## 1 Introduction  
\"A country with strong transportation, parallel by land and water.\" As one of the comprehensive transportation modes, waterway transportation undertakes nearly 90% of the world's bulk trade freight volume. Due to its characteristics of low cost and large volume, the activity of the waterway transportation industry is regarded as a barometer of world and regional economic recovery. [1]. With the rapid development of China's shipping industry, the number of ships in the oceans, especially inland rivers, has increased dramatically, leading to an increasing trend of ship traffic accidents. Therefore, in ports or waters with high traffic density and complex conditions, improving the safety of ship navigation is a key issue [2, 3]. Vessel Traffic Service (VTS) [4, 5] can accurately and effectively monitor and predict the real-time trajectory of ships, which provides a technical support for the early warning of marine traffic accidents. In order to improve the safety of ship navigation in inland river environments, it is necessary to provide real-time trajectory prediction and risk warning functions for the ship's intelligent navigation system. However, the inland river environment is complex and changeable, and traffic accidents are prone to occur, especially in crowded docks and bridge areas. Consequently, it is difficult to predict the trajectory of ships [6]. In recent years, domestic and foreign scholars have proposed a series of ship trajectory prediction models. [PERSON] [7] takes time as the independent variable, obtains the measured value of the trajectory in discrete time, and regards the trajectory as a one-dimensional Gaussian process. A prior continuous time is defined by a nonlinear time-varying stochastic differential equation driven by white noise. By obtaining the joint prior density and covariance matrix of the observed and the predicted value, the posterior distribution of the predicted value is calculated, and the smoothing trajectory is predicted by combining with dynamics. This method is computationally intensive, and its accuracy gradually decreases over time. [PERSON] [8] proposed the polynomial Kalman filter method to fit the ship trajectory. This method implements trajectory prediction in a recursive manner, which occupies less memory space in the calculation process and can achieve short-term prediction. However, the assumptions of initial state and ideal conditions of the model have a greater impact on the prediction results. Literature [9] divides the specified sea area into grids, calculates the grid state with the ship's position, speed, and direction as the key factors, and uses the K-order Markov chain to establish a state transition matrix for prediction; however, the utilization rate of historical track information is poor when calculating the grid state at each moment. [PERSON] [10] proposed a spatial clustering method based on hierarchical density clustering, adopting the DBSCAN model to cluster and denoise the original AIS trajectories to achieve the purpose of predicting ship trajectories. [PERSON] [11] proposed a new probabilistic trajectory prediction model, which described the uncertainty of the future position of the ship trajectory through a continuous probability distribution and has high prediction accuracy. With the continuous in-depth research of artificial neural networks (ANN) [12; 13], the ship trajectory prediction model based on ANN is becoming more and more popular and is widely used in the field of ship navigation [14; 15; 16]. Literature [17] uses the backpropagation (BP) neural network model to train and predict ship trajectory with longitude, latitude, and speed information in the AIS data, but the BP neural network has a weak ability to deal with nonlinear problems, and only in the case of a short track are the prediction results more accurate.