Sequential Detection of Transient Changes

Abstract

This article addresses the transient change detection problem. It is assumed that a change occurs at an unknown (but nonrandom) change-point and the duration of post-change period is finite and known. A latent detection—that is, a detection that occurs after signal disappearance—is considered as a missed detection. A new optimality criterion adapted to the detection of transient changes involves the minimization of the worst-case probability of missed detection under constraint on the false alarm rate for a given period. A suboptimal sequential transient change detection algorithm is proposed. It is based on a window-limited cumulative sum (CUSUM) test. An upper bound for the worst-case probability of missed detection and a lower and an upper bound for the false alarm rate are proposed. Based on these bounds, the window-limited CUSUM test is optimized with respect to the proposed criterion. The developed algorithm and theoretical findings are applied to drinking water distribution network monitoring.