Bayesian Signal Subspace Estimation with Compound Gaussian Sources

International audienceIn this paper, we consider the problem of low dimensional signal subspace estimation in a Bayesian con- text. We focus on compound Gaussian signals embedded in white Gaussian noise, which is a realistic modeling for various array processing applications. Following the Bayesian framework, we derive two algorithms to compute the maximum a posteriori (MAP) estimator and the so-called minimum mean square distance (MMSD) estimator, which minimizes the average natural distance between the true range space of interest and its estimate. Such approaches have shown their interests for signal subspace esti- mation in the small sample support and/or low signal to noise ratio contexts. As a byproduct, we also introduce a generalized version of the complex Bingham Langevin distribution in order to model the prior on the subspace orthonormal basis. Finally, numerical simulations illustrate the performance of the proposed algorithms

Signal subspace change detection in structured covariance matrices

International audienceTesting common properties between covariance matricesis a relevant approach in a plethora of applications. In thispaper, we derive a new statistical test in the context of structuredcovariance matrices. Specifically, we consider low rank signalcomponent plus white Gaussian noise structure. Our aim is totest the equality of the principal subspace, i.e., subspace spannedby the principal eigenvectors of a group of covariance matrices. Adecision statistic is derived using the generalized likelihood ratiotest. As the formulation of the proposed test implies a non-trivialoptimization problem, we derive an appropriate majorizationminimizationalgorithm. Finally, numerical simulations illustratethe properties of the newly proposed detector compared to thestate of the art

Détection de changement de sous-espace signal de matrices de covariance structurées

International audienceTesting common properties between covariance matrices is a relevant problem in a plethora of signal processing applications. In this paper, we derive a new statistical test in the context of structured covariance matrices. Specifically, we consider low rank signal component plus white Gaussian noise structure. Our aim is to test the equality of the principal subspace, i.e., subspace spanned by the principal eigenvectors of a group of covariance matrices. A decision statistic is derived using the generalized likelihood ratio test. As the formulation of the proposed test implies a non-trivial optimization problem, we derive an appropriate majorization-minimization algorithm. Finally, numerical simulations illustrate the properties of the newly proposed detector compared to the state of the art.Le test statistique de propriété communes entre les matrices de covariance tient une place très importante en traitement du signal. Dans cet article, nous proposons un nouveau test statistique dans le contexte de matrices de covariance structurées. Plus précisément, nous considérons un signal de rang faible corrompu par un bruit blanc gaussien additif. Notre objectif est de tester l’égalité du sous-espace signal, c’est à dire les composantes principales communes à un ensemble de matrices de covariance. Dans un premier temps, une statistique de décision est dérivée en utilisant le rapport de vraisemblance généralisée. Le maximum de vraisemblance n’ayant pas d’expression analytique dans ce cas, nous proposons un algorithme d’estimation itératif de type majoration-minimisation. Enfin, nous étudions les propriétés du détecteur proposé à l’aide de simulations numériques

Adaptive Detection of Range Spread Target in Compound-Gaussian Clutter Without Secondary Data

In this paper, we address the problem of detecting a range-spread target embedded in a non-Gaussian clutter with unknown covariance matrix and without using secondary data. We propose a new autoregressive method based on the generalized likelihood ratio test (GLRT) that requires only the cells under test. This method is used to derive two new detectors, corresponding to two different scenarios: a) when all range cells contain the target and share the same covariance matrix (homogeneous clutter), b) when different covariance matrices for different range cells are assumed (heterogeneous clutter). The proposed method is shown to outperform the state of the art on various scenarios in terms of false alarm probability and detection probability, especially in critical scenario as small data records or low number of secondary data. Finally, it exhibits the desired constant false alarm rate (CFAR) property

Robust Mean and Covariance Matrix Estimation Under Heterogeneous Mixed-Effects Model

In this paper, robust mean and covariance matrix estimation are considered in the context of mixed-effects models. Such models are widely used to analyze repeated measures data which arise in several signal processing applications that need to incorporate a same global individuals behavior with a possible individual variations. In this context, most algorithms are based on Gaussian assumption of the observations. Nevertheless, in certain situations in which there exist outliers within the data set, such assumption is not valid and leads to a dramatic performance loss. To overcome this drawback, we design an expectation-conditional maximization either algorithm in which the heterogeneous component is considered as part of the complete data. Then, the proposed algorithm is cast into a parallel scheme, w.r.t. the individuals, in order to alleviate the computational cost and a possible central processor overload. Finally, the proposed algorithm is extended to deal with missing data which refers to the situation where part of the individual responses are unobserved. Numerical simulations are performed in order to assess the performance of the proposed algorithm in regard to robust regression estimators, probabilistic principal component analysis and its recent robust version

Robust calibration of radio interferometers in multi-frequency scenario

International audienceThis paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require com-putationally efficient algorithms to overcome the new technical challenges as large collecting area, wide field of view and huge data volume. Specifically, we study the calibration of radio interferometry stations with significant direction dependent distortions. We propose an iterative robust calibration algorithm based on a relaxed maximum likelihood estimator for a specific context: i) observations are affected by the presence of outliers and ii) parameters of interest have a specific structure depending on frequency. Variation of parameters across frequency is addressed through a distributed procedure, which is consistent with the new radio synthesis arrays where the full observing bandwidth is divided into multiple frequency channels. Numerical simulations reveal that the proposed robust distributed calibration estimator outperforms the conventional non-robust algorithm and/or the mono-frequency case

NenUFAR: Instrument description and science case

International audienceNenuFAR is both a giant extension of the LOFAR and a large standalone instrument in the low-frequency range (10-85 MHz). It was designed in Nançay with national and international collaboration. Antenna radiators were modeled on the LWA antenna design whereas preamplifiers were designed in France. Antennas will be distributed in 96 mini-arrays of 19 dual-polarized elements, densely covering a disk of 400 m in diameter. A few mini-arrays are expected to lie at distances of 2-3 km. A silent control-command system was designed, and the computer dialog with LOFAR defined. Receivers will include the LOFAR backend, a local beamformer and a local correlator. NenuFAR is in construction in Nançay and it was recently granted by the SKA office the official label of SKA pathfinder. Its exploitation will expand the scope of LOFAR scientific studies as well as permit new studies, preparing for SKA science. The NenuFAR concept has many points in common with GURT (the Giant Ukrainian Radio Telescope), with which it shares some technical studies, an its exploitation will benefit from a coordination with UTR-2. We describe the instrument, technical developments and science case