RADIOMETRICTRACKINGSpace Navigation

October 24,2016 D.Kanipe

Space NavigationElements

• SCorbitdetermination• KnowledgeandpredictionofSCposition&velocity

• SCflightpathcontrol• FiringtheattitudecontrolthrusterstoalterSCstatevector(p,v,t)

• Howdoyouknowwhen,andbyhowmuch,toalterSCvelocityvector?• Comparederived SCtrajectorywithdestinationobject• CompareSCtrajectorytodestinationobjecttrajectory

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WhyDoWeNeedTheData?

• Don’tSCusuallytravelalongconicsections?• Twocomplicatingfactors

• Orbitscanbeperturbedby:• Solarpressure• Gasleaks• Thrusterfirings• Gravityfields,etc.

• The3-DstateoftheSCmustbeinferredfrommeasurementsbarelymorethan1-D

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What CanBeMeasuredFromEarth?

• SCdistancefromearth(range)• SCvelocitycomponentdirectlytowardorawayfromEarth

• SCpositionintheearth’ssky• SomeSChaveopticalinstruments

• Allowsgroundtoviewdestinationobjectwithbackgroundofstars

• NavpredictionsaidgroundstationinlocatingandtrackingtheSC

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NavigationProcess

Iterative process

Ephemeris: list of successive locations of a planet, satellite, or spacecraft.

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Ephemeris• UsedinAstronomyandCelestialNavigation• Liststhepositionofobjectsinthesky

– Naturallyoccurringandartificialsatellites– Functionoflocationandtime(ortimes)– Originallygiveninprintedtables– Sphericalpolarcoordinatesystem

• RightascensionandDeclination

– AstronomicalPhenomenaofinterest

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JohannesKepler’sAlfonsine Tables

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CelestialReferenceSystem

• Center of the earth is the center ofthe Celestial Sphere

• Infinite radius• Sphere’s poles and equatorial plane

are coincident with the earth’s• Zenith: point on the Celestial Sphere

directly overhead an observer• Nadir: direction opposite zenith• Meridian: arc passing through the

celestial poles and Zenith• The Ecliptic Plane: Plane in which

earth orbits the sun) 23.4°

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Declination&RightAscension• Declination(DEC)

• Celestialsphere’sequivalentoflatitude• Expressedindegrees

• +and– refertonorthandsouth• Celestialequatoris0° DEC• Polesare+90° and-90°

• RightAscension(RA)• Celestialequivalentoflongitude• Specifiedinhours,minutes,andseconds• AnhourofRAis15° ofskyrotation• RAzeropoint

• Whereeclipticcircleintersectstheequatorialcircle

• Wherethesuncrossesintothenorthernhemisphere;i.e.,vernalequinox 9

However

• Unfortunately,theintersectionoftheearth’sequatorandtheeclipticgraduallymoveswithtime• Vernalequinoxisdefinedasaspecificdate

• 12:00January1,2000orJuliandate2451545.0• J2000

• Forimprovedaccuracy,it’sbecomemuchmorecomplex• CelestialreferenceframedefinedbythepositionofquasarsintheInternationalCelestialReferenceFrame(ICRF)

• Fortunately,wearegoingtoignorethisinconvenience

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Telecommunications

• KPFKonMt.Wilson20kmfromLA:112kW@90.7MHz• TypicalSCmighthaveonly20Wtocoverbillionsofkm

• Signaldecreasesas1/R4

• Concentratepowerintoanarrowbeam• Cassegraindishhigh-gainantenna(HGA)• 20Wtransmitterwitha47-dbigainHGA

• Effectivepowerof1MWalonghighlydirectional beam

• Nosignificantsourcesofnoiseinspace• DSNprovidesupto74dbi gainatX-band

• Cryogenically-cooledlow-noiseamps,receivers,software• Extractdatafromvanishinglysmallsignals

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Antennas

• Unlessitisbentbyagravitationalfield,electromagneticradiationtravelsthroughspaceinastraightline

• Objectiveofantennadesign• Focusincomingmicrowaveenergy

fromalargeareaintoanarrowbeam• Concentratedenergyisthencollected

intoareceiverEarly Dish Design Cassegrain Design

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AntennaApplications

• Antennadesignmustaccommodate• Missioncoverage• Orbitalparameters• Attitudecontrolcharacteristics• Bitraterequirements

• Keytradeoffs• Beamwidth,gain,andeffectiveaperture(size)• Narrow-beamantenna:highgainandlargesize• Broad-beamantenna:lowgainandsmallsize

DD

High Gain(narrow beam)

Medium Gain(fan or conical beam)

