In this paper, we study the design and analysis of optimal detection scheme for sensors that are deployed to monitor the change in the environment and are powered by the energy harvested from the environment. In this type of applications, detection delay is of paramount importance. We model this problem as quickest change detection problem with a stochastic energy constraint. In particular, a wireless sensor powered by renewable energy takes observations from a random sequence, whose distribution will change at a certain unknown time. Such a change implies events of interest. The energy in the sensor is consumed by taking observations and is replenished randomly. The sensor cannot take observations if there is no energy left in the battery. Our goal is to design a power allocation scheme and a detection strategy to minimize the worst case detection delay, which is the difference between the time when an alarm is raised and the time when the change occurs. Two types of average run length (ARL) constraint, namely an algorithm level ARL constraint and an 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 asymptotically optimal for the formulations with the system level ARL constraint.
Probability of Error for Detecting a Change in a Parameter, Total Variation of the Posterior Distribution, and Bayesian Fisher Information
van Trees不等式将一个估计量的包络均方误差与Fisher信息的贝叶斯版本联系起来。Ziv-Zakai不等式将估计量的平均均方误差与检测参数变化的最小误差概率相关联。在这项工作中，我们通过推导一个不等式来完成这个循环，这个不等式将这个最小错误概率与Fisher信息的贝叶斯版本联系起来。我们讨论这一结果的标量和矢量参数。在这个过程中，我们发现，在计算中的一个重要的中介是总变差的后验概率分布函数的参数给定的数据。这个总变差本身就很有趣，因为它可能比这里讨论的其他品质因数更容易计算。举例说明了所得不等式的正确性.
