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Stochastic motion model for maritime traffic.  Millefiori, Leonardo; Braca, Paolo; Pallotta, Giuliana ; Bryan, Karna. CMRE-FR-2015-008. Juney 2015.

Driven by real-world issues in maritime surveillance, we consider the problem of long-term prediction for estimating the state of a non-manoeuvring target, such as the case of a vessel underway in open sea. Traditionally, target dynamic models assume a white noise process on the target velocity, which is otherwise nearly-constant. Such a process model is an implausible hypothesis for a significant portion of the maritime ship traffic, as vessels underway tend to continuously adjust their velocity around a desired speed. Also vessels are obliged to observe traffic regulations in some areas and will seek to optimise fuel consumption. Using historical ship traffic data, we have found that the nearly-constant velocity model with white noise tends to overestimate the actual uncertainty of the prediction. In this work we present a novel method for predicting long-term target states based on mean-reverting stochastic processes. We used the Ornstein-Uhlenbeck stochastic process, leading to a revised target state prediction equation and to a completely different time scaling law for the related uncertainty, which is shown to be orders of magnitude below than under the nearly-constant velocity assumption. To support the proposed model, a large-scale analysis of a significant portion of the real-world maritime traffic in the Mediterranean Sea is presented in this paper. As modelling long-term prediction is not a commonly addressed problem in the target tracking literature, it is possible that this approach could offer a new methodology also for other moving target applications.