## 1 Introduction  
AUVs are capable of autonomously navigating in underwater environments without real-time human intervention, and they are typically equipped with a suite of advanced sensors and navigation systems to ensure accurate positioning and navigation. Traditional underwater vehicles are powered by cables, limiting their flexibility, while AUVs typically cruise using their own batteries. AUVs were initially designed and developed to autonomously and independently perform tasks such as environmental sensing, localization, and analysis in complex environments [1]. However, due to the complexity of the underwater environment, which is very different from that predicted on land, underwater environments often have a high degree of uncertainty and dynamic changes [2], and thus, the sensors of AUVs can be affected, resulting in errors between the data they transmit and the true localization. Considering the limited energy of AUVs, as well as the influence of water quality and light on visual sensors [3], resulting in deviations in visual navigation, accurately determining the trajectory of AUVs and predicting their short-term trajectory is of paramount importance. Through trajectory tracking and short-term prediction of AUVs, their movements can be promptly monitored, enabling the timely avoidance of obstacles, salvage operations in case of wrecks, and other necessary measures. Numerous researchers and scholars currently use the construction of kinetic models to track the trajectory of AUVs [4]. However, the development of such kinetic models is subject to several limitations. In addition to considering the impact of natural factors, it is essential to account for the influence of the AUV's intrinsic characteristics, such as its shape and configuration. Furthermore, distinct kinetic models must be constructed for different AUV models [5; 6; 7]. [PERSON] et al. [8] proposed a novel Computational Fluid Dynamics (CFD) simulation technique that integrates static and dynamic grids. This approach is utilized to simulate the hydrodynamic coefficients of a quadrotor underwater vehicle, model the underwater vehicle's motion and propeller behavior, and replicate both uniform and variable speed movements of the quadrotor underwater vehicle. [PERSON] et al. [9] developed dynamical equations for the quadrotor by integrating an analytical semi-empirical estimation method, which relies on the hydrodynamic and geometrical characteristics of the underwater vehicle, with a parametric trajectory method based on extended Kalman filtering. This approach aims to accurately replicate the operational state of an underwater vehicle. [PERSON] and [PERSON] [10] utilized computational hydrodynamics to analyze trawler operations. [PERSON] [11] employed a novel node positioning method to model and analyze a cable-towed body, aiming to eliminate numerical errors associated with the nonlinear finite element method. The target object is represented as a rigid body with six degrees of freedom, thereby enhancing the directional stability of the cable-towed body. Additionally, [PERSON] [12] introduced a simulation framework to model underwater scenarios for AUVs. [PERSON] [13] designed an AUV path tracking system to address the nonlinear path tracking problem. [PERSON] [14] formulated tracking equations using the Hamiltonian-Jacobi-Isaacs method to achieve both tracking and control of AUVs. [PERSON] [15] proposed a nonlinear adaptive controller to investigate the path tracking problem of underdriven autonomous underwater vehicles (AUVs) in the presence of constant unknown currents and uncertain parameter models. Additionally, numerous researchers and scholars have treated the motion of AUVs as rigid body motion in order to establish dynamic equations for tracking and prediction [16; 17; 18]. Although kinetic equations have yielded some results in the tracking and localization prediction of AUVs, it is necessary to establish different kinetic equations for different vehicle models.