Journal ArticleDOI
Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection
TLDR
It is shown that a proper initialization of the recursive procedure leads to an adaptive NMF with the constant false alarm rate (CFAR) property and that it is very effective to operate in heterogeneous environments of relevant practical interest.Abstract:
Adaptive detection of signals embedded in Gaussian or non-Gaussian noise is a problem of primary concern among radar engineers. We propose a recursive algorithm to estimate the structure of the covariance matrix of either a set of Gaussian vectors that share the spectral properties up to a multiplicative factor or a set of spherically invariant random vectors (SIRVs) with the same covariance matrix and possibly correlated texture components. We also assess the performance of an adaptive implementation of the normalized matched filter (NMF), relying on the newly introduced estimate, in the presence of compound-Gaussian, clutter-dominated, disturbance. In particular, it is shown that a proper initialization of the recursive procedure leads to an adaptive NMF with the constant false alarm rate (CFAR) property and that it is very effective to operate in heterogeneous environments of relevant practical interest.read more
Citations
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Journal ArticleDOI
Complex Elliptically Symmetric Distributions: Survey, New Results and Applications
TL;DR: Applications of CES distributions and the adaptive signal processors based on ML- and M-estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival estimation and beamforming.
Journal ArticleDOI
Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis
TL;DR: The derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts and shows the convergence of this recursive scheme, ensured whatever the initialization.
Journal ArticleDOI
Robust Shrinkage Estimation of High-Dimensional Covariance Matrices
TL;DR: This work addresses high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes and proposes a simple, closed-form and data dependent choice for the shrinkage coefficient, based on a minimum mean squared error framework.
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Performance Analysis of Covariance Matrix Estimates in Impulsive Noise
TL;DR: A statistical study of the main covariance matrix estimates used in the literature is performed through bias analysis, consistency, and asymptotic distribution to compare the performance of the estimates and to establish simple relationships between them.
Journal ArticleDOI
Geodesic Convexity and Covariance Estimation
TL;DR: This work considers g-convex functions with positive definite matrix variables, and proves that Kronecker products, and logarithms of determinants are g- Convex, and applies these results to two modern covariance estimation problems: robust estimation in scaled Gaussian distributions, and Kroneker structured models.
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
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An Adaptive Detection Algorithm
TL;DR: A likelihood ratio decision rule is derived and its performance evaluated in both the noise-only and signal-plus-noise cases.
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Matched subspace detectors
TL;DR: The generalized likelihood ratio (GLR) is the uniformly most powerful invariant detector and the utility of this finding is illustrated by solving a number of problems for detecting subspace signals in subspace interference and broadband noise.