Anomaly Detection and Tracking Based on Mean–Reverting Processes with Unknown Parameters

Piecewise mean-reverting stochastic processes have been recently proposed and validated as an effective model for long-term object prediction. In this paper, we exploit the Ornstein-Uhlenbeck (OU) dynamic model to represent an anomaly as any deviation of the long-run mean velocity from the nominal condition. This amounts to modeling the anomaly as an unknown switching control input that can affect the dynamics of the object. Under this model, the problem of joint anomaly detection and tracking can be addressed within the Bayesian random set framework by means of a hybrid Bernoulli filter (HBF) that sequentially estimates a Bernoulli random set (empty under nominal behavior) for the unknown long-run mean velocity, and a random vector for the kinematic state of the object. An additional challenge is represented by the fact that two extra parameters, i.e. the reversion rate and the noise covariance of the underlying OU process, need to be specified for Bayes-optimal prediction. We propose a multiple-model adaptive filter (MMA-HBF) for anomaly detection, tracking and simultaneous estimation of the OU unknown parameters. The effectiveness of these tools is demonstrated on a simulated maritime scenario.