Clutter Subspace Estimation in Low Rank Heterogeneous Noise Context

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

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

International audienceIn the context of an 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 on cancelling 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 performances of the LR Adaptive Normalized Matched Filter (LR-ANMF) detector based on these different clutter subspace estimators. Numerical simulations illustrate its CFAR property and robustness to outliers

Multistatic and Multiple Frequency Imaging Resolution Analysis-Application to GPS-Based Multistatic Radar

International audienceThis paper focuses on the computation of the generalized ambiguity function (GAF) of a multiple antennas multiple frequencies radar system (MAMF). This study provides some insights into the definition of resolution parameters of a MAMF radar system. It turns out that the range and azimuth resolutions are not the most suitable criteria to specify the MAMF radar resolution. Therefore a new set of resolution parameters is introduced like the resolution ellipse which expresses the resolution anywhere in the image plane or δ→max, (δ→min) which expresses the highest (lowest) bound of the spatial radar resolution. To point out the pertinence of our study, we illustrate it with a MAMF radar system built around GPS satellites. The effect of the radar system geometry on resolution is investigated. For several scenarios, the GAF and its numerical form, the point spread function (PSF), are computed and their results are compared

Through the Wall Radar Imaging via Kronecker-structured Huber-type RPCA

The detection of multiple targets in an enclosed scene, from its outside, is a challenging topic of research addressed by Through-the-Wall Radar Imaging (TWRI). Traditionally, TWRI methods operate in two steps: first the removal of wall clutter then followed by the recovery of targets positions. Recent approaches manage in parallel the processing of the wall and targets via low rank plus sparse matrix decomposition and obtain better performances. In this paper, we reformulate this precisely via a RPCA-type problem, where the sparse vector appears in a Kronecker product. We extend this approach by adding a robust distance with flexible structure to handle heterogeneous noise and outliers, which may appear in TWRI measurements. The resolution is achieved via the Alternating Direction Method of Multipliers (ADMM) and variable splitting to decouple the constraints. The removal of the front wall is achieved via a closed-form proximal evaluation and the recovery of targets is possible via a tailored Majorization-Minimization (MM) step. The analysis and validation of our method is carried out using Finite-Difference Time-Domain (FDTD) simulated data, which show the advantage of our method in detection performance over complex scenarios

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

International audienceIn 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

Performances of Low Rank Detectors Based on Random Matrix Theory with Application to STAP

International audienceThe paper addresses the problem of target detection embedded in a disturbance composed of a low rank Gaussian clutter and a white Gaussian noise. In this context, it is interesting to use an adaptive version of the Low Rank Normalized Matched Filter detector, denoted LR-ANMF, which is a function of the estimation of the projector onto the clutter subspace. In this paper, we show that the LR-ANMF detector based on the sample covariance matrix is consistent when the number of secondary data K tends to infinity for a fixed data dimension m but not consistent when m and K both tend to infinity at the same rate, i.e. m/K → c ∈ (0, 1]. Using the results of random matrix theory, we then propose a new version of the LR-ANMF which is consistent in both cases and compare it to a previous version, the LR-GSCM detector. The application of the detectors from random matrix theory on STAP (Space Time Adaptive Processing) data shows the interest of our approach

Une nouvelle décomposition tensorielle orthogonale, l'Alternative Unfolding HOSVD. Application au STAP Polarimétrique

National audienceDans cet article, on propose d'étendre les méthodes rang faible de traitement d'antenne à des cas multidimensionnelles. Deux types de méthodes peuvent être envisagés : l'approche vectorielle et l'approche tensorielle. L'approche vectorielle consiste à mettre les données sous forme de vecteurs et d'appliquer les traitements classiques. Dans ce cas, la structure des données n'est pas prise en compte ce qui peut nuire aux performances et à la robustesse. Afin d'éviter ces problèmes, une approche tensorielle est proposée. On s'intéressera plus particulièrement au cas du Space Time Adaptive Processing (STAP) rang faible. Afin de prendre en compte la nature des données STAP, une nouvelle décomposition tensorielle est proposée : la AU-HOSVD. A partir de cette décomposition, un filtre STAP tensoriel rang faible est proposé. Afin d'illustrer l'intérêt de notre approche, on l'applique à un cas particulier de STAP multidimensionnel : le STAP polarimétrique. On montre grâce à des simulations numériques de Signal to Interference plus Noise Ratio (SINR) loss que les performances de nos filtres sont meilleures que celles données par une approche vectorielle

Low-rank filter and detector for multidimensional data based on an alternative unfolding HOSVD: application to polarimetric STAP

International audienceThis paper proposes an extension of the classical Higher Order Singular Value Decomposition (HOSVD), namely the Alternative Unfolding HOSVD (AU-HOSVD), in order to exploit the correlated information in multidimensional data. We show that the properties of the AU-HOSVD are proven to be the same as those for HOSVD: the orthogonality and the low-rank (LR) decomposition. We next derive LR-filters and LR-detectors based on AU-HOSVD for multidimensional data composed of one LR structure contribution. Finally, we apply our new LR-filters and LR-detectors in Polarimetric Space Time Adaptive Processing (STAP). In STAP, it is well known that the response of the background is correlated in time and space and has a LR structure in space-time. Therefore, our approach based on AU-HOSVD seems to be appropriate when a dimension (like polarimetry in this paper) is added. Simulations based on Signal to Interference plus Noise Ratio (SINR) losses, Probability of Detection (Pd) and Probability of False Alarm (Pfa) show the interest of our approach: LR-filters and LR-detectors which can be obtained only from AU-HOSVD outperform the vectorial approach and those obtained from a single HOSVD

New SAR Target Imaging Algorithm based on Oblique Projection for Clutter Reduction

International audienceWe have developed a new Synthetic Aperture Radar (SAR) algorithm based on physical models for the detection of a Man-Made Target (MMT) embedded in strong clutter (trunks in a forest). The physical models for the MMT and the clutter are represented by low-rank subspaces and are based on scattering and polarimetric properties. Our SAR algorithm applies the oblique projection of the received signal along the clutter subspace onto the target subspace. We compute its statistical performance in terms of probabilities of detection and false alarms. The performances of the proposed SAR algorithm are improved compared to those obtained with existing SAR algorithms: the MMT detection is greatly improved and the clutter is rejected. We also studied the robustness of our new SAR algorithm to interference modeling errors. Results on real FoPen (Foliage Penetration) data showed the usefulness of this approach