Quickest Change Detection with a Censoring Sensor in the Minimax Setting

TL;DR

This paper addresses quickest change detection using a censoring sensor with energy constraints, proposing an asymptotically optimal strategy that maximizes post-censoring divergence and reduces computational complexity.

Contribution

It introduces an asymptotically optimal censoring strategy for energy-constrained quickest change detection, with a specific structure that simplifies computation.

Findings

Optimal censoring strategy maximizes post-censoring K-L divergence.

Asymptotic optimality of the strategy for Lorden's and Pollak's problems.

Strategy uses full available energy and has a single-interval no-send region.

Abstract

The problem of quickest change detection with a wireless sensor node is studied in this paper. The sensor that is deployed to monitor the environment has limited energy constraint to the classical quickest change detection problem. We consider the "censoring" strategy at the sensor side, i.e., the sensor selectively sends its observations to the decision maker. The quickest change detection problem is formulated in a minimax way. In particular, our goal is to find the optimal censoring strategy and stopping time such that the detection delay is minimized subject to constraints on both average run length (ARL) and average energy cost before the change. We show that the censoring strategy that has the maximal post-censoring Kullback-Leibler (K-L) divergence coupled with Cumulative Sum (CuSum) and Shiryaev-Roberts-Pollak (SRP) detection procedure is asymptotically optimal for the Lorden's and Pollak's problem as the ARL goes to infinity, respectively. We also show that the asymptotically optimal censoring strategy should use up the available energy and has a very special structure, i.e., the likelihood ratio of the no send region is a single interval, which can be utilized to significantly reduce the computational complexity. Numerical examples are shown to illustrate our results.