## 1 Introduction  
Maritime trade is the most important form of international trade, and according to the 2019 Global Maritime Transport Development Report published by the United Nations Conference on Trade and Development (UNCTAD), maritime trade carries more than 80% of the world's trade volume [1]. The increasing demand for waterway transportation and the growing traffic pressure in complex areas such as coasts and harbors increase the risk of traffic accidents such as ship collisions [2; 3; 4]. In 2021, there were 126 traffic accidents involving transport vessels in China, resulting in 150 deaths, 46 sunk vessels, and direct economic losses of RMB 226 million. The accident investigation reports show that more than 80% of marine accidents were caused by human factors, and 70% of these collisions were caused by the negligence of the lookout personnel [5]. The Internet of Things (IoT) has played a significant role in the transportation domain [6]. At present, ship collision avoidance mainly uses ARPA radar and Ship Automatic Identification System (AIS) and other equipment as auxiliary; the analysis of the navigational situation and the formulation of collision avoidance decisions depend on the experience of the crew [7]. Due to crew fatigue and the lack of experience of junior crew members, relying only on a manual to make decisions often affects navigational safety. Therefore, the development of intelligent navigation of ships and unmanned ships is an inevitable trend. Ship trajectory prediction is an important method for the intelligent perception of ships. In the process of navigation, ships inevitably interact with other ships in the surrounding area. In this increasingly complex navigation environment, ship trajectory prediction can provide information and reference for ship avoidance decisions, which is a key skill to improve ship perception and ensure ship safety. Therefore, improving the accuracy of ship trajectory prediction is of great significance for ship collision avoidance, intelligent navigation, and collision crisis warning [8; 9; 10; 11; 12; 13; 14; 15]. A lot of research has been conducted by scholars, and the methods of modeling and predicting ship trajectories can be broadly divided into methods based on traditional models and methods based on neural network models. The ship trajectory prediction problem is a nonlinear problem, and for the nonlinear problem, a finite element scheme is a good tool [16]. At the early stage of trajectory prediction research, most scholars used the prediction of ship trajectories based on the construction of physical motion models, including curve models [13], lateral models [17], and ship models [3]. The physical model describes the ship operation model by analyzing the problem and establishing a series of mathematical formulas, taking into account the influence of various factors during ship navigation as much as possible. [PERSON] et al. [18] used the adaptive bandwidth kernel density estimation method to statistically analyze the historical motion patterns and then used the filter to estimate the ship motion state and achieved good prediction results. The Kalman filter method [19] is able to estimate the future position of a ship's trajectory based on a series of data in the presence of noise when the measurement variance is known, using the dynamic data of the predicted target. [PERSON] et al. [20] improved the systematic noise variance in the Kalman filter so that it changes dynamically with the motion state of the ship to improve the prediction accuracy of the ship's trajectory. Although this type of prediction method can obtain ideal prediction results, it requires the target motion trajectory to satisfy a certain distribution and is more suitable for ideal state trajectory prediction research.