## 4 Results
### Global Deployment Optimization  
Using the optimization of GSs (number and placement) with the method detailed in the previous section and shown in Figure 3, the solutions of three-heavy observing coverage to track the LEO constellation used in this study are shown in Figure 5.  
Figure 4: Flow chart of the optimization method for GS regional deployment. The three best deployments with the highest 3-HC observing rates use 95, 138 and 148 GSs with observing rates of 97.37%, 97.97% and 97.98%, respectively. In view of the observing rates of each configuration, which are fairly close to each other, and according to the number of GSs used, the first configuration of 95 GSs is the best choice with a 97.37% observing rate, as shown in Figure 5.  
The deployment of the optimal configuration of 95 GSs and a 97.37% observing coverage is shown in Figure 6.  
In order to determine the performance of the GS deployment, a grid of \(3^{\circ}\times 3^{\circ}\) of the LEO flight area is created (the flight area of the LEO satellite is the 3D space that a satellite of a constellation could occupy at any epoch). The LEO flight area is formed as \(\{lat,long,Alt\}\), where \(Alt\) is the orbit height, which is fixed for all the satellites (\(Alt=1176.6\) km), and \(\{lat,long\}\) is the geographic coordinates. For each grid, the number of visible GSs per satellite corresponding to the grid position was checked. Figure 5: Solution of objective optimization for 3-heavy observing coverage deployment. The parameter \(n_{GS}\) refers to the number of GSs used in deployment, while \(R_{\text{obs}}\) refers to the observing rate to reach 3-HC for this deployment. Figure 6: GSs distribution for tracking the LEO constellation with 3-HC. The sub-satellite position is the point at which a line between the satellite and the center of the Earth intersects the Earth's surface, and the location of this point is expressed in terms of latitude and longitude, as illustrated in Figure 7.  
With the grid of the flight area of the LEO satellite (sub-satellite position), Figure 8 shows the observing coverage multiplicity, which is the number of GSs visible to the corresponding flight area position (latitude, longitude). In the global deployment of 3-HC, the minimum number of GSs visible to each satellite each time over 5 degrees of elevation is two, and the maximum number of GSs is nine. Only in a few positions (2.63%), however, does the minimum number of GSs correspond to two. Otherwise, the minimum GSs visible per satellite is about 97.37%. * SPDOP Distribution  
In order to determine the SPDOP distribution for this deployment, the flight area of the LEO satellites is used. The SPDOP value is calculated for each \(3^{\circ}\times 3^{\circ}\) grid and the altitude corresponding to the LEO orbit height \(\{lat,long,Alt\}\). The distribution plot is projected as the sub-satellite position. The SPDOP distribution for 3-HC optimal distribution is shown in Figure 9.  
Figure 8: Observing coverage multiplicity of GSs for 3-HC. Figure 7: Sub-satellite position point. The SPDOP value of the 3-HC deployment shows an even distribution compared to the 2-HC deployment, with a mean value of 1.86 and maximum value of 21.8. For some satellite positions, SPDOP is not determined because the number of GSs is less than three (the areas indicated in white), but this represents only 2.63% of the whole area. SPDOP is less than two for more than 82% of the satellite positions and is more than five for only 2.82%. In addition, the dispersion value is low where the standard deviation of SPDOP is equal to 1.045. Therefore, the SPDOP value shows uniform distribution for all satellite point positions, which means there is a uniform distribution of orbit determination for all LEO satellites in the constellation. For global deployment, with 3-HC for the LEO constellation, SPDOP shows a good distribution with a mean value of 1.86. Therefore, it improves the accuracy of the orbit determination with 3-HC GS deployment for the LEO constellation.