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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,Yokosuka239,JapanAbstract-ThefourdimensionalaccuracyofGPSpositioningusingfoursatellitesateveryinstantisreexamined.UserreceiversusuallyselectsuitablefoursatellitesthathavebestgeometrybasedonPDOPorGDOP.However,itismorereasonabletoselectasetoffoursatellitesthathasminimumVDOPformeasuringverticalposition,whiletoselectasetoffoursatellitesthathasminimumHDOPformeasuringhorizontalposition.Inthisstudies,weproposeamethodofusingVDOPandHDOPasthecriteriatoselectthesetoffoursatellitesusedformeasuringverticalandhorizontalpositionsrespectively,andcompareitsperformancewiththatoftheconventionalmethodbycomputersimulation.ItisclarifiedthatthecombinationsofthefoursatellitesthatminimizeVDOP,HDOPandPDOParegenerallydifferenteachother,andlimitedamountofimprovementinVDOPandHDOPisobtainedbyoptimizingthemseparately.Dependenceoftheamountoftheimprovementonlatitudeandmaskangleisalsoexamined.instantandusedforpositionfur.However,itisconsideredtobemorereasonabletouseVDOPorHDOPforverticalorhorizontalpositionfixrespectively,sinceVDOPandPDOPvaluesaregenerallydifferenteachother.Itiswell-knownfortheGPSmeasurementthatverticalaccuracyisinferiortohorizontalaccuracybecauseofrestrictionofgeometryresultedfromearthmasking.Thisstudyhasbeenmotivatedfromanexpectationthattheverticalaccuracymightbeimprovedbyaselectionofthefoursatellitesconcentratedontheverticalaccuracy.ThispaperproposesaselectionpolicyofthefoursatellitesthatusesVDOPandHDOPforverticalandhorizontalmeasurementrespectivelyascriteriatoobtaingoodaccuracy.Performanceofthismethodisevaluatedbycomputersimulationanditsdependenceonlatitudeandmaskangleisdiscussed.AmountofimprovementinaccuracycomparedwiththeconventionalmethodusingPDOPisalsodiscussedstatistically.DEFINITIONOFPOSITIONACCURACYINTRODUCTIONConsiderthefollowingbasicmeasurementequationLowcostGPSreceiverisgrowingintypeandfortheGPSusingnvisiblesatellites[l]:numberinaccordancewithgrowinginterestofpublicGX=y(1)user.Itishopedforthesereceiverstohaveashighperformanceandaslowpriceaspossible.Inthesereceivers,asetoffoursatellitesthathasminimumPDOPisusuallyselectedfromvisiblesatellitesateverywherex=[RxRyR,BIT(2)2670-7803-1435-2/94$3.0001994IEEEG=e,T-1e:-1........e,'-1(3)Intheseequation,R,,5,R,arethethreecomponentofusepositionvector,Bistheuserclockbias,andthereforexisthefourdimensionalvectortobedeterminedbythepositionfix.yisavectorgivenbymeasurementwhichincludesmeasureddistancesfromusertoeachsatellite,satellitepositionsgivenbyephemerides,andsatelliteclockbiases(known).el,e,,-,enareunityvectorsdirectingfromusertoeachsatellite.ThenGisanrows4columnmatrixwhichrepresentsthegeometryofuserandsatellitestobeused.Arectangularcoordinatewithzaxisintheverticaldirectionatuserpointisadoptedforconvenience.Forn24,theleastsquaresolutionofEq.(l)isobtainedasfollows:x=(G~G)-'G~Y.