robust M-estimation for array processing_ a random matrix approach

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1、1RobustM-EstimationforArrayProcessing:ARandomMatrixApproachRomainCouillet1,Fred′ericPascal′2,andJackW.Silverstein31Telecommunicationdepartment,Supelec,GifsurYvette,France.′2SONDRALaboratory,Supelec,GifsurYvette,France.′3DepartmentofMathematics,NorthCarolinaStateUniversity

2、,NC,USA.Abstract—Thisarticlestudiesthelimitingbehaviorofarobustrecognizedinadaptiveradarandsonarprocessing,whereM-estimatorofpopulationcovariancematricesasboththethesignalsunderstudyarecharacterizedbyimpulsivenoisenumberofavailablesamplesandthepopulationsizearelarge.andou

3、tlyingdata.RobustestimationtheoryaimsattacklingUsingtoolsfromrandommatrixtheory,weprovethatthethisproblem[5].Amongothersolutions,theso-calledrobustdifferencebetweenthesamplecovariancematrixand(ascaledversionof)therobustM-estimatortendstozeroinspectralnorm,M-estimatorsofth

4、epopulationcovariancematrix,originallyalmostsurely.ThisresultisappliedtoprovethatrecentsubspaceintroducedbyHuber[4]andinvestigatedintheseminalworkmethodsarisingfromrandommatrixtheorycanbemaderobustofMaronna[6],haveimposedthemselvesasanappealingwithoutalteringtheir?rstorde

5、rbehavior.alternativetotheSCM.Thisestimator,whichwedenoteC^N,isde?nedimplicitlyasasolutionof1I.INTRODUCTIONXnC^=1u1xC^