# Navigation Resource Allocation Algorithm for LEO Constellations Based on Dynamic Programming
## 3 Navigation Resource Allocation Algorithm Based on Dynamic Programming
### Algorithm Process
Through simulation analysis using STK 11.6 software, it was found that over a period of 7 days, there are a total of 556,021 visible links between the two constellations, all of which are intermittent, with durations ranging from 0.6 s to 5.8 h. For example, Figure 10 shows the set of visible links between the LEO satellite I0101 and BDS satellites over a period of 4 h. For the LEO satellite I0101, there are a total of 77 intermittent links within this 4-h period. Similarly, the visibility situation between 216 LEO satellites and BDS satellites over 7 days is even more complex and variable. Due to the symmetrical characteristics of global coverage in the east-west and north-south hemispheres within a complete orbital period of the constellation, only 19 ground stations in the northern hemisphere along the 0\({}^{\circ}\) longitude from 0\({}^{\circ}\) to 90\({}^{\circ}\)N, sampled every 5\({}^{\circ}\), are selected for simplicity when evaluating global coverage performance [31], as shown in Figure 11.

Through simulation analysis using STK 11.6 software, it was found that over a period of 7 days, there are a total of 152,190 visible links between the LEO constellation and the 19 ground stations, all of which are intermittent, with durations ranging from 1.1 s to 14.8 min. For example, Figure 12 shows the set of visible links between the LEO satellite I0101 and a ground station over a period of 4 h. For the LEO satellite I0101, there are a total of 19 intermittent links within this 4-h period. Similarly, the visibility situation between 216 LEO satellites and the ground stations over 7 days is even more complex and variable. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **BDS Constellation** & \multicolumn{2}{c}{**LEO Constellation**} \\ \hline Orbital type & GEO/IGSO/MEO & Near-Polar & Inclined \\ Number of satellites & \(3/3/24\) & 72 & 144 \\ Number of orbital planes & \(1/3/3\) & 6 & 12 \\ Number of satellites per plane & \(3/1/8\) & 12 & 12 \\ Orbital Altitude & 36,000 km/36,000 km/21,500 km & 1175 km & 1150 km \\ Inclination & \(0^{\circ}/55^{\circ}/55^{\circ}\) & \(55^{\circ}\) & \(87^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of BDS and LEO constellation. Figure 9: The distribution diagram of the LEO constellation and BDS constellation. The blue lines represent the orbital planes of the BDS constellation, the yellow lines indicate the near-polar orbital planes of the LEO constellation, and the red lines denote the inclined orbital planes of the LEO constellation. Figure 11: Distribution map of ground stations used for evaluating constellation global coverage. The blue circles represent ground stations in the northern hemisphere along the 0\({}^{\circ}\) longitude from 0\({}^{\circ}\) to 90\({}^{\circ}\)N.

Figure 10: Visual links between LEO satellite S0101 and BDS satellites within 4 h. Lines of different colors represent different visible links. Based on the resource allocation schemes obtained from different algorithms in Table 3, the set of visible links between the LEO constellation and the ground stations can be used to derive the global coverage performance of the different constellation resource allocation schemes, as shown in Figure 16. The results indicate that all three constellation allocation schemes meet the requirement for single coverage at all times. Additionally, the average minimum coverage multiplicities for ground stations achieved by the constellation allocation schemes obtained from the three algorithms are 1.2, 3.2, and 2.5, respectively; the average coverage multiplicities are 4.5, 7.9, and 7.5, respectively; and the maximum coverage multiplicities are 8.7, 13.2, and 12.7, respectively.