The Empirical Likelihood method applied to covariance matrix estimation
Signal Processing
Knowledge-aided covariance matrix estimation and adaptive detection in compound-Gaussian noise
IEEE Transactions on Signal Processing
Distributed target detection with polarimetric MIMO radar in compound-Gaussian clutter
Digital Signal Processing
Detection performance analysis of tests for spread targets in compound-gaussian clutter
ICICA'12 Proceedings of the Third international conference on Information Computing and Applications
Covariance structure regularization via entropy loss function
Computational Statistics & Data Analysis
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Recently, a new adaptive scheme [Conte (1995), Gini (1997)] has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by compound-Gaussian noise, which is the product c of the square root of a positive unknown variable tau (deterministic or random) and an independent Gaussian vector x, c=radictaux. Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When tau is assumed deterministic and unknown, the FP is the exact maximum-likelihood (ML) estimate of the noise covariance structure, while when tau is a positive random variable, the FP is an approximate maximum likelihood (AML). This estimate has been already used for its excellent statistical properties without proofs of its existence and uniqueness. The major contribution of this paper is to fill these gaps. Our derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts. Moreover, the corresponding iterative algorithm used for the FP estimate practical determination is also analyzed and we show the convergence of this recursive scheme, ensured whatever the initialization.