Quickest Change Detection in Anonymous Heterogeneous Sensor Networks

TL;DR

This paper develops and proves the optimality of a mixture CuSum algorithm for quickest change detection in anonymous heterogeneous sensor networks, addressing computational efficiency and false alarm rate characterization.

Contribution

It introduces a mixture CuSum test for anonymous heterogeneous sensors and proves its optimality under Lorden's criterion, along with a computationally efficient variant.

Findings

The mixture CuSum algorithm is optimal for anonymous heterogeneous sensor networks.

A computationally efficient test is proposed for large networks.

Theoretical characterization of false alarm rates is developed.

Abstract

The problem of quickest change detection (QCD) in anonymous heterogeneous sensor networks is studied. There are $n$ heterogeneous sensors and a fusion center. The sensors are clustered into $K$ groups, and different groups follow different data-generating distributions. At some unknown time, an event occurs in the network and changes the data-generating distribution of the sensors. The goal is to detect the change as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where at each time step, the fusion center receives $n$ unordered samples, and the fusion center does not know which sensor each sample comes from, and thus does not know its exact distribution. A simple optimality proof is first derived for the mixture likelihood ratio test, which was constructed and proved to be optimal for the non-sequential anonymous setting in (Chen and Wang, 2019). For the QCD problem, a mixture CuSum algorithm is further constructed, and is further shown to be optimal under Lorden's criterion. For large networks, a computationally efficient test is proposed and a novel theoretical characterization of its false alarm rate is developed. Numerical results are provided to validate the theoretical results.