# Spatial Grid-Based Position Calculation Method for Satellite-Ground Communication Links
## 1 Introduction
However, for all of the above methods, when calculating the relative positions of satellites to each other and to ground-based observation points, the existing through-view analysis methods need to construct satellite relative coordinate and Earth-centered, Earth-fixed coordinate systems in real time, and use floating numbers to calculate the relative positions between different satellite orbits and even different constellations. The complexity of this algorithm is high [12; 13]. Therefore, calculation takes a long time when multiple orbits, multiple constellations and fast-moving targets are involved. Different from the above methods of calculating latitude and longitude data, the spatial grid data model and its indexing method are simple to divide and efficient to calculate spatially [14]. Among them, geographic coordinate subdivision grid with one-dimension integer coding on 2n tree (GeoSOT) is a unified location framework for two-three-dimensional, multi-level nested, equal latitude and longitude divisions [15]. Previous studies [16; 17] found that GeoSOT-3D is significantly helpful in improving the efficiency of spatial computation by avoiding the conversion of coordinate systems and using grid coordinates in binary format, which is more beneficial than floating-point numbers in terms of computational efficiency. [PERSON] [18] used the GeoSOT grid model and proposed a set of algorithms to perform satellite link analysis by querying the grid passages. It builds a grid index table using grid retrieval instead of inter-satellite link computation, and the computation speed is improved by about 20 times. However, this method uses a storage query instead of computation, and spatial storage will show an exponential increase in the face of complex constellations and finer spatial requirements. Using the GeoSOT grid model, [PERSON] [19] proposed an overall grid coding algebraic computing framework to verify the feasibility and efficiency of grid coding computation. Based on previous research, this paper proposes a GeoSOT-based grid calculation model for the satellite-ground position (GCSGP) model to achieve fast calculation of the relative positions of satellites and the ground. The GeoSOT can uniformly represent the objects in the satellite internet, avoiding frequent conversion between the spatial coordinate system of the satellite and the geodetic coordinate system of the ground base station in the calculation. We discretize the whole of Earth space using the GeoSOT grid, and use binary grid code calculation instead of longitude, latitude and altitude floating calculation,thus increasing the efficiency of satellite-ground position calculation. The feasibility and efficiency of the proposed GCSGP model under the grid satellite maximum service time strategy are also verified. In Section 1, we introduce the research background of satellite position calculation and the research status of existing literature, and put forward the overall research method. In Section 2, we first introduce the GeoSOT grid coding model and coverage area grid modeling method. On this basis, a grid-based spatial computing model of the coverage area is proposed. In Section 3, the specific data and experimental process of the experiment are determined. In Section 4, according to the experimental results, the feasibility experimental analysis based on the grid computing model, the comparative experimental analysis of grid computing efficiency and the experimental analysis of grid computing accuracy are carried out, respectively. In Section 5, we summarize and propose ideas for future research.