T. W. Anderson, An Introduction to Multivariate Statistical Analysis

E. Conte, A. De-maio, and G. Ricci, Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection, IEEE Transactions on Signal Processing, vol.50, issue.8, pp.1908-1915, 2002.
DOI : 10.1109/TSP.2002.800412

E. Conte, A. De-maio, and G. Ricci, Covariance matrix estimation for adaptive CFAR detection in compound-Gaussian clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.38, issue.2, pp.415-426, 2002.
DOI : 10.1109/TAES.2002.1008976

K. Yao, M. K. Simon, and E. Biglieri, A Unified Theory on Wireless Communication Fading Statistics based on SIRV, Fifth IEEE workshop on SP advances in Wireless Communications, 2004.

T. J. Barnard and F. Khan, Statistical Normalization of Spherically Invariant Non-Gaussian Clutter, IEEE Journal of Oceanic Engineering, vol.29, issue.2, pp.303-309, 2004.
DOI : 10.1109/JOE.2004.828204

K. Yao, A representation theorem and its application to spherically invariant random processes, IEEE Trans. on IT, vol.19, pp.600-608, 1973.

E. Conte, M. Lops, and G. Ricci, Adaptive Radar Detection in Compound-Gaussian Clutter, Proceedings of Eusipco'94, pp.526-529, 1994.

M. Abramowitz, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

C. Annexe, First and Second Order Moments of the Normalized Sample Covariance Matrix of Spherically Invariant R REFERENCES

E. Conte, M. Lops, and G. Ricci, Asymptotically optimum radar detection in compound-Gaussian clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.31, issue.2, pp.617-625, 1995.
DOI : 10.1109/7.381910

F. Gini, Sub-optimum coherent radar detection in a mixture of Kdistributed and Gaussian clutter, IEE Proc. Radar, Sonar and Navigation, pp.39-48, 1997.

E. Jay, J. P. Ovarlez, D. Declercq, and P. Duvaut, BORD: bayesian optimum radar detector, Signal Processing, vol.83, issue.6, pp.1151-1162, 2003.
DOI : 10.1016/S0165-1684(03)00034-3

E. Jay, Détection en environnement non-Gaussien, 2002.

K. Yao, A representation theorem and its applications to spherically invariant random processes, IEEE Trans. Inform. Theory, vol.19, issue.5, pp.600-608, 1973.

J. B. Billingsley, Ground Clutter Measurements for Surface-Sited Radar, 1993.

E. J. Kelly, An Adaptive Detection Algorithm, IEEE Transactions on Aerospace and Electronic Systems, vol.22, issue.2, pp.115-127, 1986.
DOI : 10.1109/TAES.1986.310745

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, A CFAR adaptive matched filter detector, IEEE Transactions on Aerospace and Electronic Systems, vol.28, issue.1, pp.208-216, 1992.
DOI : 10.1109/7.135446

E. Conte, M. Lops, and G. Ricci, Adaptive radar detection in compound- Gaussian clutter, Proc. of the European Signal Processing Conf, 1994.

F. Gini, M. V. Greco, and L. Verrazzani, Detection problem in mixed clutter environment as a Gaussian problem by adaptive preprocessing, Electronics Letters, vol.31, issue.14, pp.1189-1190, 1995.
DOI : 10.1049/el:19950808

R. S. Raghavan and N. B. Pulsone, A generalization of the adaptive matched filter receiver for array detection in a class of a non-Gaussian interference, Proc. of the Adaptive Sensor Array Processing (ASAP) Workshop, pp.499-517, 1996.

F. Gini and M. V. Greco, Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter, Signal Processing, vol.82, issue.12, pp.1847-1859, 2002.
DOI : 10.1016/S0165-1684(02)00315-8

R. A. Horn and C. R. Johnson, Matrix analysis, 1985.

F. Pascal, J. P. Ovarlez, P. Forster, and P. Larzabal, Constant false alarm rate detection in spherically invariant random processes, Proc. of the European Signal Processing Conf, pp.2143-2146, 2004.

