Bayesian quickest detection with stochastic energy constraint

In this paper, Bayesian quickest change-point detection problem with a stochastic energy constraint is considered. This work is motivated by applications of renewable energy powered wireless sensor networks. In particular, a renewable energy powered wireless sensor is deployed to detect the change in the probability distribution of the observation sequence. The energy in the sensor is consumed by taking observations and is replenished randomly. The sensor cannot store extra energy if its battery is full and cannot take observations if it has no energy left. Hence, the sensor needs to use its energy efficiently. Our goal is to design a power allocation scheme and a detection strategy to minimize the average detection delay while keeping a low false alarm probability. We show that this problem can be written into a set of iteratively defined functions and then solved by the tools from the optimal stopping theory. It turns out that the optimal solution has a very complex structure. For practical applications, we propose a low complexity algorithm, in which the sensor adopts a greedy power allocation scheme with a threshold detection rule. We show that this algorithm is first order asymptotically optimal as the false alarm probability goes to zero.