338 research outputs found
Multi-variate quickest detection of significant change process
The paper deals with a mathematical model of a surveillance system based on a net of sensors. The signals acquired by each node of the net are Markovian process, have two different transition probabilities, which depends on the presence or absence of a intruder nearby. The detection of the transition probability change at one node should be confirmed by a detection of similar change at some other sensors. Based on a simple game the model of a fusion center is then constructed. The aggregate function defined on the net is the background of the definition of a non-cooperative stopping game which is a model of the multivariate disorder detectionvoting stopping rule, majority voting rule, monotone voting strategy, change-point problems, quickest detection, sequential detection, simple game
Bayesian Quickest Detection of Propagating Spatial Events
Rapid detection of spatial events that propagate across a sensor network is
of wide interest in many modern applications. In particular, in communications,
radar, environmental monitoring, and biosurveillance, we may observe
propagating fields or particles. In this paper, we propose Bayesian single and
multiple change-point detection procedures for the rapid detection of
propagating spatial events. It is assumed that the spatial event propagates
across a network of sensors according to the physical properties of the source
causing the event. The multi-sensor system configuration is arbitrary and
sensors may be mobile. We begin by considering a single spatial event and are
interested in detecting this event as quickly as possible, while controlling
the probability of false alarm. Using a dynamic programming framework we derive
the structure of the optimal procedure, which minimizes the average detection
delay (ADD) subject to a false alarm probability upper bound. In the rare event
regime, the optimal procedure converges to a more practical threshold test on
the posterior probability of the change point. A convenient recursive
computation of this posterior probability is derived by using the propagation
pattern of the spatial event. The ADD of the posterior probability threshold
test is analyzed in the asymptotic regime, and specific analysis is conducted
in the setting of detecting attenuating random signals. Then, we show how the
proposed procedure is easy to extend for detecting multiple propagating spatial
events in parallel. A method that provides false discovery rate (FDR) control
is proposed. In the simulation section, it is clearly demonstrated that
exploiting the spatial properties of the event decreases the ADD compared to
procedures that do not utilize this information, even under model mismatch.Comment: 14 pages, 5 figure
Delay Optimal Event Detection on Ad Hoc Wireless Sensor Networks
We consider a small extent sensor network for event detection, in which nodes
take samples periodically and then contend over a {\em random access network}
to transmit their measurement packets to the fusion center. We consider two
procedures at the fusion center to process the measurements. The Bayesian
setting is assumed; i.e., the fusion center has a prior distribution on the
change time. In the first procedure, the decision algorithm at the fusion
center is \emph{network-oblivious} and makes a decision only when a complete
vector of measurements taken at a sampling instant is available. In the second
procedure, the decision algorithm at the fusion center is \emph{network-aware}
and processes measurements as they arrive, but in a time causal order. In this
case, the decision statistic depends on the network delays as well, whereas in
the network-oblivious case, the decision statistic does not depend on the
network delays. This yields a Bayesian change detection problem with a tradeoff
between the random network delay and the decision delay; a higher sampling rate
reduces the decision delay but increases the random access delay. Under
periodic sampling, in the network--oblivious case, the structure of the optimal
stopping rule is the same as that without the network, and the optimal change
detection delay decouples into the network delay and the optimal decision delay
without the network. In the network--aware case, the optimal stopping problem
is analysed as a partially observable Markov decision process, in which the
states of the queues and delays in the network need to be maintained. A
sufficient statistic for decision is found to be the network-state and the
posterior probability of change having occurred given the measurements received
and the state of the network. The optimal regimes are studied using simulation.Comment: To appear in ACM Transactions on Sensor Networks. A part of this work
was presented in IEEE SECON 2006, and Allerton 201
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