Second-Order Asymptotic Optimality in Multisensor Sequential Change Detection

Abstract

A generalized multisensor sequential change detection problem is considered, in which a number of (possibly correlated) sensors monitor an environment in real time, the joint distribution of their observations is determined by a global parameter vector, and at some unknown time there is a change in an unknown subset of components of this parameter vector. The goal is to detect the change as soon as possible, while controlling the rate of false alarms. We establish the second-order asymptotic optimality (with respect to Lorden's criterion) of various generalizations of the CUSUM rule; that is, we show that their additional expected worst case detection delay (relative to the one that could be achieved if the affected subset was known) remains bounded as the rate of false alarm goes to 0, for any possible subset of affected components. This general framework incorporates the traditional multisensor setup in which only an unknown subset of sensors is affected by the change. The latter problem has a special structure which we exploit in order to obtain feasible representations of the proposed schemes. We present the results of a simulation study where we compare the proposed schemes with scalable detection rules that are only first-order asymptotically optimal. Finally, in the special case that the change affects exactly one sensor, we consider the scheme that runs in parallel the local CUSUM rules and study the problem of specifying the local thresholds.

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