F. Pascal, P. Forster, J. P. Ovarlez, and P. Larzabal, Theoretical analysis of an improved covariance matrix estimator in non-Gaussian noise, Proc. IEEE-ICASSP, pp.69-72, 2005.
URL : https://hal.archives-ouvertes.fr/halshs-00158387

D. F. Annexe, Y. Pascal, J. Chitour, P. Ovarlez, P. Forster et al., Covariance Structure Maximum Likelihood Estimates in Comp Publications Revues à comité de lectureCovariance Structure Maximum Likelihood Estimates in Compound Gaussian Noise : Existence and Algorithm AnalysisPerformance Analysis of Covariance Matrix Estimates in Impulsive NoiseFirst and Second Order Moments of the Normalized Sample Covariance Matrix of Spherically Invariant Random Vectors, An Improved Estimation Scheme for the GLRT Detection in Non Gaussian Noise, 2006.

C. F. Pascal, J. Ovarlez, P. Forster, P. Larzabal-[-c2-]-f, J. Pascal et al., Constant False Alarm Rate Detection in Spherically Invariant Random ProcessesRadar Detection in Compound-Gaussian ClutterBayesian Optimum Radar Detector Performance Against Ground DataTheoretical Analysis of an Improved Covariance Matrix Estimator in Non-Gaussian Noise, Conférences avec actes et à comité de lecture Proc. of the IEEE-RADAR 2004 Proc. of the IEEE International Conference on Acoustics , Speech, and Signal Processing, ICASSP-05Propriété CFAR-Matrice du Détecteur BORD -Application Radar sur Signaux Expérimentaux non Gaussien Actes du Vingtième Colloque GRETSI 2005, pp.2143-2146, 2004.

J. [. Pascal, P. Ovarlez, P. Forster, and . Larzabal, On a SIRV-CFAR detector with radar experimentations in impulsive noise Publications Séminaires [S1]Utilisation de Techniques non Gaussiennes pour la Détection sur des Images Polarimétriques Journée scientifique "Idendification RadarDétection et Estimation en Environnement Non Gaussien -Application sur données réelles, 2005 et Janvier 2006. [S3] "Détection Radar en Environnement de Fouillis Non-Gaussien", Comité d'Evaluation et d'Orientation (CEO), 2004.

R. Pascal, Détection en environnement non Gaussien : loi d'un rapport de vraisemblance, 2003.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1964.
DOI : 10.1119/1.1972842

R. A. Altes, Target position estimation in radar and sonar, and generalized ambiguity analysis for maximum likelihood parameter estimation, Proceedings of the IEEE, vol.67, issue.6, pp.920-930, 1979.
DOI : 10.1109/PROC.1979.11355

T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 1984.

T. J. Barnard and D. D. Weiner, Non-Gaussian clutter modeling with generalized spherically invariant random vectors, IEEE Transactions on Signal Processing, vol.44, issue.10, pp.2384-2390, 1996.
DOI : 10.1109/78.539023

S. Bausson, F. Pascal, P. Forster, J. Ovarlez, and P. Larzabal, First- and Second-Order Moments of the Normalized Sample Covariance Matrix of Spherically Invariant Random Vectors, IEEE Signal Processing Letters, vol.14, issue.6, 2006.
DOI : 10.1109/LSP.2006.888400
URL : https://hal.archives-ouvertes.fr/halshs-00158262

J. B. Billingsley, Ground Clutter Measurements for Surface-Sited Radar, 1993.

E. Conte and M. Longo, Characterization of radar clutter as a spherically invariant random process, IEE Proc.-Pt.F, pp.191-197, 1987.

E. Conte, M. Longo, and M. Lops, Modelling and simulation of non-Rayleigh radar clutter, IEE Proc.-Pt.F, pp.121-138, 1991.
DOI : 10.1049/ip-f-2.1991.0018

E. Conte and G. Ricci, Performance prediction in compound-Gaussian clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.30, issue.2, pp.611-616, 1994.
DOI : 10.1109/7.272284

E. Conte and G. Ricci, Sensitivity study of GLRT detection in compound-Gaussian clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.34, issue.1, pp.308-316, 1998.
DOI : 10.1109/7.640288

E. Conte, M. Lops, and G. Ricci, Incoherent radar detection in compound-Gaussian clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.35, issue.3, pp.790-800, 1999.
DOI : 10.1109/7.784052

E. Conte, A. De-maio, and C. Galdi, Signal detection in compound-Gaussian noise: Neyman-Pearson and CFAR detectors, IEEE Transactions on Signal Processing, vol.48, issue.2, pp.419-428, 2000.
DOI : 10.1109/78.823969

A. Farina, A. Russo, and F. A. Studer, Advanced models of target and disturbances and related processors, Proc. CCIR, pp.151-158, 1985.

