# Spatial Grid-Based Position Calculation Method for Satellite-Ground Communication Links
## 4 Discussion  
Compared with traditional characterization, grid characterization has the following advantages. (1) The traditional model is inconsistent in the basic unit of satellite ground coverage capability representation, and it is unable to unify the expression of different types of satellite observation resources, while the GeoSOT coding-based grid dissection model takes the geospatial grid as the basis, quantifies the ground coverage capability of observation resources into a spatial grid, appends the temporal information to form a temporal-spatial grid of satellite resources and finally uses a unified coding model to characterize the spatio-temporal grid, which can realize the unified expression of multiple types and large numbers of space and Earth resources. (2) The traditional model cannot intuitively determine whether the observed target is within the satellite's ground coverage range. Since the current discrete subsatellite trajectory and load width are simply used to characterize the satellite's observation capability, when judging the spatial relationship between the observed target and the satellite's ground coverage range, it is necessary to abstract the line and surface-shaped observed target into a point, and calculate and judge whether the distance from the point to the subsatellite trajectory is within the load width. The distance from the point to the subsatellite trajectory is calculated and determined to be within the payload width. The literature reference in [20] is about position calculations based on the specific position of the satellite in relation to the receiver, followed by pseudo-range observations. When the observation task is heavy,  
Figure 12: Spatial distance calculation time comparison. the computation time should not be underestimated. In contrast, the GCSGP model uses a spatio-temporal grid (collection) to visually represent the ground coverage, and the spatial relationships are more efficient. With one million positions, the traditional calculation takes 0.72 s, while the grid calculation takes only 0.12 s.  
However, the use of grid coordinates instead of latitude and longitude coordinates improves efficiency, but gives up some accuracy. In the altitude accuracy experiment in Figure 10, we set the receiver inclination angle to 45\({}^{\circ}\) and tested the grid error test from a 500 km to 20,000 km altitude. The results show that the grid of 10-15 levels can achieve an error within 1% at all altitudes, and shows a decreasing trend with increasing altitude. In the angular accuracy experiments in Figure 11, the error decreases with increasing receiver inclination; for example, in the ninth-level grid, the error is 7.3% at 10\({}^{\circ}\) inclination, while the error is only 1.3% at 45\({}^{\circ}\) inclination. In both the height and angle accuracy test results, we found that the error of the test decreases as the grid level increases. This is because the larger the number of dissection levels, the smaller the grid cell size, so the more accurately the coverage grid at the boundary can fit the original coverage boundary. The characterization accuracy is thus improved. As is shown in Figure 13, the blue area is at the boundary of the ground coverage area, and the red object is the dissection grid, with the number of dissection levels increasing from left to right. For level \(A\), the grid drawn on the left is a covering grid according to the principle of covering boundary determination. For level \(A+1\), the four subgrids of this grid are also covering grids, but for the profiling level \(A+2\), seven of all the subgrids of the four subgrids of this grid are not covering grids. This paper proposes a grid calculation model for satellites on the ground, mainly to provide solutions for rapid interconnection and information interaction of satellite constellations for large-scale and complex network communications in low orbit.