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