Quickest Change Detection of a Markov Process Across a Sensor Array

Details Quickest Change Detection of a Markov Process Across a Sensor Array Quickest Change Detection of a Markov Process Across a Sensor Array

2008-12-19

arxiv.org/abs/0812.3742v1

Computer Science

Information Theory

40 pages, 5 figures, Submitted to IEEE Trans. Inform. Theory

Scientific paper

Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process, is considered. The problem of minimizing the average detection delay subject to false alarm constraints is formulated as a partially observable Markov decision process (POMDP). Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, we show that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. We establish the asymptotic optimality (in the vanishing false alarm probability regime) of this threshold test 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 wrongly assumes that the change propagates instantaneously.

Affiliated with

Also associated with

No associations

Rating

Quickest Change Detection of a Markov Process Across a Sensor Array does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quickest Change Detection of a Markov Process Across a Sensor Array, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quickest Change Detection of a Markov Process Across a Sensor Array will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-726960