## 3 Multi-Beam Fast Tracking and Satellite Capture Method
### A Multi-Beam Scheme for Antenna Non-Loss of Satellite  
The workflow of the optimal pointing analyzer is analyzed below. The optimal pointing analyzer has different workflows for two different states of the SOTM system when the carrier is in a high maneuvering moving state. The first scenario is when the carrier is in a high maneuvering moving state, but the antenna beam is still capable of tracking the communication satellite, albeit with a reduced communication quality. The other scenario is when the SOTM antenna fails to maintain track of the satellite due to the high maneuvering state of the carrier, resulting in communication interruption.  
For the first state of the SOTM system, as the communication has not been interrupted, the direction of the SOTM antenna beam is relatively close to the location of the satellite. Firstly, the array antenna is divided into four sub-beams, and the optimal pointing analyzer obtains the coordinate values of the four sub-beam pointing positions in the directional pattern for the four detection devices. As shown in Figure 10, the four beam-pointing positions in the figure are A, B, C, and D, with coordinates \((A_{a},E_{a})\), \((A_{b},E_{b})\), \((A_{c},E_{c})\), and \((A_{d},E_{d})\), respectively. Here, \(A_{x}\) represents the azimuth coordinate of beam \(X\) in the directional pattern, which is the azimuth angle of beam \(X\); \(E_{x}\) represents the elevation coordinate of beam \(X\) in the directional pattern, which is the elevation angle of beam \(X\). Point E is located at the center of beams A, B, C, and D in the directional diagram. As the pointing direction of the SOTM antenna is relatively close to the location of the satellite in the current SOTM state and the sub-beams are widened, the point corresponding to the satellite in the directional pattern will be within the range formed by connecting points A, B, C, and D. Additionally, point E will be relatively close to the point corresponding to the satellite in the directional pattern. Therefore, point E is used as the target pointing direction of the array antenna. The coordinates of point E can be easily obtained. When the error in obtaining the coordinates of points A, B, C, and D is not considered, the coordinates of point E are:  
\[\left\{\begin{aligned} & A_{e}=\frac{A_{c}+A_{d}}{E_{e}+E_{b}  
\[\left\{\begin{array}{l}A_{e}=\frac{A_{e}+A_{d}+A_{e}+A_{b}}{4}\\ E_{e}=\frac{E_{e}+E_{b}+E_{e}+E_{d}}{4}\end{array}\right., \tag{3}\]  
After obtaining point E's coordinate values in the directional pattern, the array antenna runs as a whole and uses single-beam alignment to obtain the increment of the azimuth and elevation angle values of point E relative to point C (or D) and point A (or B), respectively.  
Considering the time-consuming nature of the array antenna's electronic beam control, which operates at the millisecond level, the slight decrease in communication rate caused by the multi-beam searching process for antenna pointing can be disregarded due to its short duration. Therefore, in this multi-beam searching scheme for antenna pointing, the array antenna obtains multiple sub-beams through division and communicates as a whole, which can be regarded as parallel in macroscopic time and will not affect the normal operation of communication.