# Spatial Grid-Based Position Calculation Method for Satellite-Ground Communication Links
## 1 Introduction  
With the rapid development of space technology and modern internet, satellite internet, which consists of space satellite nodes interlinked with ground network clusters, has been developed tremendously. Satellite internet has increased the breadth of network coverage and is able to reach remote areas such as oceans and polar regions, playing an important role in the national economy and national security. With the satellite network formed by satellite nodes, information can be transmitted rapidly without geographical constraints, achieving a global response in a short time, and will occupy an important position in future communications [1; 2; 3; 4]. However, in satellite networks, especially low earth orbit (LEO) satellite networks, because of the high-speed movement of satellites, the network topology changes quickly, meaning satellite and ground base station communication links are easy to break. For example, the satellite delivery speed in the classical LEO constellation can reach 7 km/s [5], the safe and efficient transmission of data between the satellite and the terminal is the basis for the normal operation of the entirety of three satellite internet. The upstream and downstream data of the satellite network are transmitted through the link between the terminal and the satellite, and the quality of this link can easily become a bottleneck for information transmission [6]. There are multiple satellites within the visual range of the terminal, and in order to ensure reliable data transmission o, it becomes crucial to select the appropriate satellite for the terminal to establish a link to. The establishment of a stable satellite-ground link begins with the selection of the most suitable satellite according to selection criteria. In the current research on satellite-ground link switching selection, there are three basic criteria, namely service time, satellite elevation angle and the number of available satellite channels [7]. [PERSON] [8] optimized three aspects of link switching frequency, routing update frequency and relay satellite configuration, and proposed a link-planning algorithm with a minimum number of link switches; [PERSON] [6] proposed an access satellite-selection strategy from the aspects of data transmission traffic and balancing data transmission. Tish strategy uses the maximum sum of inter-satellite distance to reduce data blockage. [PERSON] [5] proposed a load-balanced satellite switching strategy based on the minimum switching frequency algorithm, considering satellite workload balancing, and optimizing the power allocation of satellites to improve system capacity. In addition to the above models for strategy selection, there are now computational methods using mathematical or graphical models that allow for the selection of a satellite's spatial position with respect to a particular criterion. [PERSON] proposed a graph-based satellite switching framework [9] that allows for the integration of existing satellite switching criteria and the selection of the most suitable satellite. [PERSON] [10] also used graphs to solve satellite selection and proposed a velocity-aware handover prediction model to perform dynamic satellite switching prediction, which solves the problem of both users and satellites changing in the multi-link state. [PERSON] [11] developed a model for calculating the geometric parameters of satellite links, including distance and pointing direction, and used mathematical models to theoretically derive the path change law of space links. The above studies optimized satellite switching from the perspective of rule models, mathematical models or graph models, respectively, to improve the efficiency of satellite utilization.