# Spatial Grid-Based Position Calculation Method for Satellite-Ground Communication Links
## 3 Experiment and Result
### Accuracy and Computational Efficiency Analysis Experiments  
In terms of the accuracy and computational efficiency of the GCSGP model, we will analyze the effect of satellite altitude and receiver elevation angle on the accuracy of the experiment under a grid of 9-15 size level. Under the fixed variables of altitude and elevation angle, the accuracies of the grid coordinates with respect to latitude and longitude at a certain level are tested by selecting the coordinates of a fixed distance from the center point and the coordinates of the point at the edge of the receiver range, respectively.  
The use of the grid instead of latitude and longitude will certainly bring up some errors in spatial position representation. The GeoSOT grid will produce different errors at different layer scales. In this experiment, we take satellite BEIDOU-3M9(C23) as an example, and analyze the accuracy error at different levels under two factors of satellite altitude and receiver angle.  
Figure 9: Simulation experiments of satellite visibility.  
From Figure 10, we can see that the error of the grid at level 9 is larger when the altitude is below 2500 km, and the error decreases significantly when the altitude is higher; grids of 10-15 levels are available with the required accuracy at the test height of the satellite distribution.  
From Figure 11, it can be learned that the larger the angle at the same height, the larger the critical edge distance of the center point of phase convergence at a fixed height, and the smaller the area share of the unit grid area at that height, and the system error will be reduced. At the same time, for receivers with small inclination angles, the use of grids tends to cause larger computational errors. Using a higher-level grid (e.g., 14 levels) can result in better performance.  
We compare the calculation time of satellite-ground position using latitude and longitude coordinates with that using grid coordinates. We generate 10,000 to 10,000,000 satellite  
Figure 11: Impact of maximum angle on grid calculation.  
Figure 10: Effect of height on the accuracy of grid calculation under 9–15 levels.  
trajectory points, calculate GeoSOT-3D codes for each point at 9-15 levels and perform the following operations separately.  
A. Calculate the Euclidean distance between N trajectory points and the terminal and record the calculation time.  
B. For N trajectory points (same as in A), use their grid coordinates to calculate the grid distance between the satellite position and the terminal, and record the time.  
Figure 12 shows the total time consumed by conventional GPS for spatial distance calculation and grid distance calculation. We choose the grid of the 10 th level for satellite position characterization. It can be seen that the grid code calculation time is lower than that of the conventional latitude and longitude.  
The experimental results in Figure 12 show that the total time consumed for grid distance calculation is much smaller than that of the traditional latitude and longitude approach, and the time calculation is reduced by about 7 times, mainly because the use of grid code calculation avoids the conversion of polar coordinates and a large number of trigonometric and square calculations, which reduces its complexity.