Non-Bayesian quickest detection with a stochastic energy constraint

Motivated by applications of wireless sensors powered by energy harvested from the environment, we study non-Bayesian quickest change detection problems with a stochastic energy constraint. In particular, a wireless sensor powered by renewable energy is deployed to detect the change of probability density function in a random sequence. The energy in the sensor is consumed by taking observation and is replenished randomly. The sensor cannot take observations if there is no energy left. Our goal is to design power allocation scheme and detection strategy to minimize the delay between the time the change occurs and an alarm is raised. Two types of average run length (ARL) constraint, namely an algorithm level ARL and a system level ARL, are considered. We show that a low complexity scheme, in which the sensor takes observations as long as the battery is not empty coupled with the Cumulative Sum (CUSUM) test for detection, is optimal for the setup with the algorithm level ARL constraint, and is asymptotically optimal for the setup with the system level ARL constraint.