12,348 research outputs found
Resource-Constrained Adaptive Search and Tracking for Sparse Dynamic Targets
This paper considers the problem of resource-constrained and noise-limited
localization and estimation of dynamic targets that are sparsely distributed
over a large area. We generalize an existing framework [Bashan et al, 2008] for
adaptive allocation of sensing resources to the dynamic case, accounting for
time-varying target behavior such as transitions to neighboring cells and
varying amplitudes over a potentially long time horizon. The proposed adaptive
sensing policy is driven by minimization of a modified version of the
previously introduced ARAP objective function, which is a surrogate function
for mean squared error within locations containing targets. We provide
theoretical upper bounds on the performance of adaptive sensing policies by
analyzing solutions with oracle knowledge of target locations, gaining insight
into the effect of target motion and amplitude variation as well as sparsity.
Exact minimization of the multi-stage objective function is infeasible, but
myopic optimization yields a closed-form solution. We propose a simple
non-myopic extension, the Dynamic Adaptive Resource Allocation Policy (D-ARAP),
that allocates a fraction of resources for exploring all locations rather than
solely exploiting the current belief state. Our numerical studies indicate that
D-ARAP has the following advantages: (a) it is more robust than the myopic
policy to noise, missing data, and model mismatch; (b) it performs comparably
to well-known approximate dynamic programming solutions but at significantly
lower computational complexity; and (c) it improves greatly upon non-adaptive
uniform resource allocation in terms of estimation error and probability of
detection.Comment: 49 pages, 1 table, 11 figure
Stochastic Analysis of the LMS Algorithm for System Identification with Subspace Inputs
This paper studies the behavior of the low rank LMS adaptive algorithm for the general case in which the input transformation may not capture the exact input subspace. It is shown that the Independence Theory and the independent additive noise model are not applicable to this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to the Independence Theory model). The new theory is applied to a network echo cancellation scheme which uses partial-Haar input vector transformations. Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the Independence Theory based model available in the literature
Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism
Testing for the significance of a subset of regression coefficients in a
linear model, a staple of statistical analysis, goes back at least to the work
of Fisher who introduced the analysis of variance (ANOVA). We study this
problem under the assumption that the coefficient vector is sparse, a common
situation in modern high-dimensional settings. Suppose we have covariates
and that under the alternative, the response only depends upon the order of
of those, . Under moderate sparsity levels, that
is, , we show that ANOVA is essentially optimal under some
conditions on the design. This is no longer the case under strong sparsity
constraints, that is, . In such settings, a multiple comparison
procedure is often preferred and we establish its optimality when
. However, these two very popular methods are suboptimal, and
sometimes powerless, under moderately strong sparsity where .
We suggest a method based on the higher criticism that is powerful in the whole
range . This optimality property is true for a variety of designs,
including the classical (balanced) multi-way designs and more modern ""
designs arising in genetics and signal processing. In addition to the standard
fixed effects model, we establish similar results for a random effects model
where the nonzero coefficients of the regression vector are normally
distributed.Comment: Published in at http://dx.doi.org/10.1214/11-AOS910 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Higher criticism for detecting sparse heterogeneous mixtures
Higher criticism, or second-level significance testing, is a
multiple-comparisons concept mentioned in passing by Tukey. It concerns a
situation where there are many independent tests of significance and one is
interested in rejecting the joint null hypothesis. Tukey suggested comparing
the fraction of observed significances at a given \alpha-level to the expected
fraction under the joint null. In fact, he suggested standardizing the
difference of the two quantities and forming a z-score; the resulting z-score
tests the significance of the body of significance tests. We consider a
generalization, where we maximize this z-score over a range of significance
levels 0<\alpha\leq\alpha_0.
We are able to show that the resulting higher criticism statistic is
effective at resolving a very subtle testing problem: testing whether n normal
means are all zero versus the alternative that a small fraction is nonzero. The
subtlety of this ``sparse normal means'' testing problem can be seen from work
of Ingster and Jin, who studied such problems in great detail. In their
studies, they identified an interesting range of cases where the small fraction
of nonzero means is so small that the alternative hypothesis exhibits little
noticeable effect on the distribution of the p-values either for the bulk of
the tests or for the few most highly significant tests.
In this range, when the amplitude of nonzero means is calibrated with the
fraction of nonzero means, the likelihood ratio test for a precisely specified
alternative would still succeed in separating the two hypotheses.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Statistics
(http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000026
Adaptive channel selection for DOA estimation in MIMO radar
We present adaptive strategies for antenna selection for Direction of Arrival
(DoA) estimation of a far-field source using TDM MIMO radar with linear arrays.
Our treatment is formulated within a general adaptive sensing framework that
uses one-step ahead predictions of the Bayesian MSE using a parametric family
of Weiss-Weinstein bounds that depend on previous measurements. We compare in
simulations our strategy with adaptive policies that optimize the Bobrovsky-
Zaka{\i} bound and the Expected Cram\'er-Rao bound, and show the performance
for different levels of measurement noise.Comment: Submitted to the 25th European Signal Processing Conference
(EUSIPCO), 201
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