2,039 research outputs found
Non-Bayesian Quickest Detection with Stochastic Sample Right Constraints
In this paper, we study the design and analysis of optimal detection scheme
for sensors that are deployed to monitor the change in the environment and are
powered by the energy harvested from the environment. In this type of
applications, detection delay is of paramount importance. We model this problem
as quickest change detection problem with a stochastic energy constraint. In
particular, a wireless sensor powered by renewable energy takes observations
from a random sequence, whose distribution will change at a certain unknown
time. Such a change implies events of interest. The energy in the sensor is
consumed by taking observations and is replenished randomly. The sensor cannot
take observations if there is no energy left in the battery. Our goal is to
design a power allocation scheme and a detection strategy to minimize the worst
case detection delay, which is the difference between the time when an alarm is
raised and the time when the change occurs. Two types of average run length
(ARL) constraint, namely an algorithm level ARL constraint and an system level
ARL constraint, are considered. We propose a low complexity scheme in which the
energy allocation rule is to spend energy to take observations as long as the
battery is not empty and the detection scheme is the Cumulative Sum test. We
show that this scheme is optimal for the formulation with the algorithm level
ARL constraint and is asymptotically optimal for the formulations with the
system level ARL constraint.Comment: 30 pages, 5 figure
Data-Efficient Quickest Outlying Sequence Detection in Sensor Networks
A sensor network is considered where at each sensor a sequence of random
variables is observed. At each time step, a processed version of the
observations is transmitted from the sensors to a common node called the fusion
center. At some unknown point in time the distribution of observations at an
unknown subset of the sensor nodes changes. The objective is to detect the
outlying sequences as quickly as possible, subject to constraints on the false
alarm rate, the cost of observations taken at each sensor, and the cost of
communication between the sensors and the fusion center. Minimax formulations
are proposed for the above problem and algorithms are proposed that are shown
to be asymptotically optimal for the proposed formulations, as the false alarm
rate goes to zero. It is also shown, via numerical studies, that the proposed
algorithms perform significantly better than those based on fractional
sampling, in which the classical algorithms from the literature are used and
the constraint on the cost of observations is met by using the outcome of a
sequence of biased coin tosses, independent of the observation process.Comment: Submitted to IEEE Transactions on Signal Processing, Nov 2014. arXiv
admin note: text overlap with arXiv:1408.474
Data-Efficient Quickest Change Detection with On-Off Observation Control
In this paper we extend the Shiryaev's quickest change detection formulation
by also accounting for the cost of observations used before the change point.
The observation cost is captured through the average number of observations
used in the detection process before the change occurs. The objective is to
select an on-off observation control policy, that decides whether or not to
take a given observation, along with the stopping time at which the change is
declared, so as to minimize the average detection delay, subject to constraints
on both the probability of false alarm and the observation cost. By considering
a Lagrangian relaxation of the constraint problem, and using dynamic
programming arguments, we obtain an \textit{a posteriori} probability based
two-threshold algorithm that is a generalized version of the classical Shiryaev
algorithm. We provide an asymptotic analysis of the two-threshold algorithm and
show that the algorithm is asymptotically optimal, i.e., the performance of the
two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed
observation cost, as the probability of false alarm goes to zero. We also show,
using simulations, that the two-threshold algorithm has good observation
cost-delay trade-off curves, and provides significant reduction in observation
cost as compared to the naive approach of fractional sampling, where samples
are skipped randomly. Our analysis reveals that, for practical choices of
constraints, the two thresholds can be set independent of each other: one based
on the constraint of false alarm and another based on the observation cost
constraint alone.Comment: Preliminary version of this paper has been presented at ITA Workshop
UCSD 201
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