## 1 Introduction  
Satcom-on-the-Move (SOTM) refers to the installation of satellite signal antennas on moving carriers, which can control the direction of the antenna to align with the communication satellite in real-time during the movement of the SOTM carrier, thus achieving a stable transmission link between the satellite and SOTM [1, 2, 3, 4]. With the development of technology, satellite communication is becoming increasingly widespread [5, 6, 7, 8]. Currently, the application of array antennas in SOTM systems is a very important development direction [9, 10, 11]. Array antennas in SOTM systems are generally used on moving carriers with high height restrictions, including civilian vehicles, unmanned aerial vehicles (UAV), commercial aircraft, etc. [12, 13, 14, 15]. Multi-beam array antennas have achieved significant research results in radar and conventional satellite communication fields [16, 17], but their application in SOTM is still in the early stages, and there is currently limited research in this area. The current systems that use array antennas generally employ a combination of electronic beam steering and mechanical tracking control methods [18]. [PERSON]. [19] designed a stepper motor servo control system based on the analysis of the SOTM servo control system and proposed a speed-position dual-closed-loop PID controller with disturbance compensation. In Ref. [20], a modeling method for a three-axis SOTM antenna based on a novel modified Denavit-Hartenberg method was investigated, which addresses the gimbal lock issue by adding a roll axis in addition to the conventional azimuth and elevation axes. [PERSON]. [21] designed an Active Disturbance Rejection Controller based on particle swarm optimization to overcome the issues of response speed and accuracy for the SOTM antenna servo control system. Ref. [22] designed a Ku-band SOTM structure that included multiple distributed panels capable of mechanical oscillation and presented a new pseudo-monopulse tracking method. The SOTM systems utilize Global Navigation Satellite Systems (GNSS), compasses, and inertial navigation systems to measure the position and attitude of the carrier, automatically adjusting the azimuth angle and elevation angle of the antenna beam to align with the target communication satellite. The application of the SOTM systems is becoming increasingly widespread [23; 24], and their operating conditions are becoming more complex, as they are unknown and dynamically changing [25]. Due to the carrier's motion, its location and attitude are constantly changing [26], and current methods can meet the satellite tracking requirements of array carriers in general motion states. However, when the carrier's attitude changes beyond certain conditions, from reference [27], this condition is generally described as angular velocity \(\omega>30^{\circ}/\mathrm{s}\), or angular acceleration \(\alpha>40^{\circ}/\mathrm{s}^{2}\), conventional methods may cause a decline in the communication effectiveness of the SOTM system and even cause the antenna to lose the tracking of the satellite and interrupt the communication. After the antenna loses the communication satellite, reacquisition relies on the antenna beam scanning and mechanical tracking system azimuth and elevation axis movements, which increases the time it takes to reacquire the satellite. Currently, research on the high maneuverability of carriers mainly focuses on the estimation of carrier attitude and location [28; 29; 30; 31; 32; 33], and research on array antenna tracking satellites under a high maneuvering state is limited. The contributions of this paper are as follows: Uninterrupted satellite communication is essential in various applications, such as military and emergency communication. To maintain the high communication quality of SOTM systems while the carrier is in a high maneuvering state of motion, we propose a fast multiple-beam reacquisition scheme for array antennas.