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Bandiera F.,University of Salento | Besson O.,ISAE University | Ricci G.,University of Salento
IEEE Transactions on Signal Processing | Year: 2011

In this paper, we deal with the problem of adaptive detection of distributed targets embedded in colored noise modeled in terms of a compound-Gaussian process and without assuming that a set of secondary data is available. The covariance matrices of the data under test share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure and possibly the power levels are assumed to be random, with appropriate distributions. Within this framework we propose GLRT-based and ad-hoc detectors. Some simulation studies are presented to illustrate the performances of the proposed algorithms. The analysis indicates that the Bayesian framework could be a viable means to alleviate the need for secondary data, a critical issue in heterogeneous scenarios. © 2011 IEEE.


Bandiera F.,University of Salento | Besson O.,ISAE University | Ricci G.,University of Salento
IEEE Transactions on Signal Processing | Year: 2010

We address the problem of adaptive detection of a signal of interest embedded in colored noise modeled in terms of a compound-Gaussian process. The covariance matrices of the primary and the secondary data share a common structure while having different power levels. A Bayesian approach is proposed here, where both the power levels and the structure are assumed to be random, with some appropriate distributions. Within this framework we propose MMSE and MAP estimators of the covariance structure and their application to adaptive detection using the NMF test statistic and an optimized GLRT herein derived. Some results, also in comparison with existing algorithms, are presented to illustrate the performances of the proposed detectors. The relevant result is that the solutions presented herein allows to improve the performance over conventional ones, especially in presence of a small number of training data. © 2010 IEEE.


Deu J.-F.,French National Conservatory of Arts and Crafts | Matignon D.,ISAE University
Computers and Mathematics with Applications | Year: 2010

A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model. © 2009 Elsevier Ltd. All rights reserved.


Bury Y.,ISAE University | Jardin T.,ISAE University
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2012

This Letter aims at understanding the dynamical process that leads to the onset of chaos in the flow past a blunt-based axisymmetric bluff body. On the basis of direct numerical simulations, conducted for Reynolds numbers ranging from 100 to 900, we show that the flow undergoes multiple transitions, successively giving rise to the SS, RSP a, RSP b, RSP c and RSB wake states. In particular, the RSP c state, revealed in this work via long-term computations, is characterized by intermittent vortex stretching denoting the onset of chaos before the symmetry breaking and the occurrence of the RSB state. © 2012 Elsevier B.V.


Jardin T.,ISAE University | Bury Y.,ISAE University
Journal of Fluid Mechanics | Year: 2012

We numerically investigate the influence of pulsed tangential jets on the flow past a circular cylinder. To this end a spectral-Lagrangian dual approach is used on the basis of time-series data. The analysis reveals that the flow response to unsteady forcing is driven by strong interactions between shear layers and pulsed jets. The latter preferentially lead to either the lock-on regime or the quasi-steady vortex feeding regime whether the excitation frequency is of the order of, or significantly greater than, the frequency of the natural instability. The intensity of the wake vortices is mainly influenced by the momentum coefficient through the introduction of opposite-sign vorticity in the shear layers. This feature is emphasized using a modal-based time reconstruction, i.e. by reconstructing the flow field upon a specific harmonic spectrum associated with a characteristic time scale. The quasi-steady regime exhibits small-scale counter-rotating vortices that circumscribe the separated region. In the lock-on regime, atypical wake patterns such as 2P or P + S can be observed, depending on the forcing frequency and the momentum coefficient, highlighting remarkable analogies with oscillating cylinders. © 2012 Cambridge University Press.


Abramovich Y.I.,W R Systems, LTD | Besson O.,ISAE University
IEEE Transactions on Signal Processing | Year: 2013

In Abramovich et al. [Bounds on Maximum Likelihood Ratio-Part I: Application to Antenna Array Detection- EstimationWith PerfectWavefront Coherence, IEEE Trans. Signal Process., vol. 52, pp. 1524-1536, June 2004], it was demonstrated, for multivariate complex Gaussian distribution, that the probability density function (p.d.f.) of the likelihood ratio (LR) for the (unknown) actual covariance matrix does not depend on this matrix and is fully specified by the matrix dimension and the number of independent training samples . This invariance property hence enables one to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically as likely as . This expected likelihood quality assessment allowed significant improvement of MUSIC DOA estimation performance in the so-called threshold area, and for diagonal loading and TVAR model order selection in adaptive detectors. Recently, the so-called complex elliptically symmetric (CES) distributions have been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix . Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario ( T ≤ M ) while Part II deals with the undersampled scenario (T ≤ M ).. © 1991-2012 IEEE.


