# Research on Airspace Conflict Detection Method Based on Spherical Discrete Grid Representation
## 1 Introduction  
As the carrier of aviation activities, airspace is limited and non-renewable, which decides that only one aviation user can occupy one airspace at the same time and the same height, and in the same range. Therefore, with the rapid increase of air users in public transport aviation, general aviation, military aviation, and so on, frequent use of airspace leads to severe aviation safety and collision situations. How to use airspace safely and efficiently on a large scale has become a major problem for air traffic control departments. For the study of the airspace CD problem, the traditional solution is to perform cross-operations on the longitude and latitude ranges of airspace to determine whether there is a conflict. This method is complex, computationally intensive, and time-consuming, and is only applicable to the detection of small-scale airspace conflicts. Moreover, the longitude and latitude grids have large deformation in high latitudes and cannot accurately characterize the airspace range. At the same time, the traditional solution cannot encode airspace data, and it is not convenient for information storage and management in the process of airspace control. In order to solve the above problems, [PERSON] [1] proposed the discrete global grid system (DGGS), which solves the problem that the grid becomes larger with the higher latitude. [PERSON] [2] uses a variety of projection methods to solve the problem of projecting regular icosahedron onto the Earth's surface. [PERSON] et al. [3] obtained that the evaluation index of a regular icosahedron is better than that of a regular octahedron according to the two standard evaluation indexes of grid distance and the \"grid wall midpoint\" criterion. [PERSON] et al. [4] establishes the corresponding relationship between plane and sphere on the basis of a regular icosahedron. [PERSON] et al. [5] proposed a spherical diamond discrete grid regular icosahedron dissection method, the resulting grid at different levels,angular deformation, and area deformation are kept to a minimum. [PERSON] et al. [6] studied the coding model and its mapping method based on a regular icosahedral spherical diamond discrete grid and realized the conversion method between grid coding and geographical coordinates. At present, with the development of spatial geographic grid research, there are more and more CD methods based on gridded airspace. [PERSON] [7] proposed a CD algorithm based on a four-dimensional spatial and temporal grid to represent aircraft trajectories in airspace, which determines whether there is a conflict by checking grid occupancy. [PERSON] et al. [8] proposed a CD algorithm based on spatial data structure by storing the trajectory information in a square grid space and using a conflict detection method based on correlated spatial data structure as well as a CD method based on spatio-temporal data structure to achieve fast CD; [PERSON] [9] proposed a new 4D airspace modeling method that combines traffic, weather, restricted areas and other objects in 4D airspace for CD and disambiguation. [PERSON] et al. [10] proposed a new multi-level grid spatio-temporal index for a new low-altitude flight CD algorithm; [PERSON] et al. [11] proposed a method to characterize the conflicting airspace based on the earth profile grid model and calculate the conflicting airspace using a multinomial tree structure; [PERSON] et al. [12] proposed a raster model-based airspace CD and deconfliction technique and established a numerical model of airspace conflict; [PERSON] et al. [13] established a deterministic CD and deconfliction module, used the R-tree algorithm with low time complexity to effectively reduce the number of comparisons between aircraft 4 DTs, and proposed a Monte Carlo tree search algorithm; [PERSON] et al. [14] proposed a method to determine the airspace conflict by using the GJK algorithm to transform the airspace grid (AG) set into a coordinate set and by judging the inclusion relationship between the Minkowski difference set and the coordinate origin.