Chapter4VLBITrackingObservables4.1VLBISystemDescriptionThissectionintroducestheconceptofVLBItrackingandexaminesmajorsystemelements.VLBItechnologymakesuseofthebroadbandmicrowaveradiationemittedbyextragalacticradiosourcessuchasquasars.Thesignalsaretypicallyveryweak(<1Jyor10–26WHz–1m–2ofaperture;hencetheneedforrelativelylargeantennas,low-noisereceivers,andwidebandrecord-ingdevices.TheDSNhadanoperationalVLBIsystemforspacecrafttracking(referredtoastheNarrowChannelBandwidth[NCB]VLBISystem[1,2]from1984through1998.ThesystemoperatedatS-bandandX-bandon34-and70-mantennas.Systemtemperatureswereapproximately20KatS-bandand30KatX-band.Thesystemrecordedopenloopat500kbit/s.Therecordrateof500kbit/swaschosentofacilitatenear-real-timedatatransmissionandprocessingfornavigationsupport.Thismoderatedatarateledtothedescrip-tivesystemtitle“narrow,”incontrastwithotherradioastronomysystems,whichoperateatdataratesofhundredsofmegabitspersecond.ObservablesgeneratedbytheVLBIsystemaresometimesreferredtoas“instantaneousangles,”eventhoughseveralminutesofintegrationtimearetypicallyneces-sarytoreducetheerrorcausedbysystemnoisetoalevelcomparabletoothermeasurementerrors.ConsiderthesituationinFig.4-1,wherethewavefrontfromadistantsourcearrivesasaplanewaveattwowidelyseparatedantennas.Thesignalsareamplified,heterodynedtobaseband,digitized,timetaggedandrecorded.Therecordedsignalsaresubsequentlycross-correlatedtodeterminethediffer-enceinthesignaltimeofarrivalatthetwostations.ThisdifferentialarrivaltimeisreferredtoastheVLBIdelayandiscomposedofageometricdelayplus4750Chapter4tones.Thedifferentialdelaybetweenspacecraftandquasaristermed?DOR,andyieldsahighlyaccuratemeasureofthespacecraftangularpositionintheradiosourcereferenceframe.Ambiguousmeasurementsofphasedelaysyieldinformationonlyonthedelayrate.Thismeasurementtypeisimportant,however,sinceitmaybeobtainedfromspacecraftthatemitonlyacarriersignal.Severalhoursofphase-delay-ratedatamaybeusedtoinferangularcoordinatesinmuchthesamewayasDopplermeasurements[7].Foraplanetaryorbiter,phase-delay-ratedatadirectlymeasuretheorientationoftheorbitplaneaboutthelineofsightfromEarthtotheplanet,asnotedinSection3.6.Aseparatereceivingsystem,whichoperatesatahigherdataratethantheNCBsystem,isusedintheDSNtosupportthesourcecatalogdevelopmenteffort.Datawereacquiredfrom1978to1989usingtheMarkIIVLBIsystem[13],andsincethenusingtheMarkIIIVLBIsystem[14].TheinstallationofMarkIIIterminalsoperatingat112Mbit/s,coupledwithlow-noiseamplifiershaving400-MHzbandwidthandotherimprovements,havegreatlyincreasedthesensitivityofthesystem.Theseimprovementscontinuetoenablefurtheradvancesinsourcepositionandbaselineaccuracies.NavigationtotheplanetsusingVLBItrackingrequiresknowledgeofplan-etaryephemeridesintheradioreferenceframe.Theplanetaryephemerideshaveevolvedfrommanydecadesofobservations,largelyEarth-basedopticalandradar,supplementedwithplanetaryencounterdataandlaserrangingtothemoon[15].Analysesofthesedatahaveproducedlunarandplanetaryephemer-idesinaself-consistentreferenceframetiedtothedynamicalequinoxandpre-cessedtotheepochJ2000[16].ThemostrecentephemeridesarealsofittoVLBITrackingObservables51frame-tiedatathatdirectlyaligntheplanetaryephemeriswiththeICRF[17,18].TheinternalprecisionoftheplanetaryephemerisreferenceframerivalsthatoftheICRF,atthe5-nradlevel[19],butmostindividualbodiesarenotknowntothislevel.Withintheplanetaryephemerisframe,thepositionsofVenus,Mars,Earth,andthemoonareallknowntothe5-nradlevel,dueprimarilytoaccuratemea-surementsmadeoverthelast30years.SourcesofthesemeasurementsincludeLLR,preciseradiorangingtotheVikingandPathfinderlanders,radarrangingtoVenus,and?DORmeasurementsoftheMagellanorbiteratVenus.ThepositionofMercuryisknownonlytothe25-nradlevel.Oftheouterplanets,Jupiter’spositionisbestknownatthe100-nradlevel,duetorangingtotheVoyagerandUlyssesspacecraft,and?DORmeasurementsoftheUlyssesandGalileospacecraft[20,21].Thepositionsoftheotherlargeouterplanetsareknownonlytoaboutthe250-nradlevel,whilethepositionofPlutoisuncertainatthemicroradianlevel[22,23].Theremaininguncertaintyintheorientationoftheplanetaryephemerisframewithrespecttotheradioframeisatthe5-nradlevelinallcomponents[17].Thisaccuracyhasonlyrecentlybeenachieved.TheoffsetintheoriginofrightascensionwashundredsofnanoradiansuntilthefirstVLBImeasurementsweremadeofspacecraftatplanetaryencounters.TheMarsVikingandthePio-neerVenusorbitersprovidedanearlyopportunityformeasuringtheplanetary-radioframeoffset.Thepositionofeachorbiterrelativetotheplanetwasdeter-minedfromEarth-basedDopplertracking.DeltaVLBIphase-delay-ratemea-surementsbetweentheorbiterandanangularlynearbyradiosourcethenprovidedameasureoftheframetie.Accuraciesofabout100nradinbothrightascensionanddeclinationwereachieved[24].Experimentstorefinetheframetieincludedmeasurementsofmillisecondpulsarsandthetimingofocculta-tionsofradiosourcesbyplanetaryobjects.Butthefirstsignificantimprove-mentinknowledgeoftheframetiewasmadeintheearly1990sbycomparingtheterrestrialreferenceframesassociatedwithVLBIandLLRdataanalyses.TheVLBIsolutionstietheDSNstationstotheradioframe,whiletheLLRsolutionsarecloselytiedtotheplanetaryephemerisreferenceframe[16].ThetiebetweentheDSNandtheLLRstationsisdeterminedfromcommonsitemeasurementsmadebytheNASACrustalDynamicsProject,usingVLBIandSLR.Theframetiewasdeterminedbythismethodto15nradineachcompo-nent[25].Thisaccuracywasconfirmedandimprovedtothe5-nradlevelbytheacquisitionof18?DORmeasurementsoftheMagellanorbiteratVenusbetween1990and1994[17,26].Whilethe?VLBIsystemislargelyself-calibrating,anumberoferrorsdonottotallycancelwhenmeasurementstoindividualsourcesaredifferenced.52Chapter4Forexample,thecancellationoferrorsduetoPM,UT,stationlocations,andmediadelaysisdependentupontheangulardistancebetweensources.Inordertominimizetheseeffectsinthetrackingobservable,itisnecessarytoselectradiosourcesangularlyclosetothespacecraftandapplythemostaccurateavailablecalibrationsfortheseeffects.Previously,theNCBVLBIsystemitselfprovidedtheDSNwithaccuratemeansfortimelydeterminationofUT,PM,andclockparameters.TheGPScalibrationsystem,anchoredbymonthlywide-bandVLBImeasurements,isnowusedforthispurpose.TheGPScalibrationsystemisalsousedtogenerateline-of-sightcalibrationsforionosphericdelaysandcalibrationsforzenithtroposphericdelays(seeChapter3.Themajorsourcesoferrorinpresentday?VLBIobservationsaretypicallymeasurementsignal-to-noiseratios(SNRs,uncalibratedtropospheredelays,baselineerrors,andinstrumentaldelays(seeFig.4-2.Modelsforestimatingthesemeasurementerrorshavebeendeveloped[27].Thissectionsummarizesthemajorsystemdesignandcalibrationlimitationstooverallperformance.ExpectationsforfuturesystemimprovementsarepresentedinChapter5.ThemagnitudeofeacherrorsourceinVLBIishighlydependentuponsys-temoperatingparameters.Forexample,SNRforquasarmeasurementsdependsuponquasarfluxdensity,recordingbandwidth,systemtemperature,antennadiameterandefficiency,andintegrationtime.Althoughtrade-offsmaybemadebetweensuchvariablesasantennasize,sourcestrength,andintegrationtime,theymaybeconstrainedbyotherconsiderations,suchastheavailabilityofsuf-ficientlystrongsourcesangularlyclosetothespacecraft.Ideally,onewouldliketofindstrong(1-Jysourceswithinafewdegreesofthespacecraft,butthissitu-ationismoretheexceptionthantherule.ConsiderthemapofavailablesourcesforVLBItrackingoftheGalileospacecraft,showninFig.4-3.Catalogsourceswithina15-degbandabouttheGalileotrajectoryvaryinstrengthfrom1Jydownto0.1Jy.Itshouldbenotedthatthescarcityofknownsourcesneartheencountercoordinatesisduetotheintersectionoftheeclipticandgalacticplanes.Thedirectionspecifiedby18-hrightascensionand–23-degdeclinationisintheplaneoftheMilkyWay,directlytowardthegalacticcenter.Thelargequantityofradioemissionsorigi-natingwithinourowngalaxyhashamperedeffortstosurveyandcatalogcom-pactextragalacticradiosourcesinthisdirection.For?DORmeasurements,asourcestrengthof0.4Jywasrequiredusinga70-mand34-mDSNantennapairwiththenow-retiredNCBVLBIsystemanda10-minintegrationtime.ThenewVSRdesignhasthecapabilitytosupportahigherdatarecordingratethatwilllowerthesourcedetectionthresholdbyafactoroftwoormore.Thisincreasedsensitivitywillallowtheselectionofaweakersourceangularlyclosertothespacecraft,ortheuseofsmallerantennas.VLBITrackingObservables53Fig.4-2.Errorbudgetforspacecraft-quasar?DORdelaymeasurementsforboththeprior-andnext-generationtrackingsystems,consistentwithsystemcharacteristicsgiveninTable4-1.Whilemosterrorsscaledownwithangularseparationbetweenthespace-craftandthequasar,instrumentalerrorsdependmoreonthecharacteristicsoftheradiosignals.Inparticular,dispersiveinstrumentaleffectsin?DORmea-surementsareinverselyproportionaltothetotalspannedbandwidthoftherecordedsignals.Limitationsonspannedbandwidtharetypicallyimposedbythespacecraftradiodesign;thequasarsaresufficientlybroadband.Moreover,theDSNfrontendcanaccommodate400MHzatX-bandand100MHzatS-band.Ontheotherhand,forallspacecraftcurrentlyinflightatthetimeofpublication,thewidestDORtonespacingis38MHzatX-band.Internationalfrequencyallocationslimitspacecrafttransmissionsto50MHzatX-band.However,theallocatedbandwidthatKa-bandis500MHz[28].Future?DORsystems,operatingatKa-bandandutilizingtonesseparatedby200MHz,willgreatlyreduceinstrumentalandotherdispersiveerrors.54Chapter4Fig.4-3.AngularcomponentsofGalileospacecrafttrajectoryduringtheJupiterapproach.Alsoshownarecatalogradiosourceswithin15degofthetrajec-toryandhavingfluxgreaterthan0.1Jy.4.2SpacecraftVLBISystemPerformanceInterferometricmeasurementsdirectlydetermineangularcomponentsofspacecraftstate.Theinclusionof?DORdatawithlongarcsofDopplerandrangedatadesensitizestrajectorysolutionstomismodeleddynamicforces,andcanimproveknowledgeofspacecraftpositionbyafactoroffiveormore.Therealizedimprovementintrajectoryaccuracywithrespecttoatargetdependsonknowledgeofthetargetpositionintheradioframe.BoththeGalileoandMarsObserverprojectshadarequirementfor?DORmeasurementswithaone-sigmaaccuracyof50nradduringtheirinterplanetarycruisephases.Require-mentstodeliverlanderstothesurfaceofMarsareexpectedtobeintherangeof5to10nrad.Thecontributionofindividualerrorsourcestotheoverallmeasurementaccuracyisknownastheerrorbudget.Anerrorbudgetfor?DORmeasure-mentsisshowninFig.4-2.Theestimatelabeled“1992”assumesaspacecraftDORtonespacingof38MHzatX-bandalongwithuseoftheNCBsystem,andhenceappliestobothGalileoandMarsObserver.TheperformanceoftheNCBVLBIsystemonGalileoandMarsObserverwasbalancedinthaterrorsduetothermalnoise,stationinstrumentation,platformparameters,andmediadelaysVLBITrackingObservables55werecomparableinsize.Measurementerrorswereestimatedusingtheformula-tionsin[27].SeeTable3-3forassumptionsoncalibrationsystemaccuracies.SeeTable4-1forassumptionsonreceivingsystemcharacteristicsandobserva-tiongeometry.AsshowninFig.4-2,thetypicalaccuracyofthe?DORsystemin1992was16nrad.However,someitemsintheerrorbudgetdependstronglyongeometry.WithotherassumptionsfixedasinTables3-3and4-1,measure-mentaccuracyof50nradwaspossibleforeventhemostunfavorablegeome-triesinvolvingspacecraftintheeclipticobservedfromDSNbaselines.Inthefinalanalysis,theperformanceoftheNCBsystemwasadequatetomeetnavi-gationrequirementsoftheGalileoandMarsObservermissions.InterferometricmeasurementshavealsobeenmadeofseveralspacecraftnotequippedwithDORtones.Differentialone-wayrangemeasurementswereacquiredbyusingharmonicsofaspacecrafttelemetrysubcarriersignal.ThistechniquewasemployedtoenhancecruisenavigationfortheVoyager[29],Magellan[30],andUlysses[20]spacecraft.However,forthesespacecraft,thewidestspacingofdetectabletelemetrysignalswassomewhatlessthanthe38MHzprovidedbytheDORtonesofGalileoandMarsObserver.Specifi-Table4-1.Spacecraft-to-quasar?DORassumedcharacteristics.CharacteristicsAssumedValueSpacecraftobservingtime10minSpacecraft-to-quasarangularseparation10degMinimumelevationangle15degElevationangledifference5degQuasarflux0.4JyObservingbandX-bandSpannedbandwidth38.25MHzSystemnoisetemperature30KVLBI1992VLBI2001Quasarcoordinates5nrad3nradQuasarobservingtime10min20minRadioandplanetaryframetie25nrad5nradDSNantennas70mand34m34mand34mChannelbandwidth0.25MHz1MHzChannelrecordingmultiplexedparallelPhasedispersion1deg0.5deg56Chapter4cally,themaximumusabletonespacingsforVoyager,Magellan,andUlyssesatX-bandwere,respectively,14MHz,31MHz,and6MHz.Sincesystemnoiseandphase-dispersionerrorsscaledinverselywithmaximumtonespacing,thesecomponentsoftheerrorbudgetwereincreasedbyacorrespondingamountfromthe1992levelshowninFig.4-2.Figure4-4displaysMagellan?DORresidualsacquiredearlyincruise.Theresidualsareshownfortwotrajectories.Thewhitesymbolsrepresentthe?DORpass-throughresidualsrelativetoatrajectorydeterminedfromDopplerdataspanningthetimeintervalshowninthefigure.Theblacksymbolsarethe?DORresidualstoatrajectoryfittoboththeDopplerandthe?DORdata(weightedat50nrad.NotethattheGoldstone-to-Madridbaselineisorientednearlyeast-west,sothatmeasurementsonthisbaselinearesensitivetospace-craftrightascension,whereasmeasurementsonthecantedGoldstone-to-Can-berrabaselineareequallysensitivetorightascensionanddeclination.Comparisonofthe?DORresidualsfortheGoldstone-to-MadridbaselinefromthetwosolutionsshowsthattheDoppler-onlysolutiondoesagoodjobofdeterminingrightascension,althoughasmalldriftoverthe17-ddataarcisapparent.Sincerightascensionhasbeendeterminedfairlywell,large?DORresidualsfortheGoldstone-to-Canberrabaselinemustbeattributedtoatrajec-toryerrorinthedeclinationcomponent.ComparisonoftheseresidualsforthetwosolutionsshowsthatthespacecraftdeclinationdeterminedfromDoppleraloneisbiasedbyatleast2.3μradanddriftsby1.6μradoverthe17-ddataarc.Whenthe?DORdataarefit,residualsforbothbaselinesarereducedtotheFig.4-4.Magellan?DORresidualsfortwoestimatedtrajectorysolutions.VLBITrackingObservables57levelofthedataaccuracy,whichis50nrad.Forthiscase,animprovementofafactorof46insolutionaccuracywasachieved.TheinaccuracyoftheDoppler-onlysolutionwasdueprimarilytomismod-eledsolarpressureaccelerations.TheeffectofthemismodelingwastomovethespacecraftpositionestimateinthedirectionleastwelldeterminedbyDop-pler;thatisdeclination.The?DORdataexposedthemodelingproblem.Fur-ther,thesedatadirectlymeasuredeachangularcomponent,andhenceproducedanaccuratesolutioneveninthepresenceofmismodeledaccelera-tions.ThetwosolutionsillustratedinFig.4-4wereinterimsolutionsdevelopedforthepurposeofdataevaluation.AsimilarmodelingproblemwithsmallforcescontributedtothelossoftheMarsClimateOrbiterin1999.Atrajectoryerroraccumulatedinthedeclinationdirection,resultingininconsistenciesinsolutionsobtainedfromdifferentdataprocessingstrategies.Theseinconsistencieswerenotresolvedtoidentifytheactualerror.Unfortunately,noangulardatatypeswereemployedasacheckagainstthistypeofproblem.Severalreviewswereconductedafterwards.IntheReportonProjectManagementinNASA,bytheMarsClimateOrbiterMishapInvestigationBoard[31],oneofthe“l(fā)essonslearned”inthesectiononsystemsengineeringstates:Developanddeployalternativenavigationalschemestosingle-vehicle,DeepSpaceNetworktrackingforfutureplanetarymissions.Forexample,utilizing“relativenavigation”wheninthevicinityofanotherplanetispromising.Theplannedimplementationofarobust,next-generation?DORcapabilityaddressesthispoint.4.3UtilityofOpen-LoopRecordingsOpen-looprecordingsofradiosources,asisdoneinVLBI,canbemadeevenifonedoesnothavegoodaprioriknowledgeofsourcepositionorsignalfrequency.Withopen-looprecordings,intheeventthatthesignalisweakerthanexpected,lessstable,oroffinfrequency,extraeffortcanbeappliedduringsignalprocessingtogenerateobservables.Bycontrast,systemsthatrelyonreal-timesignaldetectionmayfailundertheseconditions.Open-looprecordingswereusedinascientificinvestigationduringtheentryoftheGalileoprobeintotheJovianatmosphere.Theprimeradiolinkdur-ingdescentwasatransmissionfromtheprobetotheGalileoorbiterthatwasflyingoverhead.Theorbiterusedaclosed-loopradiosystemtotracktheprobesignalinrealtime.TheseDopplermeasurementsprovidedaone-dimensionalprofileoftheatmosphericwinds.Atthesametime,open-looprecordingsweremadeoftheprobesignalattworadiotelescopeobservatoriesonEarth.EventhoughthesignalreceivedonEarthwasabilliontimesweakerthantheprimeradiolinkduetothepropagationdirectionbeingofftheprobeantennaboresite58Chapter4andthesignificantlylargerdistancetotheprobe,thesignalwassuccessfullydetectedinnonrealtimeandprovidedavaluablesecondprofileofwindveloc-ityintheJovianatmosphere[32].Open-looprecordingsandsubsequentspecializedsignalprocessingwereusedin1999toverifyapproachnavigationfortheMarsPolarLander(MPL[33,34]andtosearchforthesignalthatmighthavebeentransmittedbyMPLfromthesurfaceofMars[35].Anotheruseofopen-looptechniques(underspe-cialcircumstancescouldbeinsitutrackingbetweenorbitersatMars.Analysesoftheseopen-looprecordings,aftertransmissiontoEarth,could,ifnecessary,provideadditionalinformationbeyondthatofonboardclosed-loopsystems.References[5]T.T.Pham,A.P.Jongeling,andD.H.Rogstad,“EnhancingTelemetryandNavigationPerformancewithFullSpectrumArraying,”2000IEEEAerospaceConferenceProceedings,BigSky,Montana,pp.491–498,March18–25,2000.