Clutter Subspace Estimation in Low Rank Heterogeneous Noise Context

Abstract

International audienceThis 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

A robust signal subspace estimator

“…Otherwise, suppose σ 2 τ k and β k τ k , then ρ(Π R , z k ) ≈ 1/(σ 2 +β k ): the contribution of the sample is not canceled but is lowered proportionally to the outlier to noise ratio (ONR). The proposed estimator is therefore susceptible to naturally reject samples that would perturb the subspace estimation process, which is not the case of previous solutions [11,12,14].…”

“…Nevertheless, [11,12] exhibited the fact that these CM estimators may reject outliers as well as samples with high SNR (that should rather be promoted in the subspace estimation process). Hence, the M -estimators, may not be the most adapted tool to construct a robust signal subspace estimator.…”

“…In [11][12][13][14][15] were developed direct estimators of the signal subspace, that do not rely on an intermediate CM estimate. Especially, [11][12][13][14] considered the case of Compound Gaussian [10] sources, leading robust subspace estimators from the point of view of the signal distribution. In this work, we propose to develop a new estimator, that is also robust to the introduction of outliers.…”

“…In comparison, the exact MLE (assuming non-equals c r ) has no closed form. While different algorithms to compute this exact MLE are proposed in [11,12], it is shown in [11] that neglecting the difference between eigenvalues has few impact in terms of subspace estimation accuracy. Note that we will test our results on contexts that do not fit the hypothesis c r = 1 ∀r in the simulation section.…”

Robust adaptive detection of buried pipes using GPR

“…Several strategies exist to reduce the needed number of secondary data. For example, if the clutter is known to be low-rank and this rank is known, the covariance matrix can be replaced by an orthogonal projector [40], [41]. In most cases, the covariance matrix is known to have a particular structure which allows to reduce the number of variables we wish to estimate [42], [43], [44].…”