(2011) Optimal filtering with Kalman filters and smoothers ― A manual for matlab toolbox EKFUKF.pdf

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1、OptimalFilteringwithKalmanFiltersandSmoothersaManualfortheMatlabtoolboxEKF/UKFVersion1.3JouniHartikainen,ArnoSolin,andSimoSärkkäDepartmentofBiomedicalEngineeringandComputationalScience,AaltoUniversitySchoolofScience,P.O.Box1100,FI-00076AALTO,Espoo,Finlandjouni.hartikainen@aalto.fi,arno.sol

2、in@aalto.fi,simo.sarkka@aalto.fiAugust16,2011AbstractInthispaperwepresentadocumentationforanoptimalfilteringtoolboxforthemathematicalsoftwarepackageMatlab.Thetoolboxfeaturesmanyfilteringmeth-odsfordiscrete-timestatespacemodels,includingthewell-knownlinearKalmanfilterandseveralnon-linearextensi

3、onstoit.Thesenon-linearmethodsaretheextendedKalmanfilter,theunscentedKalmanfilter,theGauss-HermiteKalmanfilterandthethird-ordersymmetriccubatureKalmanfilter.Algorithmsformul-tiplemodelsystemsareprovidedintheformofanInteractingMultipleModel(IMM)filterandit’snon-linearextensions,whicharebasedonb

4、anksofextendedandunscentedKalmanfilters.AlsoincludedinthetoolboxaretheRauch-Tung-Striebelandtwo-filtersmoothercounter-partsforthefilters,whichcanbeusedtosmooththepreviousstateestimates,afterobtainingnewmeasurements.Theusageandfunctionofeachmethodisillustratedwitheightdemonstrationproblems.Co

5、ntents1Introduction42Discrete-TimeStateSpaceModels:LinearModels62.1Discrete-TimeStateSpaceModels.................62.2LinearStateSpaceEstimation...................82.2.1DiscretizationofContinuous-TimeLinearTime-InvariantSystems...........................82.2.2KalmanFilter..................

6、......92.2.3KalmanSmoother.....................102.2.4Demonstration:2DCWPA-model.............113NonlinearStateSpaceEstimation153.1ExtendedKalmanFilter.......................153.1.1TaylorSeriesBasedApproximations............153.1.2LinearApproximation...................163.1.3QuadraticAppro

7、ximation.................163.1.4ExtendedKalmanfilter...................173.1.5TheLimitationsofEKF..................193.1.6ExtendedKalmansmoother................203.2Demonstration:Trackingarandomsinesignal...........203.3UnscentedKalmanFilter......................263.