A-Complementary-Filter-for-Attitude-Estimation

AComplementaryFilterforAttitudeEstimationofaFixed-WingUAVMarkEuston,PaulCoote,RobertMahony,JonghyukKimandTarekHamelAbstract—Thispaperconsidersthequestionofusinganon-linearcomplementaryfilterforattitudeestimationoffixed-wingunmannedaerialvehicle(UAV)givenonlymeasurementsfromalow-costinertialmeasurementunit.Anonlinearcomplementaryfilterisproposedthatcombinesaccelerometeroutputforlowfrequencyattitudeestimationwithintegratedgyrometeroutputforhighfrequencyestimation.Therawaccelerometeroutputincludesacomponentfortheairframeacceleration,thatoccursprimarilyastheaircraftturns,aswellasthegravitationalaccelerationthatisrequiredforthefilter.Theairframeac-celerationisestimatedusingasimplecentripetalforcemodel(basedonadditionalairspeedmeasurements),augmentedbyafirstorderdynamicmodelforangle-of-attack,andusedtoobtainestimatesofthegravitationaldirectionindependentoftheairplanemanoeuvres.Experimentalresultsareprovidedonareal-worlddatasetandtheperformanceofthefilterisevaluatedagainsttheoutputfromafullGPS/INSthatwasavailableforthedataset.I.INTRODUCTIONAttitudedeterminationisanessentialtaskforanUn-mannedAerialVehicle(UAV).WiththegrowingrangeofapplicationsinUAV’s,andthepushtomakevehiclescheaperandmorereliable,itisofinteresttodeveloprobustandsimplealgorithmsforattitudeestimation[1],[9].Thereisalargeliteratureonattitudefilteringtechniques,seeforexampletherecentreviewarticlebyCrassidisetal.[6].Mostoftheadvancedfiltertechniques(particlefiltering,etc.)arecomputationallydemandingandunsuitableforthesmallscaleembeddedprocessorsinUAVavionicsystems.ThetwomethodsthatarecommonlyusedareextendedKalmanfilter-ing(EKF)orsomeformofconstantgainstateobserver,oftentermedacomplimentaryfilterduetoitsfrequencyfilteringpropertiesforlinearsystems[12].ExtendedKalmanFilteringhasbeenstudiedforarangeofaerospaceapplications[7],[9],[6],[16].Suchfilters,however,haveproveddifficulttoapplyrobustly[14],[4],[16].Inpractice,manyapplicationsusesimplelinearsingle-inputsingle-outputcomplementaryfilters[16],[5].Inrecentwork,anumberofauthorshavedevelopednonlinearanalogousofsingle-inputsingle-output(SISO)filtersforattitudeestimation[15],[19],[18],[13],[11],[2].ToimplementtheseschemesonaUAVusinginertialmeasurementunit(IMU)datatheaccelerometeroutputisusedtoestimatethegravitationaldirection.Therecentworkbytheauthors[8],[12]allowsthefullestimationofvehicleattitude(uptoaconstantheadingerror)aswellasgyrobiasesbasedjustontheaccelerometerandgyrometerM.Euston,P.Coote,J.KimandR.MahonyarewithDepartmentofEngineering,AustralianNationalUniversity,ACT,0200,Australia.e-mail:[e-mail]3S-CNRS,Nice-SophiaAntipolis,France.e-mail:[e-mail]filterfails,however,whenthevehicledynamicsaresufficientlylargethataccelerometeroutputnolongerprovidesagoodestimateofthegravitationaldirection.ThisisparticularlythecaseforafixedwingUAVmanoeuveringinalimitedspaceandmakingrepeatedrapidturns.Inthispaper,wedevelopanonlinearcomplementaryfilter,augmentedbyasimplefirstordermodelofvehicledynamicsthatprovidesexcellentattitudeestimatesforafixedwingUAV.Thekeycontributionistodevelopamodelofthenon-inertialaccelerationoftheairframethatcanbeusedtocompensatetheaccelerometeroutputtoobtainazerobiasestimateofthegravitationaldirection.Themodelisbasedonasimplecentripetalforcemodelderivedfromtheairspeedandtherateofturnofthevehicle.However,theangle-of-attackoftheairplaneissignificantlyhigherduringasharpturn,andthismustbemodelledtocorrectlyalignthecompensationtermsfortheaccelerometeroutput.Weaddressthisproblembyincorporatingasimplefirstordermodeloftheangle-of-attackdynamicsoftheairframedrivenbythepitchratemeasurementobtainedfromthegyrometeroutput.Thecombinedsystemissimpletoimplementandachievesexcellentperformance,giventheminimaldatathatisavailable.Thealgorithmisverifiedonexperimentaldatafromafixedwingaerialroboticvehicle.TheperformanceofthealgorithmisconfirmedbycomparisonwithanattitudeestimateobtainedfromafullINS/GPSstochasticfilterthathasbeenrunontheexperimentaldata.II.EXPLICITCOMPLEMENTARYFILTERAcomplementaryfilterforattitudeestimationperformslow-passfilteringonalow-frequencyattitudeestimate,ob-tainedfromaccelerometerdata,andhigh-passfilteringonabiasedhigh-frequencyattitudeestimate,obtainedbydirectintegrationofgyrometeroutput,andfusestheseestimatestogethertoobtainanall-passestimateofattitude.Whenthepitchandrollofaairplanearemodelledasdecoupledprocesses,aSISOfiltercandesignedforeachsignalthatusesthetheanglebetweentheaccelerometeroutputandthebody-fixed-frameasattitudereferenceandtheseparategyrometeraxisoutputasvelocityreferenceinaclassicallinearcomplementaryfilter[3].WhenalowpassestimateofthefullattitudecanbereconstructedfromtheIMUmeasurements,forexampleifmagnetometerdataisalsoavailableandthefullcoupledrotationmatrixforattitudecanbecomputedasanalgebraicfunctionofthegravitationalandmagneticfieldsmeasuredinthebody-fixed-frame,thennonlinearextensionsofthecomplementaryfiltershavebeenavailableforfifteenyears[15],[18].MagnetometersarerarelyusefulonsmallscaleUAVsduetotheperturbationofFig.1.ExplicitComplementaryFilterwithacc