# A Space-Interconnection Algorithm for Satellite Constellation Based on Spatial Grid Model
## 1 Introduction  
With the rapid development of satellite communication technology, satellite networks have become an important part of the next generation of global communication systems as an important supplement to the ground network [1; 2; 3]. Today, many countries consider the construction of satellite Internet as part of their national strategies [4; 5; 6]. China has clearly included satellite Internet in the category of \"new infrastructure\" and positioned it as a space-based communications network infrastructure that complements global high-speed coverage, blind spot coverage in urban hotspots, outdoor applications, and high-mobility applications. Commercial institutions, governments, and themilitary around the world have a strong demand for low-orbit satellite constellations. A series of plans with broad market prospects have therefore been developed. The plans are mainly based on low-orbit micro-satellite constellations, with great advantages in terms of functional density, development cost, launch difficulty, etc. [7; 8; 9]. These constellations can effectively solve the practical problem of networking in remote areas, such as oceans and deserts, and they have irreplaceable advantages in emergency communications, disaster warnings, and maritime rescue [10]. However, satellite networking includes not only communication satellites, but also navigation and remote sensing satellites (Table 1). The United States, the European Union, Russia, and China have already launched the positioning, navigation, and timing (PNT) satellite constellation systems, and established low-orbit satellite constellations such as SpaceX and OneWeb [6; 9]. The existing PNT system needs to be improved in the areas of real-time observation of satellites, interconnection with communications, and navigation satellites. Considering the above issues and promoting the further integration of remote sensing satellites and PNT systems, the concept of PNTRC (positioning, navigation, timing, remote sensing, and communication) has been proposed [11]. The PNTRC is a real-time service system for space-based information, integrating communication, navigation, and remote sensing, and its primary goal is the interconnection of various space platforms. The increasing number of satellites in a constellation will cause the complexity of algorithms to increase geometrically. Therefore, it is of great significance, both theoretically and for the development of applications, to study the most efficient method of inter-connecting heterogeneous satellite constellations. In the process of satellite constellation networking, the first step is to determine whether the satellites are visible before establishing a network link between the satellites. Traditional analysis algorithms are based on research on satellites that meet the visibility conditions in a short time and under accuracy constraints [13; 14]. This requires multiple floating-point operations involving the orbital parameters in order to solve the orbital equations, which is inefficient and requires computing resources [4; 11]. Therefore, researchers have conducted several studies on how to improve the efficiency of the inter-satellite visibility analysis algorithm. In addition, most algorithms are optimized for specific constellations, lacking a general optimization algorithm [15; 16]. Discussion on visibility analysis has also taken place within the industry. The most widely used analysis method is the System Tool Kit (STK, of Analytical Graphics Inc.) software. The STK simulates data transmission between two objects, supports calculation based on access between satellites, can dynamically display the visibility between satellites in a map window, and can generate a visibility report [17]. After calculating whether the satellites are in sight, communication and data transmission between the visible satellites is one of the most important ways for the ground observation station and users to obtain target observation data that are outside of their receiving range.