Quickest Change Point Detection and Identification Across a Generic Sensor Array

Abstract: In this paper, we consider the problem of quickest change point detection and identification over a linear array of $N$ sensors, where the change pattern could first reach any of these sensors, and then propagate to the other sensors. Our goal is not only to detect the presence of such a change as quickly as possible, but also to identify which sensor that the change pattern first reaches. We jointly design two decision rules: a stopping rule, which determines when we should stop sampling and claim a change occurred, and a terminal decision rule, which decides which sensor that the change pattern reaches first, with the objective to strike a balance among the detection delay, the false alarm probability, and the false identification probability. We show that this problem can be converted to a Markov optimal stopping time problem, from which some technical tools could be borrowed. Furthermore, to avoid the high implementation complexity issue of the optimal rules, we develop a scheme with a much simpler structure and certain performance guarantee.