# Spatial Grid-Based Position Calculation Method for Satellite-Ground Communication Links
## 2 Materials and Methods  
### GeoSOT-Based Grid Modeling  
GeSOT is a binary spatial unified dissection coding system proposed by Prof. [PERSON] of Peking University, which can cover all geospatial space seamlessly and without stacking. It can uniquely identify regions in geospatial space, and different spatial objects can be finely represented through the selection of layers. The research theory based on GeoSOT is now relatively well-established and has become the standard in multiple industries. The core idea of GeoSOT Earth spherical dissection is to expand the whole sphere by three times (expanding the whole sphere to \(512^{\circ}\times 512^{\circ}\), the whole degree of latitude and longitude from \(1^{\circ}\) to \(64^{\prime}\) and the whole score from \(1^{\prime}\) to \(64^{\prime\prime}\)) and to perform regular quadrature of the value domain space layer-by-layer, in order to form a multi-scale quadratic tree grid from the global sphere (level 0) down to the centimeter-level surface element (level 32). Subsequently, on the basis of the spherical two-dimensional dissection, the elevation attribute is introduced. The elevation information is then mapped into 512 degrees, each degree being defined as the distance \(2\pi\)a/(\(360^{\circ}\)) (approximately 111.3 km) from the Earth's surface adjacent to X in longitude at the Earth's equator, forming an altitude binomial tree profile grid from 50,000 km high down to the Earth. The above spherical and elevation profile systems are unified and organized to form the final GeoSOT-3D geospatial profile grid (Figure 1). In order to provide a uniform representation of ground base station and satellite constellation positions, we chose the GeoSOT coding system as the coding basis for spatial position representation. Meanwhile, this paper uses GeoSOT for grid modeling of ground terminal and space satellite coverage area to solve the position calculation problem in satellite-ground links. Different levels correspond to different sizes of spatial grids in the GeoSOT model. The essence of coverage area grid characterization is to discretize the area. We divide the coverage area into a series of grids through the GeoSOT model, and use the grid set to represent the coverage area. For different application scenarios, we select different levels of grids to divide the coverage area. The coverage area grid characterization is firstly a formal description, which introduces a dissecting grid to describe the representation form of the satellite ground coverage area and provides a basic logical reference for concrete implementation. Secondly, the characterization is a computational framework, which obtains the ground coverage area of satellite at a specific moment by the existing coverage calculation method, then dissects it to form a coverage grid, and then introduces a time dissecting code to expand the specific moment to any time period to form a satellite space-time coverage grid. The grid characterization method is to select the highest grid level that meets the accuracy requirements of satellite applications, dissect the calculated satellite ground coverage area into this grid level and obtain a collection of grids (Figure 2). The satellite coverings of several different shapes at moment \(t\) are each dissected by the Nth level, assuming a number \(n\), and the notation is in order \(\{grid_{1},grid_{2}\ldots,grid_{n}\}\). Then, we use this collection to characterize the satellite ground coverage at this moment, i.e.,  
\[C_{s,t\to e}\rightarrow\{grid_{1},\ grid_{2},\ldots,grid_{n}\} \tag{1}\]  
Figure 1: GeoSOT model schematic. The notation in Equation (1) means mapping. In the GeoSOT profiling reference framework, all grids at all levels are uniquely coded.