Besson O.,ISAE University | Abramovich Y.I.,W R Systems, LTD
IEEE Transactions on Signal Processing | Year: 2013

In the first part of these two papers, we extended the expected likelihood approach originally developed in the Gaussian case, to the broader class of complex elliptically symmetric (CES) distributions and complex angular central Gaussian (ACG) distributions. More precisely, we demonstrated that the probability density function (p.d.f.) of the likelihood ratio (LR) for the (unknown) actual scatter matrix does not depend on the latter: it only depends on the density generator for the CES distribution and is distribution-free in the case of ACG distributed data, i.e., it only depends on the matrix dimension and the number of independent training samples , assuming that (T ≤ M) Additionally, regularized scatter matrix estimates based on the EL methodology were derived. In this second part, we consider the under-sampled scenario (T ≤ M) which deserves specific treatment since conventional maximum likelihood estimates do not exist. Indeed, inference about the scatter matrix can only be made in the -dimensional subspace spanned by the columns of the data matrix. We extend the results derived under the Gaussian assumption to the CES and ACG class of distributions. Invariance properties of the under-sampled likelihood ratio evaluated at are presented. Remarkably enough, in the ACG case, the p.d.f. of this LR can be written in a rather simple form as a product of beta distributed random variables. The regularized schemes derived in the first part, based on the EL principle, are extended to the under-sampled scenario and assessed through numerical simulations.. © 1991-2012 IEEE.


Besson O.,ISAE University | Dobigeon N.,Toulouse 1 University Capitole | Tourneret J.-Y.,Toulouse 1 University Capitole
IEEE Transactions on Signal Processing | Year: 2011

We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace ${\mmb U}$ and its estimate $\mathhat{\mmb U}$ may not be adequate as the MSE is not the natural metric in the Grassmann manifold $GN,p , i.e., the set of $p$-dimensional subspaces in $\BBRN. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between ${\mmb U}$ and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of ${\mmb U}$ but entails computing the principal eigenvectors of the posterior mean of ${\mmb{UU}}T. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative examples including a linear Gaussian model for the data and Bingham or von Mises Fisher prior distributions for ${\mmb U}$. In all scenarios, posterior distributions are derived and the MMSD estimator is obtained either analytically or implemented via a Markov chain Monte Carlo simulation method. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of ${\mmb U}$. An application to hyperspectral imagery is finally investigated. © 2011 IEEE.


Besson O.,ISAE University | Bidon S.,ISAE University
Signal Processing | Year: 2013

We propose a Bayesian approach to robust adaptive beamforming which entails considering the steering vector of interest as a random variable with some prior distribution. The latter can be tuned in a simple way to reflect how far is the actual steering vector from its presumed value. Two different priors are proposed, namely a Bingham prior distribution and a distribution that directly reveals and depends upon the angle between the true and presumed steering vector. Accordingly, a non-informative prior is assigned to the interference plus noise covariance matrix R, which can be viewed as a means to introduce diagonal loading in a Bayesian framework. The minimum mean square distance estimate of the steering vector as well as the minimum mean square error estimate of R are derived and implemented using a Gibbs sampling strategy. Numerical simulations show that the new beamformers possess a very good rate of convergence even in the presence of steering vector errors. © 2012 Elsevier B.V. All rights reserved.


Besson O.,ISAE University | Abramovich Y.I.,W R Systems, LTD
IEEE Signal Processing Letters | Year: 2013

The Slepian-Bangs formula provides a very convenient way to compute the Fisher information matrix (FIM) for Gaussian distributed data. The aim of this letter is to extend it to a larger family of distributions, namely elliptically contoured (EC) distributions. More precisely, we derive a closed-form expression of the FIM in this case. This new expression involves the usual term of the Gaussian FIM plus some corrective factors that depend only on the expectations of some functions of the so-called modular variate. Hence, for most distributions in the EC family, derivation of the FIM from its Gaussian counterpart involves slight additional derivations. We show that the new formula reduces to the Slepian-Bangs formula in the Gaussian case and we provide an illustrative example with Student distributions on how it can be used. © 1994-2012 IEEE.

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