## 1 Introduction  
With the rapid development of economic globalization, shipping has become the main form of international trade. As an important means of transportation at sea, ships have made tremendous contributions to economic development and social progress. The large-scale and diversified development of ships has also brought great security risks to maritime navigation. According to statistics from relevant departments [1], in recent years, more than 200 ships have been involved in shipwcks at sea each year and more than half of the losses were caused by collisions. Investigation [1] of these marine collision accidents has found that the actual situations encountered during maritime navigation are often highly complicated. Especially in multi-ship collision avoidance, the ambiguity of a target ship's intentions and inability to make real-time and effective collision avoidance decisions are two of the largest factors contributing to the frequent occurrence of collision accidents at sea. Considering these factors, collision avoidance decisions cannot be based only on the current navigational information but should instead be integrated into the target ship's future navigational behavior for a certain period of time. This allows for collision avoidance decisions to be made ahead of time to some extent, which effectively improves the reliability of the decisions and reduces the collision risk. Therefore, a ship trajectory prediction model with high precision and real-time prediction capability is an urgent necessity.  
Current trajectory prediction methods usually adopt the traditional Markov model [2; 3; 4; 5], particle filter algorithm [6; 7], simulated annealing algorithm [8] and Kalman filter algorithm [9]. These methods often have the following shortcomings: First, the ship kinematic equations must be established and consideration of hydrological environmental factors such as wind and current greatly increases the modeling complexity and difficulty; Second, according to the needs of marine collision avoidance decision-making, trajectory prediction must often occur in real time. It is often difficult to establish real-time and accurate mathematical models, as many are only suitable for ideal research. In contrast to traditional modeling methods, with the rapid rise of the artificial intelligence era, more machine learning algorithms are being gradually applied to trajectory prediction, among which back propagation (BP) neural networks are common [10; 11]. However, these algorithms fall easily into local optima and a problem often arises where the amount of data is too small for accurate BP neural network training [12]. As a result, the accuracy is insufficient for real-time data training and modeling at sea.  
Considering these limitations, a vessel trajectory prediction model based on adaptive chaos differential evolution algorithm [13] support vector regression (ACDE-SVR) is proposed herein. The SVR model ensures high prediction accuracy despite the limited samples; this solve the problem of insufficient accuracy of models such as neural network by the real-time acquisition of AIS data for track prediction at sea. The prediction accuracy of the support vector regression (SVR) is closely related to the selection of parameters in the model. To further improve the prediction accuracy, the heuristic algorithm is used to optimize the parameters of the SVR model. The improved differential evolution (DE) algorithm-ACDE algorithm is used for parameter optimization. The speed, course, ship position and Unix time from AIS information are used as model sample characteristics and a multi-dimensional trajectory time series during maritime navigation is successfully predicted. The results provide a better understanding of ship dynamics and contribute to improved determination of collision avoidance decisions.