# Seeking Optimal GNSS Radio Occultation Constellations Using Evolutionary Algorithms
## 2 Principles and Methods
### Simulation Scenario  
When the signal sent by a GNSS satellite passes through the atmosphere, the signal trajectory is bent due to the refraction of the atmosphere before it is received by the GNSS RO receiver onboard a LEO satellite. This phenomenon is considered a GNSS RO event. In the simulation of GNSS ROEs, two requirements should be met for the occurrence of a ROE. One is that the tangent point heights of the signal paths is between 0 and 80 km, and the other one is that the ray, connecting the GNSS satellite and the LEO satellite, is in the field of view of the antenna. What needs to be mentioned is that the receiver onboard each LEO satellite is here assumed with the sufficient number of channels to track all the intercepted GNSS signals and the channels will not interfere with each other. The multi-GNSS signals from GPS, GLONASS, Galileo, BDS, and QZSS are used as the sources for GNSS RO observations. Considering that Galileo, BDS, and QZSS have not yet reached their full planned constellation, to ensure the consistency in the simulation work, the full operational five GNSS constellations are all simulated based on their nominal constellation configurations [40; 41; 42; 43; 44]. In particular, the third generation of BDS is used. The configuration parameters for the five nominal GNSS constellations are listed in Table 3.  
Figure 1 shows the distribution of the 24 h ROEs observed by COSMIC with five navigation satellite systems, including GPS, GLONASS, Galileo, BDS, and QZSS simulated based on their nominal constellation configurations. It should be mentioned that although COSMIC can only process the signals from GPS in practice, the number of ROEs can be expected to increase almost fourfold and better spatial and temporal distributions of ROEs will be acquired if the RO payload of COSMIC could track the signals from all the five navigation satellite systems. For the simula \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**System** & **GPS** & **GLONASS** & **Galileo** & **BDS** & & & **QZSS** & \\ \hline
**Orbit** & **MEO** & **MEO** & **MEO** & **MEO** & **IGSO** & **GEO** & **QZO** & **GEO** \\ \hline Number of satellites & 24 & 24 & 24 & 24 & 3 & 3 & 3 & 1 \\ Constellation pattern & 6 planes & \begin{tabular}{c} Walker \\ (24/3/1) * \\ \end{tabular} & \begin{tabular}{c} Walker \\ (24/3/1) * \\ \end{tabular} & \begin{tabular}{c} Walker \\ (24/3/1) * \\ \end{tabular} & \
\begin{tabular}{c} Walker \\ (24/3/1) * \\ \end{tabular} &
\begin{tabular}{c} / / / / / / / / / \\ \end{tabular} \\ Inclination [deg] & 56 & 64.8 & 56 & 55 & 55 & 0 & 43 & 0 \\ Altitude (km) & 20,180 & 19,100 & 23,220 & 21,528 & 35,786 & 35,786 & 35,786 \\ \hline \hline \end{tabular}  
* t/p/f where t denotes the total number of satellites, p is the number of equally spaced planes, and f is the relative spacing between satellites in adjacent planes.  
\end{table} 
Table 3: The configurations for the five nominal Global Navigation Satellite System (GNSS) constellations. Figure 1a, the real COSMIC orbits are applied. While for the simulation of ROEs shown in Figure 1b, the COSMIC orbits are simulated based on the initial satellite positions of the real orbits, using the Simplified General Perturbations Satellite Orbit Model 4 (SGP4) orbit propagator [45]. The number of the 24 h ROEs obtained based on the real and the simulated orbits is 10,317 and 10,340, respectively, with the relative difference of only 0.2%. It can be seen from Figure 1 that the distributions of the simulated 24 h ROEs in the two subfigures are very similar. Furthermore, the fitness value is 0.51968 and 0.51080 when the real and the simulated COSMIC orbits are used, respectively and the two values are very close to each other. These comparisons verify the effectiveness of the orbit simulation in this study. In the simulations conducted in this study, for a certain type of LEO constellation, it is assumed that the number of LEO satellites varies from 6 to 12.