## 1 Introduction  
The assessment of seabed topography plays a pivotal role in supporting safe navigation and marine resource development [1]. In this regard, side-scan sonar (SSS) is recognized as a crucial tool for examining underwater terrains and, hence, has found extensive application in tasks such as cartography, surveying, and search operations. Notably, its underwater exploration capabilities have a significant role in detecting diverse seafloor objects. As a notable advancement in underwater vehicle technology, autonomous underwater vehicles (AUVs) have evolved into versatile underwater platforms with extensive applications in scientific research and military operations [2]. AUVs possess the capability to navigate significant depths underwater, providing flexible yet precise attitude control. Equipped with side-scan sonar systems, AUVs effectively minimize the distance between these systems and the seabed, consequently enhancing the resolution and clarity of geomorphological surveys. Furthermore, AUVs are distinguished by their extended operational ranges and high levels of autonomy, making them exceptionally well-suited for missions in remote and vulnerable marine environments. This underscores the substantial potential for AUVs equipped with side-scan sonar technology, transcending various applications, including underwater topographic mapping, seafloor object retrieval, deep-sea resource exploration, underwater patrolling and surveillance, and beyond [3, 4, 5]. The use of an AUV equipped with side-scan sonar allows for maximum utilization of the high-resolution capabilities of side-scan sonar. The AUV's large underwater depth enables the side-scan sonar to effectively reach a height of approximately 10 m from the seabed, ensuring high data resolution. Additionally, the AUV's flexible posture enhances operational efficiency and reduces time, while maintaining stable positioning and ensuring consistent resolution and clarity. The AUV's long range capabilities enable remote deployment and covert measurements, making it suitable for detecting landforms in sensitive sea areas. Furthermore, the AUV's strong autonomy minimizes the need for human resources. The use of an AUV equipped with side-scan sonar to approach the seabed also reduces the impact of reverberation, noise interference, and uneven underwater conditions, resulting in improved quality of the original acoustic image. Moreover, the side-scan sonar is directly embedded into the AUV device, eliminating the need for positioning cables and simplifying the calculation of positioning information. Various scholars from different countries have conducted experiments and research on the application of AUVs. For example, in 2012, the Japan Marine Technology and Engineering Center investigated ocean carbon dioxide using the \"Jinbei\" AUV equipped with side-scan sonar and a multi-beam system, obtaining corresponding experimental data [6]. Scholars such as [PERSON] and [PERSON] have studied AUV path and trajectory planning under different conditions [7; 8; 9; 10; 11]. Chinese scholars have researched the multi-beam DVL time-sharing strategy model and proposed a wide-narrow alternating operation method [12]. In 2006, the National Institute of Subsea Science and Technology of the United States conducted mission system testing on the \"Eagle ray\" AUV carrying multiple beams and performed multi-beam terrain measurement experiments [13]. The Helmholtz Research Center in Germany employed the AUV Abyss equipped with multiple beams to conduct lawn power pattern scanning in the sea area and processed the multi-beam data using MB system software and Python programs [14]. The focus of the aforementioned research experiments primarily revolved around debugging the carrier task control system [15], improving AUV positioning [16], planning the path of pure AUV equipment itself [17; 18; 19; 20; 21], and integrating AUVs with various loads and conducting experiments in different sea areas [13; 14].