Interval prediction of vessel trajectory based on lower and upper bound estimation and attention-modified LSTM with bayesian optimization

Uncertainty prediction of vessel trajectory is essential to enhance maritime situational awareness and traffic safety. Traditional approaches for trajectory prediction face challenges in accurately quantifying uncertainties, thereby limiting effectiveness in decision-making. To address this challenge, we propose a hybrid interval prediction frame of vessel trajectory using the lower and upper bound estimation (LUBE) and attention-modified long short-term memory (LSTM) network with bayesian optimization (BO). Firstly, trajectory data is preprocessed to solve the scale irregularity. Then, a novel trajectory interval prediction model for perceiving the prediction uncertainties is designed based on an advanced attention-modified LSTM with interval prediction capability. Meanwhile, a supervised training strategy with differentiating the interval widths of latitude and longitude is put forward to devise sample labels for training the model. Additionally, a new prediction interval-based objective function is proposed considering the target of maximizing coverage and minimizing width of trajectory interval. The BO algorithm optimizes the weighted parameters in the LSTM network by minimizing the objective function value. Finally, cases from two water areas are implemented to test and verify the proposed method. The results illustrate the superiority of the proposed approach in (1) outperforming other methods used for comparison in both coverage probability and width criteria of prediction interval. (2) quantifying the prediction uncertainty and improving the reliability of trajectory predictor. (3) performing anomaly detection tasks using visualized trajectory prediction intervals. The research can help maritime traffic participants obtain more reliable trajectory data, which supports making more reasonable traffic supervision decisions.