Detecting Anomalous Deviations From Standard Maritime Routes Using the Ornstein–Uhlenbeck Process

A novel anomaly detection procedure based on the Ornstein–Uhlenbeck (OU) mean-reverting stochastic process is presented. The considered anomaly is a vessel that deviates from a planned route, changing its nominal velocity <inline-formula><tex-math notation="LaTeX">$\boldsymbol{v}_0$</tex-math></inline-formula>. In order to hide this behavior, the vessel switches off its automatic identification system (AIS) device for a time <inline-formula> <tex-math notation="LaTeX">$T$</tex-math></inline-formula> and then tries to revert to the previous nominal velocity <inline-formula><tex-math notation="LaTeX">$\boldsymbol{v}_0$</tex-math></inline-formula>. The decision that has to be made is declaring that a deviation either happened or not, relying only upon two consecutive AIS contacts. Furthermore, the extension to the scenario in which multiple contacts (e.g., radar) are available during the time period <inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is also considered. A proper statistical hypothesis testing procedure that builds on the changes in the OU process long-term velocity parameter <inline-formula><tex-math notation="LaTeX">$\boldsymbol{v}_0$</tex-math></inline-formula> of the vessel is the core of the proposed approach and enables the solution of the anomaly detection problem. Closed analytical forms are provided for the detection and false alarm probabilities of the hypothesis test.

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