An efficient sequential procedure for detecting changes in multichannel and distributed systems

Abstract

In the conventional formulation of the change-point detection problem, there is a sequence of observations whose distribution changes at some unknown point in time, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. It is known that in the case where the observations are i.i.d. and the change point is modeled as deterministic but unknown, the cumulative sum (CUSUM) detection procedure of Page (1954) and the randomized Shiryaev-Roberts detection procedure proposed by Pollak (1985) minimize the expected detection lag, subject to a constraint on the false alarm rate. In this paper, we are interested in the two generalizations of this problem. The first is the generalization regarding multichannel systems. Here all the channels are either statistically identical or the change occurs in one of them at unknown point in time. It is necessary to detect the change in distribution as soon as possible after it occurs, while controlling the rate of false alarms at a given level. The second generalization corresponds to the multi-sensor situation where the information available for decision-making is distributed across a set of sensors. The sensors send quantized versions of their observations to a fusion center where the change detection is performed based on all the sensor messages. We propose multi-channel and distributed versions of the CUSUM procedure and prove that they are asymptotically optimal as the average frequency of false alarms goes to zero. The general results are applied to the two important application areas-target detection in surveillance systems and attack/intrusion detection in distributed computer networks. Experimental results show that the proposed detection methods are highly efficient.