# Clustering Method of Large-Scale Battlefield Airspace Based on Multi A * in Airspace Grid System
## 4 Airspace Clustering Steps Based on Multi-A \({}^{*}\) Algorithm
### Airspace Projection Image Preprocessing
#### 4.2.3 Grid Representation of Projected Image
The code is composed of four types of elements: the code of the Northern and Southern Hemisphere, the Gauss Kruger projection zone code (hereinafter referred to as the projection zone code), the 100 km grid code, and the coordinate grid code. The coding rules are southern and northern hemisphere codes, and 1-digit alphabetic codes are adopted. The southern hemisphere is represented by \"S\" and the northern hemisphere is represented by \"N\". The projection band code is represented by a 3-digit code. When 6\({}^{\circ}\) zones are divided, 60 zones in the world. Use 0 to make up 3 digits before the projection zone number. The projection zone number codes are 001 to 060 respectively; When 3\({}^{\circ}\) zones are divided, there are 120 zones in the world. The projection zone number is increased by 100, and the projection zone number codes are 101 to 220 respectively. The 100 km grid code adopts the mixed coding of 1 character and 2 digits. When 6\({}^{\circ}\) zone is adopted, it is represented by one character (A-H) every hundred kilometers from west to east. When a 3\({}^{\circ}\) zone is adopted, it is represented by one character (C-F) every hundred kilometers from west to east. From south to north, every hundred kilometers is represented by two digits (00-90). To illustrate the coding method, if a point is located in (39\({}^{\circ}\)55\({}^{\prime}\)14\({}^{\prime\prime}\) N, 116\({}^{\circ}\)30\({}^{\prime}\)25\({}^{\prime\prime}\) E), its 6\({}^{\circ}\) band projection band number is 20, its ordinate value is 4420.4 km, and its abscissa value is 457.3 km, then its rectangular grid codes are as shown in the Table 1.  
Figure 8: Gauss Kruger projection zoning diagram. The 300 km \(\times\) 300 km battlefield airspace set in Section 4.2.1 belongs to a small range of airspace objects, so the whole battlefield airspace and task airspace can be characterized by local rectangular coordinate grid. In this section, a small range of battlefield airspace coding rules is designed (as shown in the Figure 8), which is from west to east. Every 50 km is set as a mission belt, which is represented by one character (A-G). Each mission zone is further divided into five action areas, which are represented by a digit from west to east (0-4). From south to north, each kilometer is represented by 3 digits (000-299). The schematic diagram of battlefield airspace planning results is shown in the Figure 9. In the schematic diagram, the square airspace is marked in blue, and the circular airspace is marked in red. Different kinds of airspace are distinguished by different colors. Using the battlefield airspace coding rules, the geographic locations of 15 airspace are coded. When representing the position of the task airspace, this paper uses the grid coordinates of the central position of the task airspace, and it assists in characterizing the airspace with airspace parameters. Then, the characteristics parameters of the task airspace are characterized as shown in the Table 2.