# A Ship Trajectory Prediction Method Based on an Optuna-BILSTM Model
## 1 Introduction  
With the proliferation of maritime information-sensor applications, the shipping industry is entering the era of Shipping 4.0, which is characterized by digital transformation and the integration of advanced technologies [1]. Maritime transport accounts for more than 80 per cent of the world's trade in goods, and increased demand has led to an increase in the number of shipping accidents, putting maritime safety in the spotlight. Vessel traffic safety systems (VTSs) provide important technical support by monitoring and predicting ship trajectories. In order to improve maritime safety, intelligent ship navigation systems need to provide real-time trajectory prediction and have risk-warning capabilities [2; 3]. Existing vessel traffic safety systems face challenges in accurately predicting ship trajectories due to complex environmental conditions and computational limitations. Low accuracy and efficiency hinder the timely warning of collision or grounding risks, and further research is needed to improve prediction techniques. In recent years, more and more trajectory prediction algorithms have been proposed. [PERSON] developed a ship trajectory prediction model utilizing a simplified mathematical framework designed to accommodate varying maritime traffic conditions [4]. This model incorporates the extended Kalman filter technique for online identification and adjusts the model's parameters to enhance predictive accuracy. Scholars such as [PERSON] used a variety of Kalman filters (KFs) to identify the kinematic model of the target [5], and the obtained identification results were weighted and averaged to obtain the predicted trajectory of the target. The linear model in the mathematical model is a relatively simple recursive method; the trajectory prediction is based on the current position of the ship to calculate the future position of the ship, and the information of the ship's sailing speed and heading is assumed to be constant before the prediction [6; 7; 8; 9]. [PERSON] introduced a ship trajectory prediction methodology employing a Kalman-filter-based trajectory fitting approach, which is characterized by a step-by-step recursive computation that requiresminimal computer memory. This method is capable of facilitating short-term predictions. However, the accuracy of the model's predictions is significantly influenced by the initial state of the prediction model and the presupposed ideal conditions [10]. [PERSON] conceptualizes the position of a navigating vessel within the framework of a Gaussian distribution and employs Gaussian process modeling to forecast the vessel's trajectory [11]. This approach is suited to scenarios where the vessel's navigational state remains relatively stable. However, during maritime navigation, a ship's dynamics is frequently influenced by various environmental excitations specific to different geographical regions. [PERSON] et al. conducted an analysis and exploration of a data-driven technique for predicting ship trajectories utilizing AIS data. They proposed a single-point neighborhood search algorithm for this purpose, which forecasts the subsequent trajectory point by examining the vessel's historical trajectories [12]. Trajectory prediction has been extensively investigated across a wide array of disciplines [13; 14]. [PERSON] and [PERSON] used likelihood measures to identify maneuvers by finding the best fit from a Gaussian regression model. They used particle filters rather than the extended Kalman filter, which is more suitable for intersections, to predict future trajectories [15]. [PERSON] et al. used historical aircraft flight trajectories to model the three main motion trends--speed, yaw, and pitch--using hidden Markov models to plan the full trajectory of the aircraft with high accuracy [16]. [PERSON] et al. proposed the use of data mining to find out the factors that affect flight time and to analyze the position of the aircraft at any time based on the predicted total flight time [17].