# Spatial Grid-Based Position Calculation Method for Satellite-Ground Communication Links
## 3 Experiment and Result
### Analysis of Grid Computing Feasibility Results  
According to the GeoSOT encoding model, we apply grid encoding to the position of satellites and the terminal. After that, by calculating the grid encoding, we can obtain the grid distance between the satellite position and the terminal position at each time step, as shown in Figure 8.  
Two features should be noticed in Figure 8. One is the grid distance of each satellite, shown on the \(y\)-axis. The larger the grid distance, the closer it is to the edge of the coverage area. The other feature is the variation in grid distance, which we can obtain from the slope of each satellite's grid distance curve. If the curve has an upward trend, which means the slope of the curve is greater than zero, it indicates that the satellite is moving away from the coverage area. Therefore, a curve with a large initial grid distance and slope less than zero will represent a satellite with long residence time. A curve with a large initial grid distance and slope greater than zero will be a satellite that leaves the coverage area fastest.  
From the result graph in Figure 8, we can see that:  
1. IGSO_43603 (blue line) has the highest initial grid distance, but the grid distance of the satellite is still increasing as time increases, indicating that IGSO_43603 is at the edge of the detection region, while still accelerating away from the detection region, so we drop its ranking to the last.
2. Among the remaining candidate satellites, IGSO_37256 (purple line) has the highest initial grid distance, while the grid distance of the satellite is decreasing with time, and it has not yet reached the nearest position turning point.
3. IGSO_36828 (green line) reaches the distance nadir at the second time node, after which it starts to run away from the detection center.  
Figure 8: Grid calculation results for different satellites.  
With the experimental results, we can rank the satellites according to the available time as follows: IGSO_37256 > IGSO_37763 > IGSO_43581 > IGSO_44337 > IGSO_43539 > IGSO_36828 > IGSO_43603.  
Using the same satellite and terminal data in STK software, we can generate the experimental results as shown in Figure 9.  
The \(y\)-axis represents different satellites, and we use different colors to distinguish them. The \(x\)-axis represents the time interval. Each horizontal line represents the coverage time interval of each satellite. Take satellite IGSO_44337 as an example, which is located at the bottom of Figure 9 and is represented in red. This indicates that the link time of the satellite in the coverage area is from 20:00 to 00:20 on the 24 th. The simulation results can visualize the link time between the observation satellite and the ground terminal. By ranking the longest link time, we can make a comparison with the grid calculation ranking results. The simulation results of the satellite-ground link in Figure 9 can show more intuitively that satellite IGSO_37256 has the longest visibility time throughout the whole calculation period, followed by satellite IGSO_37763, and the satellite IGSO_43603 has the smallest visibility time. The results for the longest satellite link time are approximately the same as those obtained from our grid calculations.