Quickest change detection for UAV-based sensing

Abstract: This paper addresses the problem of quickest change detection (QCD) at two spatially separated locations monitored by a single unmanned aerial vehicle (UAV) equipped with a sensor. At any location, the UAV observes i.i.d. data sequentially in discrete time instants. The distribution of the observation data changes at some unknown, arbitrary time and the UAV has to detect this change in the shortest possible time. Change can occur at most at one location over the entire infinite time horizon. The UAV switches between these two locations in order to quickly detect the change. To this end, we propose Location Switching and Change Detection (LS-CD) algorithm which uses a repeated one-sided sequential probability ratio test (SPRT) based mechanism for observation-driven location switching and change detection. The primary goal is to minimize the worst-case average detection delay (WADD) while meeting constraints on the average run length to false alarm (ARL2FA) and the UAV's time-averaged energy consumption. We provide a rigorous theoretical analysis of the algorithm's performance by using theory of random walk. Specifically, we derive tight upper and lower bounds to its ARL2FA and a tight upper bound to its WADD. In the special case of a symmetrical setting, our analysis leads to a new asymptotic upper bound to the ARL2FA of the standard CUSUM algorithm, a novel contribution not available in the literature, to our knowledge. Numerical simulations demonstrate the efficacy of LS-CD.