799 research outputs found
Quickest Change Detection of a Markov Process Across a Sensor Array
Recent attention in quickest change detection in the multi-sensor setting has
been on the case where the densities of the observations change at the same
instant at all the sensors due to the disruption. In this work, a more general
scenario is considered where the change propagates across the sensors, and its
propagation can be modeled as a Markov process. A centralized, Bayesian version
of this problem, with a fusion center that has perfect information about the
observations and a priori knowledge of the statistics of the change process, is
considered. The problem of minimizing the average detection delay subject to
false alarm constraints is formulated as a partially observable Markov decision
process (POMDP). Insights into the structure of the optimal stopping rule are
presented. In the limiting case of rare disruptions, we show that the structure
of the optimal test reduces to thresholding the a posteriori probability of the
hypothesis that no change has happened. We establish the asymptotic optimality
(in the vanishing false alarm probability regime) of this threshold test under
a certain condition on the Kullback-Leibler (K-L) divergence between the post-
and the pre-change densities. In the special case of near-instantaneous change
propagation across the sensors, this condition reduces to the mild condition
that the K-L divergence be positive. Numerical studies show that this low
complexity threshold test results in a substantial improvement in performance
over naive tests such as a single-sensor test or a test that wrongly assumes
that the change propagates instantaneously.Comment: 40 pages, 5 figures, Submitted to IEEE Trans. Inform. Theor
Linear Beamforming for the Spatially Correlated MISO broadcast channel
A spatially correlated broadcast setting with M antennas at the base station
and M users (each with a single antenna) is considered. We assume that the
users have perfect channel information about their links and the base station
has only statistical information about each user's link. The base station
employs a linear beamforming strategy with one spatial eigen-mode allocated to
each user. The goal of this work is to understand the structure of the
beamforming vectors that maximize the ergodic sum-rate achieved by treating
interference as noise. In the M = 2 case, we first fix the beamforming vectors
and compute the ergodic sum-rate in closed-form as a function of the channel
statistics. We then show that the optimal beamforming vectors are the dominant
generalized eigenvectors of the covariance matrices of the two links. It is
difficult to obtain intuition on the structure of the optimal beamforming
vectors for M > 2 due to the complicated nature of the sum-rate expression.
Nevertheless, in the case of asymptotic M, we show that the optimal beamforming
vectors have to satisfy a set of fixed-point equations.Comment: Published in IEEE ISIT 2010, 5 page
Hidden Markov models for the activity profile of terrorist groups
The main focus of this work is on developing models for the activity profile
of a terrorist group, detecting sudden spurts and downfalls in this profile,
and, in general, tracking it over a period of time. Toward this goal, a
-state hidden Markov model (HMM) that captures the latent states underlying
the dynamics of the group and thus its activity profile is developed. The
simplest setting of corresponds to the case where the dynamics are
coarsely quantized as Active and Inactive, respectively. A state estimation
strategy that exploits the underlying HMM structure is then developed for spurt
detection and tracking. This strategy is shown to track even nonpersistent
changes that last only for a short duration at the cost of learning the
underlying model. Case studies with real terrorism data from open-source
databases are provided to illustrate the performance of the proposed
methodology.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS682 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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