Low Gain(broad beam)

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Antennas

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Antennas

• Gain:powerdensityradiatedalongtheboresightrelativetoanisotropicradiator

• Isotropicradiator:pointsourcethatradiatesequallyinalldirections.G=0

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• G==η =η

G=10log(η)+20log(f)+20log(π/c)or

G=10log(η)-20log(D)+20log(π)

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η4πf2Ac2

πf Dc

πf Dλ

f = transmission frequencyD = antenna diameterC = speed of lightλ= c/f wavelengthη = antenna efficiency

Antennas

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• ConsideratransmissionpowerlevelPt andantennagain,Gt

• ReceiverisRmetersaway• F =Fluxdensity=powerperunitarea(W/m2)• Transmitterproducesasphericallyexpandingwavefront

– Arrivesatthereceivingantennawiththefluxdensity:

• Atthereceiver– AntennahasphysicalareaAr andeffectiveareaAe =ηAr

– Gainatthereceivingantenna:Gr = = =

• Totalreceivedpower:– Pr =FAe =PtGtGrλFriisTransmissionEquation

4πR2

F = GtPt

4πR2

η4πf2Ac2

4πAeλ2

Cf

Antennas

• Inpractice,specifythegain orarea oftransmitterandreceiver

Pr =Pt()2ArAtbothareasarefixed

Pr= Pt (2)ArGt receiverareaandtransmittergainfixed

Pr= Pt ()GrAt receivergainandtransmitterareafixedPr =PtGtGr ()2 receivergainandtransmittergainfixed

• ()2 =Pathloss dilutionofthetransmittedenergy• PtGt ≡EIRP (EffectiveIsotropicRadiatedPower)• Pr =EIRPx

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Steradians

• Isotropicantennaradiatesequallyinalldirections• Gain=0• Doesnotexist

• Steradian• 3-Dradian(sr)• Area=r2

• Sphere• Spheresurfacearea=4πr2

• 4πr2/r2=4πsronasphere

• r=(180/π)• sr=(180/π)2=3282.8deg2

• Gθ2 =2.6π(3282.8)=27,000§ θ=70λ/D (λ =wavelength)

DD

Beamwidth, θ

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SpacecraftVelocityMeasurement• BasedontheDopplershiftphenomenon

• ComputingradialcomponentofSC’searth-relativevelocity• MeasuretheDopplershiftofacoherent downlinkcarrier• Hydrogen-maser-basedfrequencystandard

• GeneratesaverystableuplinkfrequencyfortheSCtouse• SCreceivesstableuplink,multipliesthatfrequencybyaconstant• ThatbecomesSC’sstabledownlinkfrequency

Toward you Away from you

Light shifts to shorter wavelengths

Blue Shift

Light shifts to longer wavelengths

Red Shift

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• Uplink:radiosignalsfromEarthtoSC• Downlink:radiosignalsfroSCtoEarth• Carrier:apureRFtoneusedinuplink/downlinksignals

• Uplink:Verystable• Downlink:difficultforSCtomaintainstablecarrier

• Carriercanbe“modulated”tocarryinformation• UsedforSCtrackingandnavigation

• GroundsendsverystablecarriersignaltoSC• SCmultipliestheuplinkfrequencybyapredeterminedconstant• Usesthatvaluetogenerateacoherent downlinkfrequency

WhatisaCoherentDownlink?

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SpacecraftDistanceMeasurement

• Arangingpulseisaddedtotheuplink• Transmissiontimerecorded

• Thetimetogofromgroundcomputerstoantennaisknown

• SCreceivespulsefromtheground• Thetimeittakestoturnthepulsearoundisknown• Returnsthepulsetotheground

• Ontheground,elapsedtimeiscomputedinlightspeed• Correctionsappliedforatmosphericeffects• Rangecomputed:

• SpeedoflightXelapsedtime

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AngularLocationoftheSC

• PositionintheskyisexpressedbyRightAscensionandDeclination• Groundantennapointingmaybeaccuratetothousandthsofadegree

• notgoodenough• VeryLongBaselineInterferometry:VLBI

• IndependentofDopplerandrange• TwogroundstationsfaraparttracksameSCsimultaneously• Eachmakeshighspeedrecordingsofdownlinkwavefrontsandtimingdata• Afterafewminutes,bothantennasslewtoaquasar

• Recordingsaremadeofthequasar’sradio-noisewavefronts• Analysisyieldsaprecisetriangulation– quasar’sRAandDECareknown• SCpositiondeterminedbycomparisontotheRAandDECofthequasar

“delta DOR”DOR=differenced one-way rangingBaseline

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