Multiple Variational Kalman-GRU for Ship Trajectory Prediction with Uncertainty

Accurate prediction of ship trajectories is crucial for ensuring safe and efficient navigation. However, predicting ship trajectories in complex and dynamic environments presents significant challenges. Ships exhibit multimode motions, manifesting as diverse motion patterns even under similar circumstances, influenced by factors such as navigational intentions and operational tasks. Moreover, trajectory prediction is further complicated by time-varying ship dynamics, encompassing sailing conditions, ship maneuvering, and environmental factors. In this article, we propose a Bayesian multiple model with an online model selection strategy to dynamically represent the latent motion mode from early observations. Each submodel integrates a variational Kalman filter and gated recurrent unit (GRU) neural network, enabling the estimation of time-varying transition coefficients and the process noise specific to different motion modalities. This hybrid methodology leverages the strengths of probabilistic recursive estimation of the Kalman filter while benefiting from the capacity of a GRU network to learn complex temporal dependencies from historical data. The proposed method was evaluated on ship trajectories across different observation lengths and prediction horizons and outperformed the baseline in terms of both accuracy and plausibility.