Quickest Change Detection of a Markov Process Across a Sensor Array

• Published in: IEEE transactions on information theory Vol. 56; no. 4; pp. 1961 - 1981
• Main Authors: Raghavan, V., Veeravalli, V.V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Application software; Applied sciences; Asymptotic properties; Bayesian analysis; Bayesian methods; Biological information theory; Change detection; Change-point problems; Computerized monitoring; Condition monitoring; Delay; Density; Detection, estimation, filtering, equalization, prediction; Disruption; distributed decision-making; Exact sciences and technology; Information science; Information theory; Information, signal and communications theory; Markov analysis; Markov processes; Object detection; optimal fusion; Optimization; quickest change detection; Sensor arrays; sensor networks; Sensors; sequential detection; Signal and communications theory; Signal, noise; Telecommunications and information theory; Testing; Thresholds; Performance evaluation; Markov process; Multisensor; Decision support system; Change detection; Threshold detection; Change point; Optimal test; sensor networks; Sequential detection; False alarm rate; Stopping rule; Posterior probability; distributed decision-making; Change-point problems; quickest change detection; A priori estimation; Delay time; optimal fusion; Dynamic programming; Sensor array; Signal detection
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2010.2040869

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 post- and 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.