自适应滤波Adaptive Filtering Algorithms and Practical Implementation.pdf

自适应滤波Adaptive Filtering Algorithms and Practical Implementation.pdf

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AdaptiveFilteringAlgorithmsandPracticalImplementationThirdEditionPauloS.R.DinizAdaptiveFilteringAlgorithmsandPracticalImplementationThirdEdition123PauloS.R.DinizFederalUniversityofRiodeJaneiroRiodeJaneiroBrazil2008SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher（SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA）,exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknoworhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,evenifthearenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaper987654321ISBN:

978-0-387-31274-3e-ISBN:

978-0-387-68606-6DOI:

10.1007/978-0-387-68606-6LibraryofCongressControlNumber:

20089235541MATLABisaregisteredtrademarkofTheMathWorks,Inc.NotetoInstructorsFortheinstructorsthisbookhasasolutionmanualfortheproblemswrittenbyDr.L.W.P.Biscainhoavailablefromthepublisher.Alsoavailable,uponrequesttotheauthor,isasetofmastertransparenciesaswellastheMATLAB1codesforallthealgorithmsdescribedinthetext.To:

MyParents,Mariza,Paula,andLuiza.PREFACEThefieldofDigitalSignalProcessinghasdevelopedsofastinthelastthreedecadesthatitcanbefoundinthegraduateandundergraduateprogramsofmostuniversities.Thisdevelopmentisrelatedtotheincreasinglyavailabletechnologiesforimplementingdigitalsignalprocessingalgorithms.Thetremendousgrowthofdevelopmentinthedigitalsignalprocessingareahasturnedsomeofitsspecializedareasintofieldsthemselves.Ifaccurateinformationofthesignalstobeprocessedisavailable,thedesignercalleasilychoosethemostappropriatealgorithmtoprocessthesignal.Whendealingwithsignalswhosestatisticalpropertiesareunknown,fixedalgorithmsdonotprocessthesesignalsefficiently.Thesolutionistouseanadaptivefilterthatautomaticallychangesitscharacteristicsbyoptimizingtheinternalparameters.Theadaptivefilteringalgorithmsareessentialinmanystatisticalsignalprocessingapplications.Althoughthefieldofadaptivesignalprocessinghasbeensubjectofresearchforoverfourdecades,itwasintheeightiesthatamajorgrowthoccurredinresearchandapplications.Twomainreasonscanbecreditedtothisgrowth,theavailabilityofimplementationtoolsandtheappearanceofearlytextbooksexposingthesubjectinanorganizedmanner.Stilltodayitispossibletoobservemanyresearchdevelopmentsintheareaofadaptivefiltering,particularlyaddressingspecificapplications.Infact,thetheoryoflinearadaptivefilteringhasreachedamaturitythatjustifiesatexttreatingthevariousmethodsinaunifiedway,emphasizingthealgorithmssuitableforpracticalimplementation.Thistextconcentratesonstudyingon-linealgorithms,thosewhoseadaptationoccurswheneveranewsampleofeachenvironmentsignalisavailable.Theso-calledblockalgorithms,thosewhoseadaptationoccurswhenanewblockofdataisavailable,arealsoincludedusingthesubbandfilteringframework.Usually,blockalgorithmsrequiredifferentimplementationresourcesthantheon-linealgorithms.Thiseditionalsoincludesbasicintroductionstononlinearadaptivefilteringandblindsignalprocessingasnaturalextensionsofthealgorithmstreatedintheearlierchapters.Theunderstandingoftheintroductorymaterialpresentedisfundamentalforfurtherstudiesinthesefieldswhicharedescribedinmoredetailinsomespecializedtexts.TheideaofwritingthisbookstartedwhileteachingtheadaptivesignalprocessingcourseatthegraduateschooloftheFederalUniversityofRiodeJaneiro（UFRJ）.Therequestofthestudentstocoverasmanyalgorithmsaspossiblemademethinkhowtoorganizethissubjectsuchthatnotmuchtimeislostinadaptingnotationsandderivationsrelatedtodifferentalgorithms.Anothercommonquestionwaswhichalgorithmsreallyworkinafinite-precisionimplementation.Theseissuesledmetoconcludethatanewtextonthissubjectcouldbewrittenwiththeseobjectivesinmind.Also,consideringthatmostgraduateandundergraduateprogramsincludeasingleadaptivefilteringcourse,thisbookshouldnotbelengthy.Anotherobjectivetoseekistoprovideaneasyaccesstotheworkingalgorithmsforthepractitioner.xItwasnotuntilIspentasabbaticalyearandahalfatUniversityofVictoria,Canada,thatthisprojectactuallystarted.Intheleisurehours,Islowlystartedthisproject.Partsoftheearlychaptersofthisbookwereusedinshortcoursesonadaptivesignalprocessingtaughtatdifferentinstitutions,namely:

