Mixed integer programming for the resolution of GPS carrier

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1、1PresentedattheIUGG95Assembly,Boulder,Colorado,July2-14,1995.MixedintegerprogrammingfortheresolutionofGPScarrierphaseambiguitiesPeiliangXuElizabethCannonGerardLachapelleDepartmentofGeomaticsEngineering,TheUniversityofCalgary2500UniversityDr.NW,CalgaryABT2N1N4,CanadaAbstractThisarXivup

2、loadistoclarifythatthenowwell-knownsortedQRMIMOdecoderwasfirstpresentedinthe1995IUGGGeneralAssembly.Weclearlygomuchfurtherinthesensethatwedirectlyincorporatedreductionintothisonestep,non-exactsuboptimalintegersolution.Exceptforthesefirstfewlinesuptothispoint,thispaperisanunalteredversio

3、nofthepaperpresentedattheIUGG1995AssemblyinBoulder.TheAmbiguityresolutionofGPScarrierphaseobservablesiscrucialinhighprecisiongeodeticpositioningandnavigationapplications.Itconsistsoftwoaspects:estimatingtheintegerambiguitiesinthemixedintegerobservationmodelandexaminingwhethertheyaresu

4、fficientlyaccuratetobefixedasknownnonrandomintegers.Weshalldiscussthefirstpointinthispaperfromthepointofviewofintegerprogramming.Aone-stepnonexactapproachisproposedbyemployingminimumdiagonalpivotingGaussiandecomposi-tions,whichmaybethoughtofasanimprovementofthesimplerounding-offmethod,sinc

5、etheweightsandcorrelationsofthefloating-estimatedambi-guitiesarefullytakenintoaccount.Thesecondapproachistoreformulatethemixedintegerleastsquaresproblemintothestandard0-1linearintegerprogrammingmodel,whichcanthenbesolvedbyusing,forinstance,thepracticallyrobustandefficientsimplexalgorithm

6、forlinearintegerprogram-ming.Itisexact,ifproperboundsfortheambiguitiesaregiven.Theoreticalresultsondecorrelationbyunimodulartransformationaregivenintheformofatheorem.arXiv:1010.1052v1[cs.IT]6Oct20101IntroductionThreetypesofobservablesmaybederivedfromtrackingGPSsatellites:pseudorange(c

7、ode)mea-surements,rawDopplershifts(orequivalentlyrangerates)andcarrierphases.Theyareusedatdifferentlevelsofaccuracyfordifferentpurposesofapplications(seee.gWellsetal.1986;Leick1990;Hofmann-Wellenhofetal.1992;Seeber1993;Melbourne1985).Thecarrierphasemeasurements,togetherwiththeaccurateco

8、deobs