A. Farina, A. Russo, F. Scannapieco, and S. Barbarossa, Theory of radar detection in coherent Weibull clutter, IEE Proceedings F Communications, Radar and Signal Processing, vol.134, issue.2, pp.174-190, 1987.
DOI : 10.1049/ip-f-1.1987.0034

F. Gini, Sub-optimum coherent radar detection in a mixture of K-distributed and Gaussian clutter, IEE Proceedings - Radar, Sonar and Navigation, vol.144, issue.1, pp.39-48, 1997.
DOI : 10.1049/ip-rsn:19970967

F. Gini, A cumulant-based adaptive technique for coherent radar detection in a mixture of K-distributed clutter and Gaussian disturbance, IEEE Transactions on Signal Processing, vol.45, issue.6, pp.1507-1519, 1997.
DOI : 10.1109/78.599993

F. Gini, M. V. Greco, A. Farina, and P. Lombardo, Optimum and mismatched detection against K-distributed plus Gaussian clutter, IEEE Trans.-AES, vol.34, issue.3, pp.860-876, 1998.

M. V. Gini, A. Greco, and . Farina, Clairvoyant and adaptive signal detection in non-Gaussian clutter: a data-dependent threshold interpretation, IEEE Transactions on Signal Processing, vol.47, issue.6, pp.1522-1531, 1999.
DOI : 10.1109/78.765121

F. Gini and M. V. Greco, Sub-optimum approach to adaptive coherent radar detection in compound- Gaussian clutter, IEEE Trans.-AES, vol.35, issue.3, pp.1095-1103, 1999.

F. Gini, Estimation of chirp radar signals in compound-Gaussian clutter: a cyclostationary approach, IEEE Transactions on Signal Processing, vol.48, issue.4, pp.1029-1039, 2000.
DOI : 10.1109/78.827537

F. Gini, Performance analysis of two structured covariance matrix estimators in compound-Gaussian clutter, Signal Processing, vol.80, issue.2, pp.365-371, 2000.
DOI : 10.1016/S0165-1684(99)00135-8

F. Gini, M. V. Greco, M. Diani, and L. Verrazzani, Performance analysis of two adaptive radar detectors against non-Gaussian real sea clutter data, IEEE Trans.-AES, vol.36, issue.4, pp.1429-1439, 2000.

F. Gini, M. V. Greco, A. Farina, and P. Lombardo, Note on "Optimum and mismatched detection against K-distributed plus Gaussian clutter", IEEE Transactions on Aerospace and Electronic Systems, vol.37, issue.1, pp.296-297, 2001.
DOI : 10.1109/7.913690

F. Gini, A. Farina, and M. V. Greco, Selected list of references on radar signal processing, IEEE Transactions on Aerospace and Electronic Systems, vol.37, issue.1, pp.329-359, 2001.
DOI : 10.1109/7.913696

J. Goldman, Detection in the presence of spherically symmetric random vectors, IEEE Transactions on Information Theory, vol.22, issue.1, pp.52-59, 1976.
DOI : 10.1109/TIT.1976.1055514

E. Jakeman and P. N. Pusey, A model for non-Rayleigh sea echo, IEEE Transactions on Antennas and Propagation, vol.24, issue.6, pp.806-814, 1976.
DOI : 10.1109/TAP.1976.1141451

E. Jay, Détection en Environnement Non-Gaussien, 2002.

E. Jay, J. Ovarlez, D. Declercq, and P. Duvaut, BORD: bayesian optimum radar detector, Signal Processing, vol.83, issue.6, pp.1151-1162, 2003.
DOI : 10.1016/S0165-1684(03)00034-3

S. M. Kay, Fundamentals of statistical signal processing -Detection theory, 1998.

J. T. Kent and D. E. Tyler, Redescending $M$-Estimates of Multivariate Location and Scatter, The Annals of Statistics, vol.19, issue.4, pp.2102-2119, 1991.
DOI : 10.1214/aos/1176348388

V. A. Korado, Optimum detection of signals with random parameters against the background of noise of unknown intensity under conditions of constant false alarm probability, Radio Engineering and Electronic Physics, vol.13, 1968.

