Quickest change detection of a Markov process across a sensor array

Authors:
Vasanthan Raghavan;Venugopal V. Veeravalli
Affiliations:
Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, Australia and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, ...;Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 6
Cited 2

Dynamic programming: deterministic and stochastic models

Dynamic programming: deterministic and stochastic models
Detection of abrupt changes: theory and application

Detection of abrupt changes: theory and application
One shot schemes for decentralized quickest change detection

IEEE Transactions on Information Theory
A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods

IEEE Transactions on Signal Processing
Information bounds and quick detection of parameter changes in stochastic systems

IEEE Transactions on Information Theory
Decentralized quickest change detection

IEEE Transactions on Information Theory

Bayesian quickest change process detection

ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Multi-variate quickest detection of significant change process

GameSec'11 Proceedings of the Second international conference on Decision and Game Theory for Security

Quantified Score

Hi-index	754.84

Visualization

Abstract

Recent attention in quickest change detection in the multisensor 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 is considered, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process. The problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework. Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. Under a certain condition on the Kullback-Leibler (K-L) divergence between the postand the pre-change densities, it is established that the threshold test is asymptotically optimal (in the vanishing false alarm probability regime). It is shown via numerical studies 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.