# Research on Offshore Vessel Trajectory Prediction Based on PSO-CNN-RGRU-Attention
## 1 Introduction  
With the rapid rise of the offshore economy and the widespread application of the Automatic Identification System (AIS) in offshore areas, the offshore shipping industry has become an indispensable link in increased trade activities and regional economies, significantly promoting economic prosperity in offshore regions. The increasing number of vessels due to growing or unintentional trade has led to a sharp rise in navigation risks. Therefore, to enhance navigational safety, [PERSON] et al. [1] focused on the development of intelligent collision avoidance technologies for vessels. The prerequisite for achieving this goal is a deep understanding of vessel movement trajectories. As a result, many scholars have shifted their research focus to the field of vessel trajectory prediction, aiming to accurately predict the future paths of vessels through scientific methods and models, thereby effectively avoiding collision risks. Scholars from around the world have explored and proposed diverse vessel trajectory prediction methods based on traditional prediction algorithms. Specifically, an approach has innovatively combined the Grey Prediction Method with the Hidden Markov Model [2]. It first utilizes the Grey Prediction Method to fit the original vessel trajectory and weakens the randomness and time variability in the trajectory by calculating the absolute ratiosequence. Subsequently, the Hidden Markov Model is introduced for more accurate trajectory predictions. In contrast, [PERSON] et al. [3] designed a Bayesian prediction model based on a particle filter, grounded in traffic route knowledge. This model has demonstrated excellent performance in experiments conducted in specific strait areas. However, the application scope of this model has certain limitations; it is primarily suitable for inland waterways or fixed channel environments and may perform poorly under the complex navigation conditions of open waters. To address the limitations of traditional prediction methods in handling nonlinear vessel trajectories--such as poor performance, large output fluctuations, and a lack of self-learning, organization, and adaptability--vessel trajectory prediction technologies based on deep learning models have gradually become a research hotspot. Researchers have innovatively combined the unique trajectory features of vessels with time series data and applied neural networks in deep learning, especially the Long Short-Term Memory (LSTM) [4; 5; 6; 7] model, to predict the operating trajectories of vessels. The Gated Recurrent Unit (GRU) [8] model has been applied to vessel trajectory prediction. Compared with the LSTM model, the GRU model can quickly learn and process data without significantly sacrificing prediction accuracy, thus improving the training speed. This approach has significantly enhanced prediction accuracy. However, in some complex scenarios, a single model still faces the challenge of insufficient prediction accuracy. Bidirectional Long Short-Term Memory (Bi-LSTM) [9] and Bidirectional Gated Recurrent Unit (Bi-GRU) [10] neural networks have been respectively introduced into the field of vessel trajectory prediction. This innovative initiative has significantly enhanced the performance of prediction models. Through a bidirectional design, these two models can simultaneously capture features in time series data from both past and future directions, thereby achieving a more comprehensive understanding of the complex relationships between data points. Composite neural network models such as CNN-GRU [11], MP-LSTM [12], TCN-Bi-LSTM [13], and RNN-Bi-LSTM [14] have been proposed and applied in the field of vessel trajectory prediction. Compared to single neural networks, these composite models exhibit significant advantages in learning capability. By integrating the characteristics of different neural network architectures, they achieve a deeper and more comprehensive understanding and modelling of vessel trajectory data.