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10
Covariance Structure Maximum Likelihood Estimates in Compound Gaussian Noise : Existence and Algorithm Analysis”, under review at
- IEEE Trans.-SP
"... Abstract—Recently, a new adaptive scheme [Conte et al. (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 squar ..."
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Cited by 82 (37 self)
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Abstract—Recently, a new adaptive scheme [Conte et al. (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 (deterministic or random) and an independent Gaussian vector x, c = x. Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When is assumed deterministic and unknown, the FP is the exact maximum-likelihood (ML) estimate of the noise covariance structure, while when 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 cor-responding 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. Index Terms—Adaptive detection, compound Gaussian, con-stant false alarm rate (CFAR) detector, maximum-likelihood (ML) estimate, spherically invariant random vectors (SIRV). I.
Generalized robust shrinkage estimator and its application to STAP detection problem
- SUBMITTED TO IEEE TRANS. ON SIGNAL PROCESSING
, 2014
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Persymmetric adaptive radar detectors
- IEEE Trans. Aerosp. Electron. Syst
, 2011
"... In the general framework of radar detection, estimation of the Gaussian or non-Gaussian clutter covariance matrix is an important point. This matrix commonly exhibits a particular structure: for instance, this is the case for active systems using a symmetrically spaced linear array with constant pul ..."
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Cited by 6 (1 self)
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In the general framework of radar detection, estimation of the Gaussian or non-Gaussian clutter covariance matrix is an important point. This matrix commonly exhibits a particular structure: for instance, this is the case for active systems using a symmetrically spaced linear array with constant pulse repetition interval. We propose using the particular persymmetric structure of the covariance matrix to improve the detection performance. In this context, this work provides two new adaptive detectors for Gaussian additive noise and non-Gaussian additive noise which is modeled by the spherically invariant random vector (SIRV). Their statistical properties are then derived and compared with simulations. The vast improvement in their detection performance is demonstrated by way of simulations or experimental ground clutter data. This allows for the analysis of the proposed detectors on both real Gaussian and non-Gaussian data. Manuscript received April 22, 2009; revised October 26, 2009; released for publication February 18 2010.
ASYMPTOTIC PROPERTIES OF THE ROBUST ANMF
"... This paper presents two approaches to derive an asymptotic distri-bution of the robust Adaptive Normalized Matched Filter (ANMF). More precisely, the ANMF has originally been derived under the assumption of Gaussian distributed noise where the variance is dif-ferent between the observation under tes ..."
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Cited by 2 (2 self)
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This paper presents two approaches to derive an asymptotic distri-bution of the robust Adaptive Normalized Matched Filter (ANMF). More precisely, the ANMF has originally been derived under the assumption of Gaussian distributed noise where the variance is dif-ferent between the observation under test and the set of secondary data. We propose in this work to relax the Gaussian hypothe-sis: we analyze the ANMF built with robust estimators, namely the M-estimators and the Tyler’s estimator, under the Complex Elliptically Symmetric (CES) distributions framework. In this con-text, we derive two asymptotic distributions for this robust ANMF. Firstly, we combine the asymptotic properties of the robust esti-mators and the Gaussian-based distribution of the ANMF at finite distance. Secondly, we directly derive the asymptotic distribution of the robust ANMF. Then, Monte-Carlo simulations show the good approximation provided by the proposed methods. Moreover, for a non-asymptotic regime, the simulations provide very promising results.
Optimal design of the adaptive normalized matched filter detector,” Submitted to
- IEEE Transactions on Signal Processing
, 2015
"... Abstract-This article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regulariz ..."
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Cited by 1 (1 self)
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Abstract-This article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regularized estimation methods which force by construction the eigenvalues of the scatter estimates to be greater than a positive regularization parameter ρ. This makes them more suitable for high dimensional problems with a limited number of secondary data samples than traditional sample covariance estimates. While an increase of ρ seems to improve the conditioning of the estimate, it might however cause it to significantly deviate from the true covariance matrix. The setting of the optimal regularization parameter is a difficult question for which no convincing answers have thus far been provided. This constitutes the major motivation behind our work. More specifically, we consider the design of the ANMF detector for two kinds of regularized estimators, namely the regularized sample covariance matrix (RSCM), appropriate when the clutter follows a Gaussian distribution and the regularized Tyler estimator (RTE) for non-Gaussian spherically invariant distributed clutters. The rationale behind this choice is that the RTE is efficient in mitigating the degradation caused by the presence of impulsive noises while inducing little loss when the noise is Gaussian. Based on recent random matrix theory results studying the asymptotic fluctuations of the statistics of the ANMF detector when the number of samples and their dimension grow together to infinity, we propose a design for the regularization parameter that maximizes the detection probability under constant false alarm rates. Simulation results which support the efficiency of the proposed method are provided in order to illustrate the gain of the proposed optimal design over conventional settings of the regularization parameter.
