729 research outputs found
On the use of the l(2)-norm for texture analysis of polarimetric SAR data
In this paper, the use of the l2-norm, or Span, of the scattering vectors is suggested for texture analysis of polarimetric synthetic aperture radar (SAR) data, with the benefits that we need neither an analysis of the polarimetric channels separately nor a filtering of the data to analyze the statistics. Based on the product model, the distribution of the l2-norm is studied. Closed expressions of the probability density functions under the assumptions of several texture distributions are provided. To utilize the statistical properties of the l2-norm, quantities including normalized moments and log-cumulants are derived, along with corresponding estimators and estimation variances. Results on both simulated and real SAR data show that the use of statistics based on the l2-norm brings advantages in several aspects with respect to the normalized intensity moments and matrix variate log-cumulants.Peer ReviewedPostprint (published version
Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case
In \cite{Abramovich04}, it was demonstrated that the likelihood ratio (LR) for multivariate complex Gaussian distribution has the invariance property that can be exploited in many applications. Specifically, the probability density function (p.d.f.) of this LR for the (unknown) actual covariance matrix does not depend on this matrix and is fully specified by the matrix dimension and the number of independent training samples . Since this p.d.f. could therefore be pre-calculated for any a priori known , one gets a possibility to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically ``as likely'' as the a priori unknown actual covariance matrix. This ``expected likelihood'' (EL) quality assessment allows for significant improvement of MUSIC DOA estimation performance in the so-called ``threshold area'' \cite{Abramovich04,Abramovich07d}, and for diagonal loading and TVAR model order selection in adaptive detectors \cite{Abramovich07,Abramovich07b}. Recently, a broad class of the so-called complex elliptically symmetric (CES) distributions has been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative of CES, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix \mSigma_{0}. Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario () while Part 2 deals with the under-sampled scenario ()
MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter
Multiple-input multiple-output (MIMO) radar has become a thriving subject of
research during the past decades. In the MIMO radar context, it is sometimes
more accurate to model the radar clutter as a non-Gaussian process, more
specifically, by using the spherically invariant random process (SIRP) model.
In this paper, we focus on the estimation and performance analysis of the
angular spacing between two targets for the MIMO radar under the SIRP clutter.
First, we propose an iterative maximum likelihood as well as an iterative
maximum a posteriori estimator, for the target's spacing parameter estimation
in the SIRP clutter context. Then we derive and compare various
Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we
address the problem of target resolvability by using the concept of angular
resolution limit (ARL), and derive an analytical, closed-form expression of the
ARL based on Smith's criterion, between two closely spaced targets in a MIMO
radar context under SIRP clutter. For this aim we also obtain the non-matrix,
closed-form expressions for each of the CRLBs. Finally, we provide numerical
simulations to assess the performance of the proposed algorithms, the validity
of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure
Heavy-tailed Independent Component Analysis
Independent component analysis (ICA) is the problem of efficiently recovering
a matrix from i.i.d. observations of
where is a random vector with mutually independent
coordinates. This problem has been intensively studied, but all existing
efficient algorithms with provable guarantees require that the coordinates
have finite fourth moments. We consider the heavy-tailed ICA problem
where we do not make this assumption, about the second moment. This problem
also has received considerable attention in the applied literature. In the
present work, we first give a provably efficient algorithm that works under the
assumption that for constant , each has finite
-moment, thus substantially weakening the moment requirement
condition for the ICA problem to be solvable. We then give an algorithm that
works under the assumption that matrix has orthogonal columns but requires
no moment assumptions. Our techniques draw ideas from convex geometry and
exploit standard properties of the multivariate spherical Gaussian distribution
in a novel way.Comment: 30 page
On the Power of Invariant Tests for Hypotheses on a Covariance Matrix
The behavior of the power function of autocorrelation tests such as the
Durbin-Watson test in time series regressions or the Cliff-Ord test in spatial
regression models has been intensively studied in the literature. When the
correlation becomes strong, Kr\"amer (1985) (for the Durbin-Watson test) and
Kr\"amer (2005) (for the Cliff-Ord test) have shown that the power can be very
low, in fact can converge to zero, under certain circumstances. Motivated by
these results, Martellosio (2010) set out to build a general theory that would
explain these findings. Unfortunately, Martellosio (2010) does not achieve this
goal, as a substantial portion of his results and proofs suffer from serious
flaws. The present paper now builds a theory as envisioned in Martellosio
(2010) in a fairly general framework, covering general invariant tests of a
hypothesis on the disturbance covariance matrix in a linear regression model.
The general results are then specialized to testing for spatial correlation and
to autocorrelation testing in time series regression models. We also
characterize the situation where the null and the alternative hypothesis are
indistinguishable by invariant tests
New multivariate central limit theorems in linear structural and functional error-in-variables models
This paper deals simultaneously with linear structural and functional
error-in-variables models (SEIVM and FEIVM), revisiting in this context
generalized and modified least squares estimators of the slope and intercept,
and some methods of moments estimators of unknown variances of the measurement
errors. New joint central limit theorems (CLT's) are established for these
estimators in the SEIVM and FEIVM under some first time, so far the most
general, respective conditions on the explanatory variables, and under the
existence of four moments of the measurement errors. Moreover, due to them
being in Studentized forms to begin with, the obtained CLT's are a priori
nearly, or completely, data-based, and free of unknown parameters of the
distribution of the errors and any parameters associated with the explanatory
variables. In contrast, in related CLT's in the literature so far, the
covariance matrices of the limiting normal distributions are, in general,
complicated and depend on various, typically unknown parameters that are hard
to estimate. In addition, the very forms of the CLT's in the present paper are
universal for the SEIVM and FEIVM. This extends a previously known interplay
between a SEIVM and a FEIVM. Moreover, though the particular methods and
details of the proofs of the CLT's in the SEIVM and FEIVM that are established
in this paper are quite different, a unified general scheme of these proofs is
constructed for the two models herewith.Comment: Published at http://dx.doi.org/10.1214/07-EJS075 in the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Adaptive subspace detectors
Includes bibliographical references.In this paper, we use the theory of generalized likelihood ratio tests (GLRTs) to adapt the matched subspace detectors (MSDs) of [1] and [2] to unknown noise covariance matrices. In so doing, we produce adaptive MSDs that may be applied to signal detection for radar, sonar, and data communication. We call the resulting detectors adaptive subspace detectors (ASDs). These include Kelly's GLRT and the adaptive cosine estimator (ACE) of [6] and [19] for scenarios in which the scaling of the test data may deviate from that of the training data. We then present a unified analysis of the statistical behavior of the entire class of ASDs, obtaining statistically identical decompositions in which each ASD is simply decomposed into the nonadaptive matched filter, the nonadaptive cosine or t-statistic, and three other statistically independent random variables that account for the performance-degrading effects of limited training data.This work was supported by the Office of Naval Research under Contracts N00014-89-J-1070 and N00014-00-1-0033, and by the National Science Foundation under Contracts MIP-9529050 and ECS 9979400
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