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Study of a GPS Satellite Selection Policy .pdf

Study of a GPS Satellite Select…

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简介:本文档为《Study of a GPS Satellite Selection Policy pdf》,可适用于专题技术领域,主题内容包含StudyofaGPSSatelliteSelectionPolicytoImprovePositioningAccuracyMasahikoKih符等。

StudyofaGPSSatelliteSelectionPolicytoImprovePositioningAccuracyMasahikoKiharaTheNationalDefenseAcademyHashirimizu,Yokosuka,JapanAbstractThefourdimensionalaccuracyofGPSpositioningusingfoursatellitesateveryinstantisreexaminedUserreceiversusuallyselectsuitablefoursatellitesthathavebestgeometrybasedonPDOPorGDOPHowever,itismorereasonabletoselectasetoffoursatellitesthathasminimumVDOPformeasuringverticalposition,whiletoselectasetoffoursatellitesthathasminimumHDOPformeasuringhorizontalpositionInthisstudies,weproposeamethodofusingVDOPandHDOPasthecriteriatoselectthesetoffoursatellitesusedformeasuringverticalandhorizontalpositionsrespectively,andcompareitsperformancewiththatoftheconventionalmethodbycomputersimulationItisclarifiedthatthecombinationsofthefoursatellitesthatminimizeVDOP,HDOPandPDOParegenerallydifferenteachother,andlimitedamountofimprovementinVDOPandHDOPisobtainedbyoptimizingthemseparatelyDependenceoftheamountoftheimprovementonlatitudeandmaskangleisalsoexaminedinstantandusedforpositionfurHowever,itisconsideredtobemorereasonabletouseVDOPorHDOPforverticalorhorizontalpositionfixrespectively,sinceVDOPandPDOPvaluesaregenerallydifferenteachotherItiswellknownfortheGPSmeasurementthatverticalaccuracyisinferiortohorizontalaccuracybecauseofrestrictionofgeometryresultedfromearthmaskingThisstudyhasbeenmotivatedfromanexpectationthattheverticalaccuracymightbeimprovedbyaselectionofthefoursatellitesconcentratedontheverticalaccuracyThispaperproposesaselectionpolicyofthefoursatellitesthatusesVDOPandHDOPforverticalandhorizontalmeasurementrespectivelyascriteriatoobtaingoodaccuracyPerformanceofthismethodisevaluatedbycomputersimulationanditsdependenceonlatitudeandmaskangleisdiscussedAmountofimprovementinaccuracycomparedwiththeconventionalmethodusingPDOPisalsodiscussedstatisticallyDEFINITIONOFPOSITIONACCURACYINTRODUCTIONConsiderthefollowingbasicmeasurementequationLowcostGPSreceiverisgrowingintypeandfortheGPSusingnvisiblesatellitesl:numberinaccordancewithgrowinginterestofpublicGX=y()userItishopedforthesereceiverstohaveashighperformanceandaslowpriceaspossibleInthesereceivers,asetoffoursatellitesthathasminimumPDOPisusuallyselectedfromvisiblesatellitesateverywherex=RxRyR,BIT()$IEEEG=e,Te:e,'()Intheseequation,R,,,R,arethethreecomponentofusepositionvector,Bistheuserclockbias,andthereforexisthefourdimensionalvectortobedeterminedbythepositionfixyisavectorgivenbymeasurementwhichincludesmeasureddistancesfromusertoeachsatellite,satellitepositionsgivenbyephemerides,andsatelliteclockbiases(known)el,e,,,enareunityvectorsdirectingfromusertoeachsatelliteThenGisanrowscolumnmatrixwhichrepresentsthegeometryofuserandsatellitestobeusedArectangularcoordinatewithzaxisintheverticaldirectionatuserpointisadoptedforconvenienceForn,theleastsquaresolutionofEq(l)isobtainedasfollows:x=(G~G)'G~Y()Ifthedistancemeasuringerrorinyaremutuallyindependentandhaveequalvariance,weobtainthecovariancematrixoftheerrorinxas(GTG)'aDenotingtheelementsof(GTG)'aswedefineDOP'sasfollows:VDOP=E()TDOP=()DOP'sarethemultiplicationfactorsoftheestimateddistancemeasurementenorfortheestimationofrelevantpositionandortimeerrorsThesmallerDOPmeansthebettergeometrywhichbringsthemoreaccurateestimationofpositionandortimeThefollowingsectiondiscusssomerelationsamongVDOP,HDOPandPDOPSIMULATIONANDDISCUSSIONComputersimulationswereperformedtoinvestigatetheaccuracyimprovementthroughselectionsofthefoursatellitestominimizeVDOPandHDOPseparatelyThefollowingconditionswereusedinthissimulation:()GPSsatelliteshadtheprimarySVconstellation,()samplepointswereplacedinnorthernhemispherewithdegreeintervalinlongitudeanddegreeintervalinlatitudewhileintwelvehourswithminutesintervalThenumberofthesamplepointsamountstoXX=,DependenceofDOP'sonlatitudehasbeenfistobtainedinthissimulationwherethefoursatelliteswhichminimizePDOPisusedExampleoftheresultsaveragedoverthesamelatitudesamplesformaskangleofdegreeisshowninFigAsimilarexampleisshowninFigwherethefoursatelliteswhichminimizeVDOPhavebeenusedBycomparingFigandFig,itisseenthatVDOPissomewhatimprovedinFigwhileHDOPandPDOParedegradedasapenaltyPDOPVDOPAHDOPMA='ae***a~mam~W'kAAAAAkLatitudeindegreeFigAverageDOPswithfoursatellitesminimizingPDOPPDOPVDOPcMA="Ra**AHDOPe,AA"mpLatitudeindegreeFigAverageDOPswithfoursatellitesminimizingVDOPtMaskangleOlooAOILatitudeindegreeFigImprovementinaverageVDOPTovisualizetheamountofimprovementinVDOPwhenthefoursatellitesminimizingVDOPwereused,thedifferenceinVDOPbetweenFigandFigwerecalculatedandplottedinFigasamountofimprovementwithmaskangleofdegreesThesimilarimprovementsinHDOPfordifferentmaskanglehavealsobeenplottedinFigInthisfigure,weseethattheimprovementinVDOPisincreasedarounddegreeoflatitudeFigshowsthesimilarimprovementinHDOPwhenthefoursatellitesminimizingHDOPwereusedItisseenthattheimprovementsinHDOParedecreasedinmiddlelatitudeMaskangleOlooAOLatitudeindegreeFigImprovementinaverageHDOPWVDOPMaskangleindegreeFlgDependenceofimprovementonmaskangleTherelationbetweenthemaskangleandtheamountofimprovementaveragedoverallsamplepointsisshowninFigAtendencyisobservedthattheimprovementdecreasesasthemaskanglebecomeslargeThisseemstocomefromthefactthataveragenumberofvisiblesatellitesdecreasesasthemaskangleincreases,andthereforetheroomforchangingthecombinationofthefoursatellitesalsodecreasesUptohereweconsideredaverageDOP'soversamplepointsinthesamelatitudeorallearthsurfaceHoweverthedistributionoftheamountofimprovementwillbemoresuggestivesinceithaslargedistortionFigtoFigshowfrequencydistributionoftheamountoftheimprovementTheupperdiagramineachfigureshowsforVDOPandtheloweroneshowsforHDOPFiguresindifferentfigurenumberscorrespondtodifferentmaskangleswhichareshownoneachfigurebyMA=TheamountofimprovementisalwaysexpressedbycomparisonwithvalueinthecaseofusingthefoursatellitesminimizingPDOPTheordinatesshowingfrequencyuselogarithmicscaletoillustratevalueshavingspreadingofseveralordersThisscalebringsdifficultyinplottingzerosamplevalue,whichweexpressedbylevelforconvenienceThemainresultsobtainedfromFigtoFigareas~ollows:()TheimprovementinVDOPandHDOPuptoisalwayspossibleinsomegeometry(ieithasnonzerofrequency)()Theimprovementuptoisobservedinsomecase,butthatexceedingisnotobservedThenpracticalupperlimitoftheimprovementisconsideredtobe()Sampleswithimprovementrangefromto(whichmeanspracticallyzeroornearlyzeroimprovement)increasewithmaskangle()ThoughtheaverageimprovementinHDOPislargerthanthatinVDOP,thefrequencydistributionofthebothDOPsshownoremarkablepeculiarityca)Q)gIImprovementinVDOPEHDOPWJgIIImprovementinHDOPFigImprovementinDOP'satmaskangledegreeEImprovementinVDOP"IImprovementinHDOPFigImprovementinDOP'satmaskangledegreetIVDOPMA=l"GinnnVDOPImprovementinVDOPImprovementinVDOPgsCULrlooooLreUI~nnnnEHDOPLHDOPMA=l"CULrMA="G"gsULreIImprovementinHDOPfmprovementinHDOPFigImprovementinDOP'satmaskangledegreeFigImprovementinDOP'satmaskangledegreeVDOPVDOPctg$cca,Ua,LLrIImprovementinVDOPImprovementinVDOPloooo$gcca,a,LLhHDOPHDOPEEa,LLa,$gImprovementinHDOPImprovementinHDOPFigImprovementinDOP'satmaskangledegreeFigImprovementinDOP'satmaskangledegree~~FVDOPImprovementinVDOPHDOPMA="ca,gELniImprovementinHDOPFigImprovementinDOP'satmaskangledegreeVDOPMA="ca,JUa,LlLrIIImprovementinVDOPHDOPLVDOPiMA="cwLr$:IImprovementinVDOPLHDOPMA="i$cwLrIImprovementinHDOPFigImprovementinDOP'satmaskangledegreeVDOPRMA="IImprovementinVDOPLHDOP"'ImprovementinHDOPFigImprovementinDOP'satmaskangledegreeImprovementinHDOPFigImprovementinDOP'satmaskangledegreeCONCLUSIONSThispaperhasdealtwiththeaccuracyofthefourdimensionalpositioningusingGPSItisassumedthattheuserreceiveralwaysselectsandusesasetoffoursatellitesAsimulationstudyhasbeenmadeWeexaminedthepossibilitytoimprovetheaccuracybyselectingthesetoffoursatellitesfordifferentsubspacesseparatelyThefollowingconclusionshavebeenderived()ThesetsoffoursatellitesthatminimizeHDOP,VDOPandPDOParesometimesthesame,buttheyaredifferentfrequently()TheaverageaccuraciesoftheverticalandhorizontalpositioningaresomewhatimprovedbyoursatelliteselectingpolicycomparedwiththoseusingthesinglecriterionofPDOP()TheamountoftheimprovementinaveragedvaluesdependsonthemaskangleInthetypicalrangeofmaskangleoftodegree,theimprovementinVDOPisaboutwhilethatinHDOPisaboutREFERENCESlRJMillikenandCJZoller,"PrincipleofOperationofNAVSTARandSystemCharacteristics,"Navigation,vo,pp,SummerCGBGreen,PDMassattandNWRhodus,"TheGPSPrimarySatelliteConstellation,"Navigation,vo,pp,Spring

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