全球定位系统(GPS)中的广义相对论效应及其对系统(3)

全球定位系统(GPS)中的广义相对论效应及其对系统静态绝对定位方程的修正

ABSTRACT

AccordingtoEinstein’sgeneralrelativity,space-timeiscurvedbecauseof

gravitation.Theeffectofcurvedspace-timearoundearthischaracterizedbySchwarzschildsolution.

TherelativisticeffectstoGlobalPositionSystem(GPS)asfollows:1)theeffectof

timedelayofthespecialrelativity;2)theeffectofthegravitationalpotentialofthegeneralrelativity;3)theeffectofcurvedspace-timearoundearthonthesignaltransmission;4)theframe-draggingeffectfortherotationofearth.5）theeffectofcurvedspace-timeofsun,moonandcelestialbodieselse.

ThestaticabsolutepositionprincipleofGlobalPositionSystem(GPS)isthemost

radicalpositionprinciple.Bymeasuringthetraveltime,accordingastheobservedquantityofdistancefromtheGPSsatellitestogroundreceiver,andbasedontheknowninstantaneoussatellites’coordinates,finallygroundreceiver’scoordinatesareobtained.Butthereisclockbiasbetweensatellites’clocksandreceiver’s.SothedistanceobservationquantityofGPSisadoptedasthepseudo-rangebetweensatellitesandreceiver.

Nowadays，itisthoroughlyconsideredthattheeffectoftimedelayofthespecial

relativityandtheeffectofthegravitationalpotentialofthegeneralrelativity.Butthedistancebetweenthesatellitesandreceiveriscalculatedintheflatspace-time.Theeffectofthetransitionofpositionsignalincurvedspace-timeisnotconsidered.

Because4)and5)areveryweak,theyareignored.Soapplyingthegeneral

relativity,giventhattheearthgravityisregardedstaticandsphericallysymmetric,thatthemassofsatellitesisneglectedandthesatellitesmoveincircularorbits,andthatthecelestialbodiesotherthanearthmakenoaffectionstothespace-time,afteraseriousofcomplicatedcalculationandproof,themorestrictequationsareobtainedfortheGPSstaticabsolutepositionbyconsideringtheeffectofthetransmissionofsignalincurvedspace-time(thatis,g00andg11componentoftheSchwarzschildmetricisthoroughly

considered)onthebasisofpreviousstaticabsolutepositionequation.

Becausethefinalcorrectedequationisnon-linear,itisdifficulttogainthesolution.

Sotheequation’scorrectedtermsarecalculatedbythesoftwareofmathematics.Afterthesupposedfoursatellites’coordinatesandreceiver’scoordinatearetakenintoaccount,thecorrectionasfollows:satelliteone(0.00138367m);satellitetwo(0.000713467m);