Optimal filtering with Kalman filters and smoothers.pdf

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1、OptimalfilteringwithKalmanfiltersandsmoothers–aManualforMatlabtoolboxEKF/UKFJouniHartikainenandSimoSärkkäDepartmentofBiomedicalEngineeringandComputationalScience,HelsinkiUniversityofTechnology,P.O.Box9203,FIN-02015TKK,Espoo,Finlandjmjharti@lce.hut.fi,simo.sarkka@hut

2、.fiFebruary25,2008Version1.2AbstractInthispaperwepresentadocumentationforoptimalfilteringtoolboxformathematicalsoft-warepackageMatlab.ThemethodsinthetoolboxincludeKalmanfilter,extendedKalmanfilterandunscentedKalmanfilterfordiscretetimestatespacemodels.Algorithmsformul

3、tiplemodelsystemsareprovidedintheformofInteractingMultipleModel(IMM)filterandit’snon-linearextensions,whicharebasedonbanksofextendedandunscentedKalmanfilters.AlsoincludedinthetoolboxaretheRauch-Tung-Striebelandtwo-filtersmoothercounter-partsforeachfilter,whichcanbeus

4、edtosmooththepreviousstateestimates,afterobtainingnewmeasurements.Theusageandfunctionofeachmethodareillustratedwitheightdemonstrationsproblems.1Contents1Introduction42Discrete-TimeStateSpaceModels52.1Linearstatespaceestimation..............................62.1.1D

5、iscretizationofcontinuous-timelineartime-invariantsystems........62.1.2Kalmanfilter..................................72.1.3Kalmansmoother................................82.1.4Demonstration:2DCWPA-model.......................92.2Nonlinearstatespaceestimation.......

6、.....................122.2.1TaylorSeriesBasedApproximations......................132.2.2ExtendedKalmanfilter.............................142.2.3ExtendedKalmansmoother..........................162.2.4Demonstration:Trackingarandomsinesignal................162.2.5Uns

7、centedTransform..............................212.2.6UnscentedKalmanfilter............................242.2.7UnscentedKalmansmoother..........................272.2.8Demonstration:UNGM-model.........................272.2.9Demonstration:BearingsOnlyTracking..........

8、..........312.2.10Demonstration:ReentryVehicleTracking...................353MultipleModelSystems433.1LinearSystems.....................................433.1.1I