Bayesian Quickest Detection in Sensor Arrays

Abstract

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 inter-dependent 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 Monte Carlo based approach to dynamic programming. The developed models and algorithms are illustrated with plenty of numerical examples.

A new approach for rapid detection of nearby thresholds in ecosystem time series

“…We use the QD method to identify a change in a statistical indicator, not the underlying ecological threshold. Recent work by Ludkovski (2012) and Han (2010) on public health surveillance problems employ similar methods where the signal gradually propagates through space. Since Ludkovski and Han exploit spatial information as well as time series information their work suggests a potentially valuable extension to spatial dynamics in ecology.…”

Bayesian Multiple Change-Point Detection of Propagating Events

“…n } denote the indicator of the event that the signal at cluster k has reached sensor l by time n. We are interested in detecting the first change point that occurs in each cluster [9],…”

“…The event may instantaneously affect the observation distribution of all the sensors in the vicinity of the event [2,5]. Alternatively, the disruption may propagate across the sensors in the network or in some cluster of the network over a short time period [6][7][8][9], e.g. propagation of radio waves through space in communication or radar systems.…”

“…The work in [8] considered a similar model to [6,7] but with an unknown change propagation pattern. In [9], Bayesian continuous-time single change-point detection in a sensor network was considered. The event was assumed to occur at a random time instant and a random location and gradually propagate through the sensor network with a random velocity triggering interdependent change points.…”

“…We are interested in detecting the leading edge of the change, i.e. the first change point observed by the sensors in each cluster area [9]; (2) For each cluster, by using the posterior probability update formulation we propose a simple posterior probability threshold test to perform the change-point detection within the cluster. The change-point detection tests are accumulated to obtain a parallel multiple change-point detection procedure.…”