Quickest change detection and identification across a sensor array

In this paper, we consider the problem of quickest change detection and identification over a linear array of N sensors, in which a change could first occur at any of these sensors and then propagate to other sensors. Our goal is not only to detect the presence of such a change as quickly as possible, but also to identify the sensor that the change pattern first reaches. We jointly design two decision rules: a stopping rule that determines when we should stop sampling and claim a change has occurred, and a terminal decision rule that decides which sensor that the change pattern reaches first. We characterize the optimal rules that 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.