# Clustering Method of Large-Scale Battlefield Airspace Based on Multi A * in Airspace Grid System
## 3 Introduction to Theoretical Basis  
In recent years, with the growing maturity of the geographical grid, more and more experts and scholars at home and abroad have integrated the airspace characteristics of the airspace with the geographical grid, designed a multi style airspace grid system and explored the airspace management based on the airspace grid system. In terms of airspace planning and representation, in 2021, [PERSON] [45] summarized the airspace gridding methods of plane grid model and airspace grid model [46], and summarized the research on airspace gridding application of airspace gridding methods. On this basis, he comprehensively analyzed the research focus and development trend of airspace gridding and digitization [47]. However, none of the three papers have specifically explained the application of airspace conflict detection and resolution under the airspace grid system. Inspired by [PERSON]'s use of grid system to describe two-dimensional sectors, [PERSON] [48] characterized three-dimensional airspace with a stack combination of element grids of fixed size and specific height range, which broke away from the limitation of traditional airspace sector boundaries and was more simple and efficient in airspace characterization. [PERSON] [49] and his team expanded the time dimension of global discrete airspace grid technology, established a global unified spatio-temporal grid model, and verified the scientificity and feasibility of establishing airspace management system based on this model. [PERSON] [50] and others proposed an airspace grid modeling algorithm based on the GeoSOT [51; 52; 53; 54] global subdivision model to solve the problem that the current airspace modeling method is relatively rough and the degree of refinement of the internal modeling of the airspace is low. The four neighbor and six neighbor grid models are used to completely express the interior and boundary of the airspace. [PERSON] [55] and his team proposed a three-dimensional grid model for refined analysis of airspace resources based on the Beidou grid location code, designed the calculation method of three-dimensional airspace grid model and explored the application scenario, which made it possible for refined management of airspace. [PERSON] [29] proposed an airspace grid representation method based on GeoSOT grid, which provides a new technical means and practical ideas for airspace representation. [PERSON] [56] established a refined management system of airspace resources based on the Beidou grid location code, studied the calculation and analysis methods of the spatio-temporal grid model, and the application methods of airspace resource gridding, providing possibilities for the refined management of airspace resources and the optimal allocation of resources. An airspace sector division refers to dividing a whole airspace into multiple airspace sectors according to the flow relationship and mission characteristics. In the area of airspace sector division, experts and scholars in the field of civil aviation have made a lot of efforts. At present, there are three common methods to divide the airspace sector. One is to use geometric division method to divide the whole area according to the distribution characteristics of air traffic flow with the main airport or main navigation facilities (such as VOR/DME) as the center, which is also called the horizontal quadrant division method. The second is to select the altitude definition value in the area according to the ascending, descending and overflying altitude, and determine the altitude range of airspace sector near the value. The last method is to comprehensively divide sectors according to the busy degree of routes, routes, use properties, and flight characteristics. The plane geometry quadrant division method is mainly based on geometric analysis tools such as Voronoi diagram [57; 58], hexagon grid [59], and tyson polygon, and it is combined with some constraints [60] and algorithms [61] to divide the sector.