(4)Ifthedistancemeasuringerrorinyaremutuallyindependentandhaveequalvariance,weobtainthecovariancematrixoftheerrorinxas(GTG)-'a%.Denotingtheelementsof(GTG)-'aswedefineDOP'sasfollows:VDOP=E(9)TDOP=@(10)DOP'sarethemultiplicationfactorsoftheestimateddistancemeasurementenorfortheestimationofrelevantpositionand/ortimeerrors.ThesmallerDOPmeansthebettergeometrywhichbringsthemoreaccurateestimationofpositionand/ortime.ThefollowingsectiondiscusssomerelationsamongVDOP,HDOPandPDOP.SIMULATIONANDDISCUSSIONComputersimulationswereperformedtoinvestigatetheaccuracyimprovementthroughselectionsofthefoursatellitestominimizeVDOPandHDOPseparately.Thefollowingconditionswereusedinthissimulation:(1)GPSsatelliteshadthe21primarySVconstellation[2],(2)samplepointswereplacedinnorthernhemispherewith12degreeintervalinlongitudeand10degreeintervalinlatitudewhileintwelvehourswith15minutesinterval.Thenumberofthesamplepointsamountsto30X9X48=12,960.DependenceofDOP'sonlatitudehasbeenfistobtainedinthissimulationwherethefoursatelliteswhichminimizePDOPisused.Exampleoftheresultsaveragedoverthesamelatitudesamplesformaskangleof5degreeisshowninFig.1.AsimilarexampleisshowninFig.2wherethefoursatelliteswhichminimizeVDOPhavebeenused.BycomparingFig.1andFig.2,itisseenthatVDOPissomewhatimprovedinFig.2whileHDOPandPDOParedegradedasapenalty.PDOPVDOPAHDOPMA=5'a-...-e......*/..4...-...........1-*-.-..*.....a.2.5~m...........a8.m.....~....-W----4'..........k......A..AA-----.A-1.--&.----A...............k0306090LatitudeindegreeFig.1AverageDOPswithfoursatellitesminimizingPDOP.PDOPVDOP5.5cMA=5"Ra4*0*3.2.AHDOP......................e,&...........A............A"...........m.........p..0306090LatitudeindegreeFig.2AverageDOPswithfoursatellitesminimizingVDOP.15tMaskangle5OlooA15O1005003060I90LatitudeindegreeFig3ImprovementinaverageVDOPTovisualizetheamountofimprovementinVDOPwhenthefoursatellitesminimizingVDOPwereused,thedifferenceinVDOPbetweenFig.1andFig.2werecalculatedandplottedinFig3asamountofimprovementwithmaskangleof5degrees.ThesimilarimprovementsinHDOPfordifferentmaskanglehavealsobeenplottedinFig.3.Inthisfigure,weseethattheimprovementinVDOPisincreasedaround30degreeoflatitude.Fig.4showsthesimilarimprovementinHDOPwhenthefoursatellitesminimizingHDOPwereused.ItisseenthattheimprovementsinHDOParedecreasedinmiddlelatitude.Maskangle5OlooA15O0306090LatitudeindegreeFig.4ImprovementinaverageHDOPWVDOP0510152025MaskangleindegreeFlg.5DependenceofimprovementonmaskangleTherelationbetweenthemaskangleandtheamountofimprovementaveragedoverallsamplepointsis269...................1showninFig.5.Atendencyisobservedthattheimprovementdecreasesasthemaskanglebecomeslarge.Thisseemstocomefromthefactthataveragenumberofvisiblesatellitesdecreasesasthemaskangleincreases,andthereforetheroomforchangingthecombinationofthefoursatellitesalsodecreases.UptohereweconsideredaverageDOP'soversamplepointsinthesamelatitudeorallearthsurface.Howeverthedistributionoftheamountofimprovementwillbemoresuggestivesinceithaslargedistortion.Fig.6toFig.15showfrequencydistributionoftheamountoftheimprovement.TheupperdiagramineachfigureshowsforVDOPandtheloweroneshowsforHDOP.FiguresindifferentfigurenumberscorrespondtodifferentmaskangleswhichareshownoneachfigurebyMA=....TheamountofimprovementisalwaysexpressedbycomparisonwithvalueinthecaseofusingthefoursatellitesminimizingPDOP.Theordinatesshowingfrequencyuselogarithmicscaletoillustratevalueshavingspreadingofseveralorders.Thisscalebringsdifficultyinplottingzerosamplevalue,whichweexpressedby0.1levelforconvenience.ThemainresultsobtainedfromFig.6toFig.15areas~ollows:(1)TheimprovementinVDOPandHDOPupto0.6isalwayspossibleinsomegeometry(i.e.ithasnon-zerofrequency)(2)Theimprovementupto1.0isobservedinsomecase,butthatexceeding1.0isnotobserved.Thenpracticalupperlimitoftheimprovementisconsideredtobe1.0.