Fast algorithms for recursive identification

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1、TP7-4:30FASTALCORI'I'HMSFORRECURSIVEIDEN'I'IFICATION*M.Morfand'1'.KailatlrL.LjungInformationSystemsLaboratoryDepartmentofAutomaticControlStanfordUniversity,LundInstituteof'I'echnologyStanfordCalifornia94305S-32001Lund,SwedenAbstractFastaleorithmscanbederivedthatareequivalenttoRecursiveidentificati

2、onalgoritlvnsareofgreatinterestfikecommonlyusedidentificationmethodsthatrequireincontrolandestimationproblenls,andrelatedareassuchasproportionaltotlresquareofthenumberofmodelparametersrecursiveleastsquares-andadaptivemcsthods.Recentlyweinmemoryandcomputationsperupdate.Acomparativestudyhavesl>ownho

3、wacertainshiftinvarianceinherentinmanyofthesemethodscanbefounde.g.in[SLG].l'heyallcanbeestimationandcontrolproblcmscanbecxploiterltoobtainwritteninaformwheresomewellknownresultsinoptimalfastalgoritlrtnsthatoftenrequireordersofmay;nitudelessestimationtheorycanbeapplied,cf.e.g.[Kalbl)]andmorecoTputa

4、tionsthanpresentlyavailablemethodstocomputerecentones[MSK],[MK],[DMK].Wealsowouldliketooptimalgains.'ehavedeveloppedfastalgorithmsforaattractsonreattentiontosquare-rootmethodsthathavev3rictyofpresentlyavailableidentificationmethodsaswellasseveralcomputationalandnumericaladvantagesnewonesthatrequi

5、recomputertimeandstorage(or[KBS],[MK],[CCMS].hardware)pernreasurementonlyproportionaltothenumberofmodelparameters,comparedtothesquareoftlrenumber'I'hefastrecursiveidentificationalgorithmsarerelatedofparametersforpreviousnlethods.Sinceparametertovariousothertopicsthatcouldbeofpotentialbenefittoiden

6、tificationcanbeformulatedasastateestimationproblem,identificationmethods.Thefastalgorithmscanbeviewedasoptimalfilterin6resultscanbeapplied.InparticularwewouldgeneralizationsofthcLevinson-P'iggins-Robinson(LWR)liketoattractattcntiontoalternatives,suchassquare-rootalgorithm[Lev],[Wie],[WR],[R'I']for

7、solvingnormalequations,InethocJsandtheiriastversionsorladderformsusingpartialarisinginestimationofstationaryautoregressiveprocesses.correlationsthathaveseveralcomputationalandnumerical(Whittlealsoderivedanlultich