Bayesian quickest change process detection

Abstract

Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of observations change at the same instant at all the sensors due to the disruption. In this work, a more general change process scenario is studied where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem is considered, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process. Insights into the structure of the optimal stopping rule are presented, that minimizes average detection delay subject to false alarm constraints. In the limiting case of rare disruptions, it is shown that this test structure reduces to a threshold rule. The asymptotic optimality (in the vanishing false alarm regime) of this threshold test is established under a certain condition on the Kullback-Leibler (K-L) divergence between the post- and the pre-change densities. In the special case of near-instantaneous change propagation across the sensors, this condition reduces to the mild condition that the K-L divergence be positive. Numerical studies show that this low-complexity threshold test results in a substantial improvement in performance over naive tests such as a single-sensor test or a test that incorrectly assumes that the change propagates instantaneously.