S. Kraut, L. L. Scharf, L. T. Mc, and . Whorter, Adaptive subspace detectors, IEEE Transactions on Signal Processing, vol.49, issue.1, pp.1-16, 2001.
DOI : 10.1109/78.890324

R. A. Maronna, Robust $M$-Estimators of Multivariate Location and Scatter, The Annals of Statistics, vol.4, issue.1, pp.51-67, 1976.
DOI : 10.1214/aos/1176343347

F. Pascal, P. Forster, J. Ovarlez, and P. Larzabal, Theoretical Analysis of an Improved Covariance Matrix Estimator in Non-Gaussian Noise, Proc. IEEE-ICASSP, pp.69-72, 2005.
URL : https://hal.archives-ouvertes.fr/halshs-00158387

F. Pascal, J. Ovarlez, P. Forster, and P. Larzabal, On a SIRV-CFAR Detector with Radar Experimentations in Impulsive Noise, Proc. of the EUropean SIgnal Processing COnf, 2006.

F. Pascal, Y. Chitour, J. Ovarlez, P. Forster, and P. Larzabal, Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis, IEEE Transactions on Signal Processing, vol.56, issue.1
DOI : 10.1109/TSP.2007.901652

F. A. Pentini, A. Farina, and F. Zirilli, Radar detection of targets located in a coherent K distributed clutter background, IEE Proc.-F, pp.238-245, 1992.

B. Picinbono and G. Vezzosi, Détection d'un signal certain dans un bruit non stationnaire et non Gaussien, Annales des Télécomm, vol.25, pp.433-439, 1970.

R. S. Raghavan, H. F. Qiu, and D. J. Mclaughlin, CFAR detection in clutter with unknown correlation properties, IEEE Transactions on Aerospace and Electronic Systems, vol.31, issue.2, pp.647-656, 1995.
DOI : 10.1109/7.381913

M. Rangaswamy, D. D. Weiner, and A. Öztürk, Non-Gaussian random vector identification using spherically invariant random processes, IEEE Transactions on Aerospace and Electronic Systems, vol.29, issue.1, pp.111-123, 1993.
DOI : 10.1109/7.249117

C. P. Robert, L'analyse Statistique Bayésienne, Economica, 1992.

C. P. Robert, The Bayesian Choice : a Decision-Theoretic Motivation, 1994.
DOI : 10.1007/978-1-4757-4314-2

C. P. Robert, Méthodes de Monte Carlo par chaînes de Markov, Economica, 1996.

K. J. Sangston, F. Gini, M. V. Greco, and A. Farina, Structures for radar detection in compound Gaussian clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.35, issue.2, pp.445-458, 1999.
DOI : 10.1109/7.766928

M. A. Tanner, Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3rd Edition, Biometrics, vol.54, issue.2, 1996.
DOI : 10.2307/3109795

G. V. Trunk and S. F. George, Detection of Targets in Non-Gaussian Sea Clutter, IEEE Transactions on Aerospace and Electronic Systems, vol.6, issue.5, pp.620-628, 1970.
DOI : 10.1109/TAES.1970.310062

A. W. Van and . Vaart, Asymptotic Statistics, 1998.

K. D. Ward, Compound representation of high resolution sea clutter, Electronics Letters, vol.17, issue.16, pp.561-563, 1981.
DOI : 10.1049/el:19810394

S. Watts, Radar detection prediction in sea clutter using the compound K-distribution model, IEE Proc.Pt-F, pp.613-620, 1985.
DOI : 10.1049/ip-f-1.1985.0115

K. Yao, A Representation Theorem and its Applications to Spherically Invariant Random Processes, IEEE Trans.-IT, vol.19, issue.5, pp.600-608, 1973.