Robust anmf test using huber’s m-estimator
- In Sensor Array and Multichannel Signal Processing Workshop (SAM
, 2012
"... Abstract—In many statistical signal processing applications, the quality of the estimation of parameters of interest plays an important role. We focus in this paper, on the estimation of the covariance matrix. In the classical Gaussian context, the Sample Covariance Matrix (SCM) is the most often us ..."
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Cited by 1 (1 self)
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Abstract—In many statistical signal processing applications, the quality of the estimation of parameters of interest plays an important role. We focus in this paper, on the estimation of the covariance matrix. In the classical Gaussian context, the Sample Covariance Matrix (SCM) is the most often used, since it is the Maximum Likelihood estimate. It is easy to manage and has a lot of well-known statistical properties. However it may exhibit poor performance in context of non-Gaussian signals, contaminated or missing data. In that case M-estimators provide a good alternative. In this paper, we extend to the complex data case, a theoretical result already proposed by Tyler in the real data case, deriving the asymptotical distribution of any homogeneous functional of degree 0 of the M-estimates. Then, applying this result to the Adaptive Normalized Matched Filter (ANMF), we obtain a robust ANMF and give the relationship between its Probability of False Alarm (Pfa) and the detection threshold. I.
ASYMPTOTIC DETECTION PERFORMANCE OF THE ROBUST ANMF
"... This paper presents two different approaches to derive the asymp-totic distributions of the robust Adaptive Normalized Matched Filter (ANMF) under both H0 and H1 hypotheses. More precisely, the ANMF has originally been derived under the assumption of partially homogenous Gaussian noise, i.e. where t ..."
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This paper presents two different approaches to derive the asymp-totic distributions of the robust Adaptive Normalized Matched Filter (ANMF) under both H0 and H1 hypotheses. More precisely, the ANMF has originally been derived under the assumption of partially homogenous Gaussian noise, i.e. where the variance is different be-tween the observation under test and the set of secondary data. We propose in this work to relax the Gaussian hypothesis: we analyze the ANMF built with robust estimators, namely the M-estimators and the Tyler’s estimator, under the Complex Elliptically Symmet-ric (CES) distributions framework. In this context, we derive two asymptotic distributions for this robust ANMF. Firstly, we combine the asymptotic properties of the robust estimators and the Gaussian-based distribution of the ANMF at finite distance. Secondly, we di-rectly derive the asymptotic distribution of the robust ANMF.
Asymptotic Detection Performance Analysis of the Robust Adaptive Normalized Matched Filter
"... Abstract—This paper presents two different approaches to derive the asymptotic distributions of the robust Adaptive Normalized Matched Filter (ANMF) under both H0 and H1 hypotheses. More precisely, the ANMF has originally been derived under the assumption of partially homogenous Gaussian noise, i.e. ..."
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Abstract—This paper presents two different approaches to derive the asymptotic distributions of the robust Adaptive Normalized Matched Filter (ANMF) under both H0 and H1 hypotheses. More precisely, the ANMF has originally been derived under the assumption of partially homogenous Gaussian noise, i.e. where the variance is different between the observation under test and the set of secondary data. We propose in this work to relax the Gaussian hypothesis: we analyze the ANMF built with robust estimators, namely the M-estimators and the Tyler’s estimator, under the Complex Elliptically Symmetric (CES) distributions framework. In this context, we analyse two asymptotic performance characterization of this robust ANMF. The first approach consists in exploiting the asymptotic distribution of the different covariance matrix estimators while the second approach is to directly exploit the asymptotic distribution of the ANMF distribution built with these estimates. I.
