Understanding the Basis of the Kalman Filter Via a Simple and intuitive derivation.pdf

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1、[lectureNOTES]RamseyFaragherUnderstandingtheBasisoftheKalmanFilterViaaSimpleandIntuitiveDerivationhisarticleprovidesasimpleunderstandthebasisoftheKalmanfil-theKalmanfilter,intheinterestsofandintuitivederivationofterviaasimpleandintuitivederivation.beingconcise,buti

2、nsteadaimstopro-theKalmanfilter,withthevidetutorswithasimplemethodofaimofteachingthisusefulRELEVANCEteachingtheconceptsoftheKalmanfil-Ttooltostudentsfromdisci-TheKalmanfilter[2](anditsvariantstertostudentswhoarenotstrongplinesthatdonotrequireastrongsuchastheextende

3、dKalmanfilter[3]mathematicians.Thereaderisexpectedmathematicalbackground.ThemostandunscentedKalmanfilter[4])istobefamiliarwithvectornotationandcomplicatedlevelofmathematicsoneofthemostcelebratedandpopu-terminologyassociatedwithKalmanfil-requiredtounderstandthisderi

4、vationislardatafusionalgorithmsinthefieldteringsuchasthestatevectorandcova-theabilitytomultiplytwoGaussianofinformationprocessing.Themostriancematrix.ThisarticleisaimedatfunctionstogetherandreducetheresultfamousearlyuseoftheKalmanfilterthosewhoneedtoteachtheKalmanf

5、il-toacompactform.wasintheApollonavigationcomputertertoothersinasimpleandintuitiveTheKalmanfilterisover50yearsoldthattookNeilArmstrongtothemoon,manner,orforthosewhoalreadyhavebutisstilloneofthemostimportantand(mostimportantly)broughthimsomeexperiencewiththeKalmanfi

6、lterandcommondatafusionalgorithmsinback.Today,Kalmanfiltersareatworkbutmaynotfullyunderstanditsfounda-usetoday.NamedafterRudolfE.ineverysatellitenavigationdevice,tions.ThisarticleisnotintendedtobeaKálmán,thegreatsuccessoftheeverysmartphone,andmanycom-thoroughandsta

7、ndaloneeducationtoolKalmanfilterisduetoitssmallcompu-putergames.forthecompletenovice,asthatwouldtationalrequirement,elegantrecursiverequireachapter,ratherthanafewproperties,anditsstatusastheoptimalpages,toconvey.THEKALMANFILTERISestimatorforone-dimensionallinearOVE

8、R50YEARSOLDBUTsystemswithGaussianerrorstatisticsPROBLEMSTATEMENTISSTILLONEOFTHEMOST[1].TypicalusesoftheKalmanfilterTheKalmanfiltermodelassumestha