HelsinkiUniversityofTechnology,Espoo,Finland;UniversityMenendezPelayoinSeville,Spain;andattheVictoriaMicronetCenter,UniversityofVictoria,Canada.TheremainingpartsofthebookwerewrittenbasedonnotesofthegraduatecourseinadaptivesignalprocessingtaughtatCOPPE（thegraduateengineeringschoolofUFRJ）.Thephilosophyofthepresentationistoexposethematerialwithasolidtheoreticalfoundation,whileavoidingstraightforwardderivationsandrepetition.Theideaistokeepthetextwithamanageablesize,withoutsacrificingclarityandwithoutomittingimportantsubjects.Anotherobjectiveistobringthereaderuptothepointwhereimplementationcanbetriedandresearchcanbegin.Anumberofreferencesareincludedattheendofthechaptersinordertoaidthereadertoproceedonlearningthesubject.Itisassumedthereaderhaspreviousbackgroundonthebasicprinciplesofdigitalsignalprocessingandstochasticprocesses,including:

discrete-timeFourier-and-transforms,finiteimpulseresponse（FIR）andinfiniteimpulseresponse（IIR）digitalfilterrealizations,multiratesystems,randomvariablesandprocesses,first-andsecond-orderstatistics,moments,andfilteringofrandomsignals.Assumingthatthereaderhasthisbackground,Ibelievethebookisselfcontained.Chapter1introducesthebasicconceptsofadaptivefilteringandsetsageneralframeworkthatallthemethodspresentedinthefollowingchaptersfallunder.Abriefintroductiontothetypicalapplicationsofadaptivefilteringarealsopresented.InChapter2,thebasicconceptsofdiscrete-timestochasticprocessesarereviewedwithspecialemphasistotheresultsthatareusefultoanalyzethebehaviorofadaptivefilteringalgorithms.Inaddition,theWienerfilterispresented,establishingtheoptimumlinearfilterthatcanbesoughtinstationaryenvironments.AppendixAbrieflydescribestheconceptsofcomplexdifferentiationmainlyappliedtotheWienersolution.ThecaseoflinearlyconstrainedWienerfilterisalsodiscussed,motivatedbyitswideuseinantennaarrayprocessing.Thetransformationoftheconstrainedminimizationproblemintoanunconstrainedoneisalsopresented.Theconceptofmean-squareerrorsurfaceisthenintroduced,anotherusefultooltoanalyzeadaptivefilters.TheclassicalNewtonandsteepest-descentalgorithmsarebrieflyintroduced.Sincetheuseofthesealgorithmswouldrequireacompleteknowledgeofthestochasticenvironment,theadaptivefilteringalgorithmsintroducedinthefollowingchapterscomeintoplay.PracticalapplicationsoftheadaptivefilteringalgorithmsarerevisitedinmoredetailattheendofChapter2wheresomeexampleswithclosedformsolutionsareincludedinordertoallowthecorrectinterpretationofwhatisexpectedfromeachapplication.Chapter3presentsandanalysesoftheleast-mean-square（LMS）algorithminsomedepth.Severalaspectsarediscussed,suchasconvergencebehaviorinstationaryandnonstationaryenvironments.ThischapteralsoincludesanumberoftheoreticalaswellassimulationexamplestoillustratehowtheLMSalgorithmperformsindifferentsetups.AppendixBaddressesthequantizationeffectsontheLMSalgorithmwhenimplementedinfixed-andfloating-pointarithmetics.ZPrefacePrefacexiChapter4dealswithsomealgorithmsthatareinasenserelatedtotheLMSalgorithm.Inparticular,thealgorithmsintroducedarethequantized-erroralgorithms,theLMS-Newtonalgorithm,thenormalizedLMSalgorithm,thetransform-domainLMSalgorithm,andtheaffineprojectionalgorithm.SomepropertiesofthesealgorithmsarealsodiscussedinChapter4,withspecialemphasistotheanalysisofthefineprojectionalgorithm.Chapter5introducestheconventionalrecursiveleast-squares（RLS）algorithm.Thisalgorithmminimizesadeterministicobjectivefunction,differinginthissensefrommostLMS-basedalgorithms.FollowingthesamepatternofpresentationofChapter3,severalaspectsoftheconventionalRLSalgorithmarediscussed,suchasconvergencebehaviorinstationaryandnonstationaryenvironments,alongwithanumberofsimulationresults.AppendixC,dealswithstabilityissuesandquantizationeffectsrelatedtotheRLSalgorithmwhenimplementedinfixed-andfloating-pointarithmetics.Theresultspresented,exceptforthequantizationeffects,arealsovalidfortheRLSalgorithmspresentedinChapters7,8,and9.AsascomplementtoChapter5,AppendixDpresentsthediscrete-timeKalmanfilterformulationwhichdespitebeingconsideredanextensionoftheWienerfilterhassomerelationwiththeRLSalgorithm.Chapter6discussessometechniquestoreducetheoverallcomputationalcomplexityofadaptivefilteringalgorithms.Thechapterfirstintroducesthesocalledset-membershipalgorithmsthatupdateonlywhentheoutputestimationerrorishigherthantheprescribedupperbound.