Guillaume Ginolhac

Performance of Two Low-Rank STAP Filters in a Heterogeneous Noise

This paper considers the Space Time Adaptive Processing (STAP) problem where the disturbance is modeled as the sum of a Low-Rank (LR) Spherically Invariant Random Vector (SIRV) clutter and a zero-mean white Gaussian noise. To derive our adaptive LR-STAP filters, the estimation of the projector onto the clutter subspace is performed from the Sample Covariance Matrix (SCM) and the Normalized Sample Covariance Matrix (NSCM). We compute the theoretical performance of both corresponding LR-STAP filters through the analysis of the Signal to Interference plus Noise Ratio (SINR) Loss, based on a perturbation analysis. Numerical simulations validate the theoretical formula and allow to show that the LR-STAP filter built from the SCM performance does not depend on the heterogeneity of the SIRV clutter whereas the LR-STAP filter built from the NSCM performance does.

Three-mode data set analysis using higher order subspace method: application to sonar and seismo-acoustic signal processing

In this paper, a three-mode subspace technique based on higher order singular value decomposition (HOSVD) is presented. This technique is then used in the context of wave separation. It can be regarded as the extension to three-mode arrays of the well-known subspace technique proposed by Eckart and Young (Psychometrica 1 (1936) 211) for matrices. Three-mode data sets are increasingly encountered in signal processing and are classically processed using matrix algebra techniques. The proposed approach aims to process naturally three-mode data with multilinear algebra tools. So in the proposed algorithms, the structure of the data set is preserved and no reorganization is performed on it. The choice of HOSVD for subspace method is explained, studying the rank definition for three-mode arrays and orthogonality between subspaces. A projector formulation for three-mode signal and noise subspaces is also given and the improvement of separation with the three-mode approach over a componentwise approach is shown. We study two applications for the proposed Higher Order Subspace approach: the reverberation problem in sonar, and the polarized seismo-acoustic wave separation problem. For the first application, we propose a three-mode version of the Principal Component Inverse algorithm (IEEE Trans. Aerospace Electron. Systems 30(1) (1994) 55). We apply the proposed technique on simulated data as well as on real sonar data where the three modes are angle, delay and distance. For the second application, we consider the polarization of the seismic wave as the third mode (in addition to time and distance modes) and show the resulting improvement of wave separation using the proposed Higher Order approach.

Spatio-temporal adaptive detector in non-homogeneous and low-rank clutter

Reducing the number of secondary data used to estimate the Clutter Covariance Matrix (CCM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Low rank CCM estimates have already been proposed but only for homogeneous and Gaussian clutter. We propose in this paper to extend the low-rank CCM methods for heterogeneous and/or non-Gaussian clutter. We derive a new detector based on low-rank techniques and exploiting properties of the Normalized Sample Covariance Matrix (NSCM). This detector is shown to exhibit a smaller SNR loss than classical STAP detectors. Moreover, the new detector has a texture-CFAR property with respect to non-Gaussian SIRV model and has more robust behavior when some targets are present in the secondary data. We also give experimental comparison results between the classical STAP detectors and the new one for STAP data.

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

This 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.

Exploiting persymmetry for low-rank Space Time Adaptive Processing

Reducing the number of secondary data used to estimate the Covariance Matrix (CM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Within this framework, the Low-Rank (LR) structure of the clutter is well-known and the corresponding LR STAP filters have been shown to exhibit a smaller SNR loss than classical STAP filters, 2r secondary data (r is the clutter rank) instead of 2m (m is the data size) is needed to reach a 3dB SNR loss. By using other features of the radar system, other properties of the CM could be exploited to further reduce the number of secondary data: this is the case for active systems using a symmetrically spaced linear array with constant pulse repetition interval. In this context, we propose to combine the resulting persymmetric property of the CM and the LR structure of the clutter to perform the CM estimation. In this paper, the resulting STAP filter is shown, both theoretically and experimentally, to exhibit good performance with fewer secondary data: 3dB SNR loss is achieved with only r secondary data.

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.

GPS ISAR passive system characterization using Point Spread Function

This paper presents research results in space-surface multistatic synthetic aperture radar (SS-MSAR) with non cooperative GPS satellites. The goal of this paper is to characterize such a system in an ISAR context, with a moving ground target.point spread function (PSF) are defined and used in this work to estimate the performance in term of resolution. These criteria are computed, and compared, for several scenarios with targets of different velocities.

Derivation of the Bias of the Normalized Sample Covariance Matrix in a Heterogeneous Noise With Application to Low Rank STAP Filter

In a previous work, we have developed a low-rank (LR) spatio-temporal adaptive processing (STAP) filter when the disturbance is modeled as the sum of a low-rank spherically invariant random vector (SIRV) clutter and a zero-mean white Gaussian noise. This LR-STAP filter is built from the normalized sample covariance matrix (NSCM) and exhibits good robustness properties to secondary data contamination by target components. In this correspondence, we derive the bias of the NSCM with this noise model. We show that the eigenvectors estimated from the NSCM are unbiased. The new expressions of the expectation of NSCM eigenvalues are also given. From these results, we also show that the estimate of the clutter subspace projector based on the NSCM used in our LR-STAP is a consistent estimate of the true one. Results on numerical data validates the theoretical approach.

SAR Processors Based on Signal or Interference Subspace Detector

In this paper, we present a new synthetic aperture radar (SAR) processor relying on subspace detectors. The scattering pattern of the constituent element of the man-made target (MMT) to detect is used to improve the detection capabilities. In the particular case of foliage penetration (FOPEN), we propose to reduce the probability of false alarms by considering the scattering pattern of almost vertical trunks (modeled here as dielectric cylinders). New subspace detectors are derived to look for either an interference or a target element in a noisy environment. A new processor based on these subspace detectors is successively applied to simulated data. In addition, results obtained with real data reveal a significant improvement in the detection capabilities both in comparison with a classical SAR processor and with the subspace signal detector SAR (SSDSAR) processor (without interference model).