Arnaud Breloy

Clutter Subspace Estimation in Low Rank Heterogeneous Noise Context

This paper addresses the problem of the Clutter Subspace Projector (CSP) estimation in the context of a disturbance composed of a Low Rank (LR) heterogeneous clutter, modeled here by a Spherically Invariant Random Vector (SIRV), plus a white Gaussian noise (WGN). In such context, the corresponding LR adaptive filters and detectors require less training vectors than classical methods to reach equivalent performance. Unlike classical adaptive processes, which are based on an estimate of the noise Covariance Matrix (CM), the LR processes are based on a CSP estimate. This CSP estimate is usually derived from a Singular Value Decomposition (SVD) of the CM estimate. However, no Maximum Likelihood Estimator (MLE) of the CM has been derived for the considered disturbance model. In this paper, we introduce the fixed point equation that MLE of the CSP satisfies for a disturbance composed of a LR-SIRV clutter plus a zero mean WGN. A recursive algorithm is proposed to compute this solution. Numerical simulations validate the introduced estimator and illustrate its interest compared to the current state of art.

Low-Complexity Algorithms for Low Rank Clutter Parameters Estimation in Radar Systems

This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. In such a context, adaptive processing based on an estimated orthogonal projector onto the clutter subspace (instead of an estimated covariance matrix) requires less samples than classical methods. The clutter subspace estimate is usually derived from the eigenvalue decomposition of a covariance matrix estimate. However, it has been previously shown that a direct maximum likelihood estimator of the clutter subspace projector can be obtained for the considered context. In this paper, we derive two algorithms based on the block majorization-minimization framework to reach this estimator. These algorithms are shown to be computationally faster than the state of the art, with guaranteed convergence. Finally, the performance of the related estimators is illustrated on realistic Space Time Adaptive Processing for airborne radar simulations.

Robust estimation of the clutter subspace for a Low Rank heterogeneous noise under high Clutter to Noise Ratio assumption

In the context of an heterogeneous disturbance with a Low Rank (LR) structure (called clutter), one may use the LR approximation for filtering and detection process. These methods are based on the projector onto the clutter subspace instead of the noise covariance matrix. In such context, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical ones. The main problem is then the estimation of the clutter subspace instead of the noise covariance matrix itself. Maximum Likelihood estimator (MLE) of the clutter subspace has been recently studied for a noise composed of a LR Spherically Invariant Random Vector (SIRV) plus a white Gaussian Noise (WGN). This paper focuses on environments with a high Clutter to Noise Ratio (CNR). An original MLE of the clutter subspace is proposed in this context. A cross-interpretation of this new result and previous ones is provided. Validity and interest - in terms of performance and robustness - of the different approaches are illustrated through simulation results.

Robust Covariance Matrix Estimation in Heterogeneous Low Rank Context

This paper addresses the problem of robust covariance matrix (CM) estimation in the context of a disturbance composed of a low rank (LR) heterogeneous clutter plus an additive white Gaussian noise. The LR clutter is modeled by a spherically invariant random vector with assumed high clutter-to-noise ratio. In such a context, adaptive process should require less training samples than classical methods to reach equivalent performance as in a “full rank” clutter configuration. The main issue is that classical robust estimators of the CM cannot be computed in the undersampled configuration. To overcome this issue, the current approach is based on regularization methods. Nevertheless, most of these solutions are enforcing the estimate to be well conditioned, while in our context, it should be LR structured. This paper, therefore, addresses this issue and derives an algorithm to compute the maximum likelihood estimator of the CM for the considered disturbance model. Several relaxations and robust generalizations of the result are discussed. Performance is finally illustrated on numerical simulations and on a space time adaptive processing for airborne radar application.

Asymptotic detection performance analysis of the robust Adaptive Normalized Matched Filter

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 Tylers 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.

CFAR property and robustness of the lowrank adaptive normalized matched filters detectors in low rank compound gaussian context

In the context of a heterogeneous disturbance with a Low Rank (LR) structure (referred to as clutter), one may use the LR approximation for detection process. Indeed, in such context, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical ones. The LR approximation consists of canceling the clutter rather than whitening the whole noise. The main problem is then the estimation of the clutter subspace instead of the noise covariance matrix itself. Maximum Likelihood estimators (MLE), under different hypothesis [1][2][3], of the clutter subspace have been recently proposed for a noise composed of a LR Compound Gaussian (CG) clutter plus a white Gaussian Noise (WGN). This paper focuses on the numerical analysis of performances of the LR Adaptive Normalized Matched Filter (LR-ANMF) detectors build from these different clutter subspace estimators. Numerical simulations and a real data set illustrate their CFAR property with respect to heterogeneity and robustness to outliers.

New asymptotic properties for the robust ANMF

The purpose of this paper is to derive new asymptotic properties of the robust adaptive normalized matched filter (ANMF). More precisely, the ANMF built with Tyler estimator (TyE-ANMF) is analyzed under the framework of complex elliptically symmetric (CES) distributions. We show that the distribution of TyE-ANMF can be accurately approximated by the well-known distribution of the ANMF built with the sample covariance matrix (SCM-ANMF) under the Gaussian assumption. To that end, the asymptotic properties of the difference between both ANMF detectors are derived. By comparison with the state of the art, the asymptotic properties of the TyE-ANMF are shown to be better approximated by the SCM-ANMF rather than using the NMF (test built with the true CM). Some Monte-Carlo simulations support that claim and demonstrate the interest of this theoretical result.

A subspace approach for shrinkage parameter selection in undersampled configuration for Regularised Tyler Estimators

Regularized Tyler Estimators (RTE) have raised attention over the past years due to their attractive performance over a wide range of noise distributions and their natural robustness to outliers. Developing adaptive methods for the selection of the regularisation parameter α is currently an active topic of research. Indeed, the bias-performance compromise of RTEs highly depends on the considered application. Thus, finding a generic rule that is optimal for every criterion and/or data configurations is not straightforward. This issue is addressed in this paper for undersampled configurations (number of samples lower than the dimension of the data). The paper proposes a new regularisation parameter selection based on a subspace reduction approach. The performance of this method is investigated in terms of estimation accuracy and for adaptive detection purposes, both on simulation and real data.

Performance analysis of direction-of-arrival and polarization estimation using a non-uniform linear COLD array

The co-centered orthogonal loop and dipole array is commonly used in sources localization using jointly the polarization and spatial diversities. For this type of array, most of the performance analysis studies present in the literature rely on asymptotic regimes. In this paper, we focus on the performance analysis in the non-asymptotic region. More precisely, we derive the McAulay-Hofstetter bound on the source parameters estimation problem, namely, the direction-of-arrival and polarization parameters. Such bound allows us to predict the so-called breakdown point location, which delimits the optimal operational area of any unbiased efficient algorithm. Additionally, we propose an iterative based Maximum-Likelihood algorithm to asses for the tightness of the proposed bound. Finally, a numerical example is provided to corroborate the presented result.

Block majorization-minimization algorithms for low-rank clutter subspace estimation

This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. We derive two algorithms based on the block majorization-minimization framework to reach the maximum likelihood estimator of the considered model. These algorithms are shown to be computationally faster than the state of the art, with guaranteed convergence. Finally, the performance of the related estimators is illustrated in terms of estimation accuracy and computation speed.