# Navigation Resource Allocation Algorithm for LEO Constellations Based on Dynamic Programming
## 2 Model Analysis of LEO Constellation Navigation Resource Allocation
### Network Model
#### 2.1.1 LEO Navigation Signal Transmission  
LEO navigation signal transmission refers to the transmission of navigation enhancement signals by LEO satellites to ground users to achieve information enhancement or signal enhancement of GNSS signals. The optimization goal is to optimize global coverage performance. Specifically, it is to use the minimum number of LEO satellites to achieve uniform global coverage when the coverage requirements are determined.  
In order to present the global coverage of the satellite navigation system more intuitively, the following takes the BDS navigation system as an example. As shown in Table 1, the BDS navigation system constellation consists of 3 GEO satellites, 3 IGSO satellites, and 24 GEO satellites.  
The trajectory data of the BDS constellation in the simulation of this article are based on the two rows of orbital ephemeris data provided by Celestrak ([[http://celestrak.com/](http://celestrak.com/)]([http://celestrak.com/](http://celestrak.com/))), accessed on 13 June 2023. The satellite position data are generated in the STK 11.6 software based on the ephemeris data at a 60 s sampling interval. Figure 2 is the generated three-dimensional spatial allocation diagram of the BDS constellation, and Figure 3 is the BDS sub-satellite point trajectory diagram. It is noteworthy that Figures 2 and 3 are not from the same moment in time.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Track Type** & **GEO** & **IGSO** & **MEO** \\ \hline Number of satellites & 3 & 3 & 24 \\ Constellation allocation & 80\({}^{\circ}\)E, 110.5\({}^{\circ}\)E, 140\({}^{\circ}\)E & Evenly distributed at 118\({}^{\circ}\)E & Walker (24/3/1) \\ Orbital inclination & 0\({}^{\circ}\) & 55\({}^{\circ}\) & 55\({}^{\circ}\) \\ Orbital height & 35,789 km & 35,786 km & 21,528 km \\ \hline \hline \end{tabular}
\end{table}
Table 1: BDS navigation system constellation parameters.  
Figure 2: BDS constellation three-dimensional space allocation diagram. The red line represents the IGSO orbit, the green line represents the GEO orbit, and the blue line represents the MEO orbit.  
The satellite cutoff altitude angle, set at \(10^{\circ}\), refers to the minimum elevation angle at which a satellite can be considered visible. This angle is chosen to avoid signal obstructions near the horizon and ensure reliable communication. The ground latitude and longitude sampling interval to \(5^{\circ}\). Through STK 11.6 software simulation, the BDS global average coverage multiplicity and GDOP value distribution are shown in Figures 4 and 5, respectively [25], which show the global coverage of BDS lasting 48 h. Due to the existence of GEO and IGSO satellites, BDS has better coverage performance in the East Eighth District (near \(120^{\circ}\)E). Moreover, the higher the coverage multiplicity, the lower the GDOP value.  
Figure 4: Global average coverage of BDS.  
Figure 5: Global GDOP value distribution of BDS.  
Figure 3: BDS constellation subsatellite point trajectory chart.