Bayesian Quickest Detection in Sensor Arrays

Abstract

We study Bayesian quickest detection problems with sensor arrays. An underlying signal is assumed to gradually propagate through a network of several sensors, triggering a cascade of interdependent change-points. The aim of the decision maker is to centrally fuse all available information to find an optimal detection rule that minimizes Bayes risk. We develop a tractable continuous-time formulation of this problem focusing on the case of sensors collecting point process observations and monitoring the resulting changes in intensity and type of observed events. Our approach uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with a Monte Carlo–based approach to dynamic programming. The developed models and algorithms are illustrated with plenty of numerical examples.

Keywords:

• Bayesian quickest detection
• Multiple change-point detection
• Particle filtering
• Sensor arrays

Subject Classification:

• 60G35
• 62L15
• 93E11
• 65C35

ACKNOWLEDGMENTS

This research was partially supported by the Hellman Family Foundation Research Grant. I am deeply grateful to the editor and the anonymous referee for many suggestions that improved the final article.

Notes

Recommended by A. G. Tartakovsky