Comparison of Kalman Filter and Wavelet

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1、ComparisonofKalmanFilterandWaveletFilterforDenoisingSedaPostalclogluKadirErkanEmineDogruBolatKocaeliUniversity,FacultyofKocaeliUniversity,FacultyofKocaeliUniversity,FacultyofTechnicalEducationDepartnentTechnicalEducationDepartmnentofTechnicalEducationDepartmentof

2、Electronics&Computer,Kocaeli,ofElectronics&Computer,TurkiyeElectronics&Computer,Kocaeli,Kocaeli,TurkiyeE-mail:erkan@kou.edu.trTurkiyeE-mail:postalcioglu@ieee.orgE-mail:ebolat@ieee.orgAbstract-Thispaperpresentsdenoisingthesignalusingzeroandshrinkstherestofthecoeff

3、icientsbythethresholdWaveletfilterandKalmanfilter.Thenoiseiszeromeanand(soft-thresholding)orleavesthemwithoutchangethevariancevalueis0,001.Kalmanfilterremovesdisturbances(hard-thresholding)[6,7].orfaultsfromthesignalbyusinginitializationandpropagationoferrorcovar

4、iancestatistics.ImplementationofKalmanfilterisimpracticalinlargescalemodelsasshownfortheoscillatorII.KALMANFILTERsystem.AsanalternativeWaveletfdterhasbeenusedforthesamesystem.Coiflet2whichisorthogonalwavelethasbeenKalmanfilterisanoptimalrecursivedataprocessinguse

5、d.Softthresholdinghasbeenapplied.Decompositionisalgorithm.Figure1representsatypicalKalmanfilterperformedatlevel9.TheresultsofWaveletfilterandKalmanapplication[8].filterareshown.ResponseofWaveletifiterisbetterwhencomparedwithKalmanfilterresult.SystemerrorsourcesI.

6、INTRODUCTIONTherearesomeimportantproblemsfortheoreticalandpracticalincommunicationandcontrolsystems.Suchasproblemsare,predictionofrandomsignals,separationofrandomsignalsfromrandomnoise[1].RudolfEmilKalmanismostfamousforhisinventionoftheKalmanfilterthatamathematic

7、aldigitalsignalprocessingtechniquewidelyusedincontrolsystems.KalmanfilterisamethodtoMeasurementerrorsourcesestimaterapidlythevalueofasystem'sresponsetoaninput.KalmanfilterremovesdisturbancesorfaultsfromthesignalFigure1ATypicalKalmanFilterApplicationbyusinginitial

8、izationandpropagationoferrorcovarianceThepurposeofKalmanfilteristoestimatethestateofstatistics[3,2].Kalmanfiltercomputesthemeanandtheasystemfrommeasurementswhi