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Long-term vessel kinematics prediction exploiting mean-reverting processes

Long-term target state estimation of non-maneuvering targets, such as vessels under way in open sea, is crucial for maritime security. The dynamics of non-maneuvering targets is traditionally modeled with a white noise random process on the velocity, which is assumed to be nearly-constant. We show that this model might be an implausible hypothesis for a significant portion of maritime ship traffic, as vessels under way tend to adjust their speed continuously around a desired value. Additionally, vessels will naturally seek to optimize fuel consumption. We developed a method to predict long-term target states based on mean-reverting stochastic processes. Specifically, we use the Ornstein-Uhlenbeck (OU) process, leading to a revised target state equation and to a completely different time scaling law for the related uncertainty, which in the long term is shown to be orders of magnitude lower than nearly-constant velocity assumption. The proper modeling provides some improvement in accuracy; but the real benefit is improved track-stitching when there are lengthy gaps in observability. In support of the proposed model, we propose a large-scale analysis of a significant portion of the real-world maritime traffic in the Mediterranean Sea.