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一种GPS精密星历的多项式插值方法
Title:PolynomialInterpolationMethodforPreciseGPSEphemeris
Introduction:
TheGlobalPositioningSystem(GPS)reliesonaccurateandup-to-dateephemerisdatatoprovidepreciselocationandtiminginformation.EphemerisdataincludestheinformationaboutthepositionsandvelocitiesoftheGPSsatellitesatagiventime.However,acquiringaccurateephemerisdatacanbechallengingduetofactorssuchassatelliteorbitperturbations,clockerrors,andsignalpropagationdelays.ToovercomethesechallengesandimprovetheaccuracyofGPSpositioning,variousinterpolationmethodshavebeendeveloped,includingpolynomialinterpolation.ThispaperaimstoexploretheapplicationofpolynomialinterpolationforpreciseGPSephemeris.
1.BackgroundandProblemStatement:
TheGPSsystemconsistsofaconstellationofsatellitesorbitingtheEarth,transmittingsignalsthatarereceivedbyGPSreceiversontheground.Thesesignalscontaininformationaboutthepositionandvelocityofthesatellites,whichisnecessaryforaccuratepositioning.However,ephemerisdataneedstobecontinuouslyupdatedduetofactorssuchassatelliteorbitperturbations,clockerrors,andsignalpropagationdelays.Thechallengeistoobtainaccurateandup-to-dateephemerisdatafromthelimitedinformationreceivedbyGPSreceivers.
2.LiteratureSurvey:
PreviousstudieshaveproposedseveralinterpolationmethodsforgeneratingpreciseGPSephemeris,suchasLagrangeinterpolation,cubicsplineinterpolation,andpolynomialinterpolation.LagrangeinterpolationiscommonlyusedinGPSreceiversduetoitssimplicity.However,itsuffersfromtheRunge'sphenomenon,wheretheinterpolatedfunctionmayoscillatesignificantlybetweenthedatapoints.CubicsplineinterpolationavoidstheRunge'sphenomenonbutrequiressolvingasystemofequations.Polynomialinterpolationoffersanalternativeapproachthatcombinessimplicityandaccuracy.ThispaperfocusesonthepolynomialinterpolationmethodforpreciseGPSephemeris.
3.Methodology:
Thepolynomialinterpolationmethodapproximatesafunctionbasedonasetofdiscretedatapoints.GivenasetofGPSephemerisdataatspecifictimes,thepolynomialinterpolationmethodaimstofindapolynomialfunctionth