPDOP of the sub-satellite position for regional GS distribution are shown in Figure 12.  
The increase in the number of GSs enhances the SPDOP value, which increases the precision of orbit determination. For the optimal deployment of 15 GSs, the mean SPDOP value is 2.0544. Using 20 GSs with optimal deployment, the mean SPDOP value is 1.3990. Figure 12: GS distribution and SPDOP of the sub-satellite position for the LEO satellite constellation: (a) 15 GSs, (b) 20 GSs and (c) 25 GSs. In the case of 25 GSs, the SPDOP is enhanced to a mean value of 1.3301.