(3)Sampleswithimprovementrangefrom0to0.05(whichmeanspracticallyzeroornearlyzeroimprovement)increasewithmaskangle.(4)ThoughtheaverageimprovementinHDOPislargerthanthatinVDOP,thefrequencydistributionofthebothDOPsshownoremarkablepeculiarity.100000c1000a.)Q)g10021010100.5I.0ImprovementinVDOP510000EHDOPW1000J&g10010I0.100.5I.0ImprovementinHDOPFig.6ImprovementinDOP'satmaskangle2.5degreeEImprovementinVDOP"..00.5I.0ImprovementinHDOPFig.7ImprovementinDOP'satmaskangle5degree270tIVDOPMA=l2.5"10000Ginnn10000VDOP00.51.00.51.0ImprovementinVDOPImprovementinVDOP1000051000g10003s100CULr.5looooLr.e10210U1001I0.100.51.000.51.00.1.~nnnnEHDOP10000LHDOP51000MA=l2.5"CULr.MA=7.5"G---"-g10003s100U100Lr.e102101I0.100.51.000.51.00.1ImprovementinHDOPfmprovementinHDOPFig.8ImprovementinDOP'satmaskangle7.5degreeFig.10ImprovementinDOP'satmaskangle12.5degree10000VDOP10000VDOPc1000t?g100$10010210cc1000a,Ua,10.1LLr.I0.100.51.000.51.0ImprovementinVDOPImprovementinVDOP5loooo$100g10010000c1000c1000a,5a,2210LL101100.51.000.51.00.10.110000hHDOP10000??HDOPE1000E1000a,2210LL10a,$100g1001100.51.000.51.00.10.1ImprovementinHDOPImprovementinHDOPFig.9ImprovementinDOP'satmaskangle10degreeFig.11ImprovementinDOP'satmaskangle15degree271-.................-........~-.-.~.FVDOPImprovementinVDOPHDOP100005MA=17.5"c1000a,g100E10L1ni00.51.0ImprovementinHDOPFig.12ImprovementinDOP'satmaskangle17.5degree10000VDOP51000MA=20"ca,J100Ua,Ll10Lr10.I00.5I.0ImprovementinVDOP10000HDOP10000LVDOPi?1000MA=22.5"cwLr$100:1010.100.5I.0ImprovementinVDOP10000LHDOPMA=22.5"i?1000$100cwLr10101I..00.51.0ImprovementinHDOPFig.14ImprovementinDOP'satmaskangle22.5degreeVDOPRMA=25"??I0001000000.51.0ImprovementinVDOP10000LHDOP".'00.51.0ImprovementinHDOPFig.13ImprovementinDOP'satmaskangle20degree00.51.0ImprovementinHDOPFig.15ImprovementinDOP'satmaskangle25degree272CONCLUSIONSThispaperhasdealtwiththeaccuracyofthefourdimensionalpositioningusingGPS.Itisassumedthattheuserreceiveralwaysselectsandusesasetoffoursatellites.Asimulationstudyhasbeenmade.Weexaminedthepossibilitytoimprovetheaccuracybyselectingthesetoffoursatellitesfordifferentsubspacesseparately.Thefollowingconclusionshavebeenderived.(1)ThesetsoffoursatellitesthatminimizeHDOP,VDOPandPDOParesometimesthesame,buttheyaredifferentfrequently.(2)TheaverageaccuraciesoftheverticalandhorizontalpositioningaresomewhatimprovedbyoursatelliteselectingpolicycomparedwiththoseusingthesinglecriterionofPDOP.(3)Theamountoftheimprovementinaveragedvaluesdependsonthemaskangle.Inthetypicalrangeofmaskangleof5to10degree,theimprovementinVDOPisabout0.07whilethatinHDOPisabout0.15.REFERENCES[l]R.J.MillikenandC.J.Zoller,"PrincipleofOperationofNAVSTARandSystemCharacteristics,"Navigation,vo1.25,pp.95-106,Summer1978.[2]C.G.B.Green,P.D.MassattandN.W.Rhodus,"TheGPS21PrimarySatelliteConstellation,"Navigation,vo1.36,pp.9-24,Spring1989.273

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