# Seeking Optimal GNSS Radio Occultation Constellations Using Evolutionary Algorithms
## 3 Results
### The Optimal Constellations  
It is shown in Figure 3 that the constellation with the best result depends on the optimization algorithm. Regarding the dependency on the algorithm, the two methods are considered and the better solution achieved by either of them, which corresponds to the highest fitness value, is selected. Tables 4 and 5 presents the parameters defining the final optimal 2D-LFCs and 3D-LFCs composed of \(n(n=6,7,8,\ldots\ldots 12)\) satellites, respectively. It is shown that, regardless of the constellation pattern and number of satellites, the inclination angles of the optimized constellations are generally high, which is important for obtaining a uniform temporal and spatial distribution over the globe. It is also shown that the altitudes of the satellites in both 2D-LFCs and 3D-LFCs are generally lower than 650 km. Moreover, the fitness values of the final optimized constellations are generally higher than 0.6, which means that the numbers of \(10^{\circ}\times 10^{\circ}\times 3\) h spatio-temporal grids with ROEs more than the expected, are generally larger than 3000. Figure 3: Fitness values of the optimal configurations for 2D-lattice flower constellation (2D-LFC) and 3D-LFC composed of 6-12 satellites based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithms. Figure 4 presents the numbers of the 24 h GNSS ROEs observed by the final optimal LEO constellations with 2D-LFC and 3D-LFC patterns composed of \(n(n=6,7,8,\ldots\ldots\ldots 12)\) satellites. It can be seen that for a certain number of LEO satellites, the numbers of ROEs observed by the optimal configurations of 2D-LFC and 3D-LFC are very close to each other, while the number of the ROEs observed by the optimized 2D-LFC is slightly larger than those observed by the optimized 3D-LFC. Figure 4 also shows that the more LEO satellites, the more GNSS ROEs will be observed. With 12 LEO satellites, the number of 24 h GNSS ROEs observed by the optimized LEO constellations increases up to almost 25,000. The spatial and temporal distributions of the ROEs observed by all the final optimized LEO constellations can be presented visually. Here, as representatives, the spatial distributions of the ROEs in 3 h intervals for one day, observed by the final optimized 2D-LFCs composed of 6 and 12 LEO satellites, are shown in Figure 5. It can be seen that as the number of satellites increases, the number of ROEs observed in each three hours increases accordingly. Independently from the number of satellites, the distributions of the ROEs observed by the optimized configurations within each 3 h are homogeneous over the globe. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Nsat**} & **Orbit Altitude** & \multirow{2}{*}{**\(\hat{\imath}^{(\circ)}\)**} & \multirow{2}{*}{**No**} & \multirow{2}{*}{**Nso**} & \multirow{2}{*}{**Nc**} & \multirow{2}{*}{**Fitness Value**} \\  & **(km)** & & & & & & & \\ \hline
6 & 415.471 & 90.398 & 3 & 2 & 1 & 0.68692 \\
7 & 477.085 & 87.532 & 7 & 1 & 4 & 0.74325 \\
8 & 500.825 & 97.762 & 8 & 1 & 3 & 0.59105 \\
9 & 491.636 & 90.274 & 3 & 3 & 1 & 0.67593 \\
10 & 430.506 & 90.462 & 5 & 2 & 2 & 0.74518 \\
11 & 483.447 & 90.488 & 11 & 1 & 1 & 0.61188 \\
12 & 467.620 & 90.697 & 3 & 4 & 1 & 0.67438 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameters of the optimal 2D-LFC configurations. Figure 4: The numbers of ROEs observed in one day by the final optimal LEO constellations with 2D-LFC and 3D-LFC patterns composed of 6–12 satellites.