Long-Term Vessel Trajectory Imputation with Physics-Guided Diffusion Probabilistic Model

Maritime traffic management increasingly relies on vessel position information provided by terrestrial and satellite networks of the Automatic Identification System (AIS). Unfortunately, the problem of missing AIS data can lead to long-term gaps in vessel trajectory, raising corresponding security concerns regarding collision risks and illicit activities. Existing imputation approaches are often constrained by vehicle-based low-sampling trajectories, hindering their ability to address unique characteristics of maritime transportation systems and long-term missing scenarios. To tackle these challenges, we propose a novel generative framework for long-term vessel trajectory imputation. Our framework considers irregular tracks of vessels, which differ from those of cars due to the absence of a structured road network, and ensures the continuity of multi-point imputed trajectories. Specifically, we first utilize a pre-trained trajectory embedding block to capture patterns of vessel movements. Subsequently, we introduce a diffusion-based model for generating missing trajectories, where observed trajectory modeling with transformer encoding architecture and embeddings of both historical vessel trajectory and external factors serve as conditional information. In particular, we design a physics-guided discriminator in the training stage, which imposes kinematic constraints between locations and angles to improve the continuity of the imputed trajectories. Comprehensive experiments and analysis on a real-world AIS dataset confirm the effectiveness of our proposed approach.