[6]A.E.E.Rogers,“Very-Long-BaselineInterferometrywithLargeEffectiveBandwidthforPhase-DelayMeasurements,”RadioScience,vol.5,no.10,pp.1239–1247,October1970.[7]W.G.MelbourneandD.W.Curkendall,“RadioMetricDirectionFinding:ANewApproachtoDeepSpaceNavigation,”paperpresentedattheAAS/VLBITrackingObservables59AIAAAstrodynamicsSpecialistConference,JacksonHole,Wyoming,September7–9,1977.[10]C.Maetal.,“TheInternationalCelestialReferenceFrameasRealizedbyVeryLongBaselineInterferometry,”TheAstronomicalJournal,vol.116,no.1,pp.516–546,July1998.[11]J.A.Steppe,S.H.Oliveau,andO.J.Sovers,“EarthRotationParametersfromDSNVLBI:1994,”inEarthOrientation,ReferenceFramesandAtmosphericExcitationFunctionsSubmittedforthe1993IERSAnnualReport:IERSTechnicalNote17,pp.R19–R32,Paris:ObservatoiredeParis,September1994.[15]E.M.Standish,“CelestialReferenceFrames:DefinitionsandAccuracies,”chapterinTheImpactofVLBIonAstrophysicsandGeophysics(M.J.ReidandJ.M.Moran,editors,proceedingsofthe129thIAUSymposium,Cambridge,Massachusetts,May10–15,1987,Dordrecht,TheNether-lands:D.Reidel,1988.[16]J.G.WilliamsandE.M.Standish,“DynamicalReferenceFramesinthePlanetaryandEarth-MoonSystems,”chapterinReferenceFramesinAstronomyandGeophysics(J.Kovalevskyetal.,editors,Dordrecht,TheNetherlands:Kluwer,1989.60Chapter4[17]E.M.Standish,“JPLPlanetaryandLunarEphemerides,DE405/LE405,”JPLInterofficeMemorandum312.F-98-048(internaldocument,JetPro-pulsionLaboratory,Pasadena,California,August26,1998.[18]E.M.Standish,“JPLPlanetaryandLunarEphemerides,DE403/LE403,”JPLInterofficeMemorandum314.10-127(internaldocument,JetPropul-sionLaboratory,Pasadena,California,May22,1995.[19]C.S.Jacobsetal.,“TheExtragalacticandSolarSystemCelestialFrames:Accuracy,Stability,andInterconnection,”AdvancesinSpaceResearch,vol.13,no.11,pp.(11161–(11174,1993.[20]W.M.Folkner,T.P.McElrath,andA.J.Mannucci,“DeterminationofPositionofJupiterfromVery-LongBaselineInterferometryObservationsofUlysses,”TheAstronomicalJournal,vol.112,no.3,pp.1294–1297,September1996.[21]R.A.Jacobsonetal.,“AComprehensiveOrbitReconstructionfortheGalileoPrimeMissionintheJ2000System,”AAS99-330,AdvancesintheAstronauticalSciences,Volume103,PartI,(K.C.Howell,F.R.Hoots,B.Kaufman,K.T.Alfriend,editors,proceedingsoftheAAS/AIAAAstrodynamicsSpecialistConference,Girdwood,Alaska,pp.465–486,August16–19,1999,SanDiego,California:Univelt,1999.[22]E.M.Standish,“AnApproximationtotheOuterPlanetEphemerisErrorsinJPL’sDE-200,”AstronomyandAstrophysics,vol.233,no.1,pp.272–274,July1990.[23]E.M.StandishandJ.G.Williams,“DynamicalReferenceFramesinthePlanetaryandEarth-MoonSystems,”InertialCoordinateSystemsontheSky,proceedingsofthe141stIAUSymposium(J.H.LieskeandV.K.Abalakin,editors,Leningrad,USSR,pp.173–180,October17–21,1989,Dordrecht,TheNetherlands:Kluwer,1990.[24]XXNewhall,R.A.Preston,andP.B.Esposito,“RelatingtheJPLVLBIReferenceFrameandthePlanetaryEphemerides,”AstrometricTech-niques,proceedingsofthe109thIAUSymposium(H.K.EichhornandR.J.Leacock,editors,Gainesville,Florida,pp.789–794,January9–12,1984,Dordrecht,TheNetherlands:D.Reidel,1986.[25