Quickest Detection of Moving Anomalies in Sensor Networks

The problem of sequentially detecting a moving anomaly is studied, in which the anomaly affects different parts of a sensor network over time. Each network sensor is characterized by a pre- and post-change distribution. Initially, the observations of each sensor are generated according to the corresponding pre-change distribution. After some unknown but deterministic time instant, a moving anomaly emerges, affecting different sets of sensors as time progresses. Our goal is to design a stopping procedure to detect the emergence of the anomaly as quickly as possible, subject to false alarms constraints. The problem is studied in a quickest change detection framework where it is assumed that the evolution of the anomaly is unknown but deterministic. A modification of Lorden's detection delay is proposed to account for the trajectory of the anomaly that maximizes the detection delay of a detection procedure. It is established that a Cumulative Sum-type test solves the resulting sequential detection problem exactly when the sensors are homogeneous. For the case of heterogeneous sensors, the proposed detection scheme can be modified to provide a first-order asymptotically optimal algorithm.