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Quickest Detection of Moving Anomalies in Sensor Networks

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Document pages: 34 pages

Abstract: The problem of sequentially detecting a moving anomaly which affectsdifferent parts of a sensor network with time is studied. Each network sensoris characterized by a non-anomalous and anomalous distribution, governing thegeneration of sensor data. Initially, the observations of each sensor aregenerated according to the corresponding non-anomalous distribution. After someunknown but deterministic time instant, a moving anomaly emerges, affectingdifferent sets of sensors as time progresses. As a result, the observations ofthe affected sensors are generated according to the corresponding anomalousdistribution. Our goal is to design a stopping procedure to detect theemergence of the anomaly as quickly as possible, subject to constraints on thefrequency of false alarms. The problem is studied in a quickest changedetection framework where it is assumed that the evolution of the anomaly isunknown but deterministic. To this end, we propose a modification of Lorden sworst average detection delay metric to account for the trajectory of theanomaly that maximizes the detection delay of a candidate detection procedure.We establish that a Cumulative Sum-type test solves the resulting sequentialdetection problem exactly when the sensors are homogeneous. For the case ofheterogeneous sensors, the proposed detection scheme can be modified to providea first-order asymptotically optimal algorithm. We conclude by presentingnumerical simulations to validate our theoretical analysis.

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