Quickest Detection of Moving Anomalies in Sensor Networks

TL;DR

This paper addresses the challenge of quickly detecting moving anomalies in sensor networks by developing a sequential detection method that accounts for the anomaly's trajectory, with proven optimality in homogeneous cases and asymptotic optimality in heterogeneous cases.

Contribution

It introduces a modified Lorden's detection delay metric and proposes a Cumulative Sum-type test for moving anomaly detection, extending to heterogeneous sensors with asymptotic optimality.

Findings

The proposed CUSUM-type test is exactly optimal for homogeneous sensors.

The detection scheme is asymptotically optimal for heterogeneous sensors.

Numerical simulations confirm the theoretical performance of the detection methods.

Abstract

The problem of sequentially detecting a moving anomaly which affects different parts of a sensor network with time is studied. Each network sensor is characterized by a non-anomalous and anomalous distribution, governing the generation of sensor data. Initially, the observations of each sensor are generated according to the corresponding non-anomalous distribution. After some unknown but deterministic time instant, a moving anomaly emerges, affecting different sets of sensors as time progresses. As a result, the observations of the affected sensors are generated according to the corresponding anomalous distribution. Our goal is to design a stopping procedure to detect the emergence of the anomaly as quickly as possible, subject to constraints on the frequency of false alarms. The problem is studied in a quickest change detection framework where it is assumed that the evolution of the anomaly is unknown but deterministic. To this end, we propose a modification of Lorden's worst average detection delay metric to account for the trajectory of the anomaly that maximizes the detection delay of a candidate detection procedure. We establish 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. We conclude by presenting numerical simulations to validate our theoretical analysis.