Non-Bayesian Quickest Change Detection With Stochastic Sample Right Constraints

Abstract—In this paper, we study the design and analysis of op-timal detection scheme for sensors that are deployed to monitor the change in the environment and are powered by energy har-vested from the environment. In this type of applications, detec-tion delay is of paramount importance. We model this problem as quickest change detection problem with stochastic energy con-straints. In particular, a wireless sensor powered by renewable en-ergy takes observations from a random sequence, whose distribu-tion will change at an unknown time. Such a change implies events of interest. The energy in the sensor is consumed by taking obser-vations and is replenished randomly. The sensor cannot take ob-servations if there is no energy left in the battery. Our goal is to de-sign optimal power allocation and detection schemes to minimize the worst case detection delay, which is the difference between the time when the change occurs and the time when an alarm is raised. Two types of average run length (ARL) constraints, namely an al-gorithm level ARL constraint and a system level ARL constraint, are considered. We propose a low complexity scheme in which the energy allocation rule is to spend energy to take observations as long as the battery is not empty and the detection scheme is the Cumulative Sum test. We show that this scheme is optimal for the formulation with the algorithm level ARL constraint and is asymp-totically optimal for the formulations with the system level ARL constraint. Index Terms—Cumulative Sum test, energy harvesting sensor, non-Bayesian quickest change detection, sequential detection. I