One Shot Schemes for Decentralized Quickest Change Detection and Quickest Detection in Coupled Systems

March 23, 2009
2:30pm-3:30pm
EE Conference Room (Mudd 1301)
Hosted by: Prof. Xiaodong Wang
Speaker: Prof. Olympia Hadjiliadis, City University of New York

Abstract

We consider the problem of sequential detection of a change in the drift of independent Brownian motions and the mean of discrete-time exponential family observations received in parallel at the sensors of decentralized systems. We examine the performance of one shot schemes in decentralized detection in the case of many sensors with respect to appropriate criteria. One shot schemes are schemes in which the sensors communicate with the fusion center only once; when they must signal a detection. The communication is clearly asynchronous and we consider the case that the fusion center employs one of two strategies, the minimal and the maximal. According to the former strategy an alarm is issued at the fusion center the moment in which the first one of the sensors issues an alarm, whereas according to the latter strategy an alarm is issued when both sensors have reported a detection. In this work we derive closed form expressions for the expected delay of both the minimal and the maximal strategies in the case that CUSUM stopping rules are employed by the sensors and for the specific value of a 0 correlation across sensors. We prove asymptotic optimality of the above strategies in the case of across-sensor independence and specify the optimal threshold selection at the sensors. Moreover, we address the problem of quickest detection in coupled systems in models that display more general dependencies in the observations captured by general Itá»™ processes. We set-up appropriate stochastic optimization problems with respect to Kullback-Leibler divergence and prove the asymptotic optimality of the N-CUSUM stopping rule in this case. We discuss applications of this work in the detection of structural damages.

Biography

Olympia Hadjiliadis is an Assistant Professor in the Department of Mathematics at Brooklyn College of the City University of New York, where she is also a member of the graduate faculty of the Department of Computer Science. She was awarded her M.Math in Statistics and Finance in 1999 from the University of Waterloo, Canada. After receiving a PhD in Statistics with distinction from Columbia University in 2005, Dr. Hadjiliadis joined the Electrical Engineering Department at Princeton as a Postdoctoral Fellow, where she was subsequently appointed as a Visiting Research Collaborator until 2008.


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