Bayesian Filtering for Dynamic Anomaly Detection and Tracking

This article presents a Bayesian approach for sequential detection of anomalies in the motion of a target and joint tracking. The anomaly is modeled as a binary (on/off) switching unknown control input that goes into action (begins to exist, or “switches on”) thereby modifying the object dynamics; and by ceasing its activity (becoming nonexistent, or “switching off”) returns the dynamics to nominal. The developed Bayesian framework brings together random finite set (RFS) theory to represent the switching nature of the anomaly, and optimal joint input and state estimation to sequentially update a hybrid state that incorporates a random vector for the kinematic state and a Bernoulli RFS for the unknown control input. In addition, a closed-form solution, the Gaussian-mixture hybrid Bernoulli filter (GM-HBF), has been developed to provide a customized solution for dynamic anomaly detection in the maritime domain characterized by linear Gaussian target dynamics. Based on the Ornstein–Uhlenbeck dynamic model for vessels, where the evolution of the object velocity is governed by a piecewise mean-reverting stochastic process, the anomaly can be represented by a change in the long-run mean velocity (i.e., the unknown control input) from the nominal condition that forces the vessel to deviate from its standard route. We demonstrate the effectiveness of the proposed GM-HBF in both simulated and real-world maritime surveillance applications and test its performance in the face of false measurements, detection uncertainty, and sensor data gaps.