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OVERVIEW Ory VA.RIOUS $ATE},},$TES P.OSIT}ONFIS'6TECMifiQTIE

Obse rr alion tc satetrtrite*

Observatioe to ar..tificiali satelil,l,te ca& be oarried ou,l usillg oae or nnore of'the folilowinng:

e - direction,r - distancqh - satellite altirnetry,drldt - Doppler,dq/dt - Doppler, sateXlite to satellite tracking

Direetion measurement

Directions are measured by photographing a satetrlite (passive and active)at night against a star baclcground. Passive satellite reflects an adequateamouril of sunftiight. while aotive satellite carry eguiprnent fbr emittingflashes. A plate is produced witfi irnages of both the satellite and the-stars.Precise measurements (to a ftw rnicrons) are made on the plate todetermine the direction of the satellite by means of known directions(from an astronomical ephemeris) to the stars.

satellite sr is simultaneously photographed.from two ground{stations randlB and two sets ofdirection .orilrr, *. At .,,,in;fr"*'- ulserv'Iri

AS1 (,1m1n),and;851.(tim,iS, -- *Yev r'!

n eff,ihg (l m n) w the direction rosa*.s of line.rB; thenwe can write the

coplranar,ity condition for the fiangte orr,,li, :, |,];,= o, which isLt m ;)

equivalent to a linear equation with three unknown s l,m,n.

,:r'jlii\ii;'

ey.repeatlr+S thp. ot s er.'u{;ion for diif feleqft s afeliftite posirion, we getaddfirtiol-ral.eqp*afiorastw,,r@ t&e saime tbree r*r.qk&own-rs- and afpftoition, otrthe co.adition; P'+m,t'*n? =I, aod I'east sq,uare.soli*ion teafftc thedireetion af ltne'AE. 'lihis tecftrn,iique is known as asfrotrianglritratiorft, andwas very ul,uohratooltof tr960's

Distance measurement

Tllree qethodb avaiilip.-blfe' for tlie meas,ureslenp of distanee. to s atelillites:laseq plaase oomparisor4 arild nfiicrowave travelltime.

It. Ilasen measuremen{

Frinci,plb S atelililter ltas.er Rang,jqg :

c tr a1er pqlbe is maqsnnittedito a sateltite, oqgry,iqg retiro (comen cgbe)reftectors ag-dl tber re$rrylr pul,be is detectgdi,'

c The exaot epoch of tnansmissionr, r,, is measur_edf as is the interva*(ela-9sed,)rtin'1e bet'weea.mansrrission'anarrehrrar deteetion aituU"ut0.OI seconds to, a satel{ilte lt500kn* away).'

o TI'le rarage is theru c{qntt.z'1(r is velooit5i of }ight in vaeuo) at enrooht + [r/2. Coqrgotionr for oatrliDratiornr and tinop'ospfterie reftaotion areapplied to &is r,ange I r = c(: N I 2),* C

"o,,r,orin + Cr,oposphen

Laser ffaoker sy stem: oonsists, o,f:o The transmifier - usu.a!$ Qiswitohedruhy l,aser at n$$Xz (ten purtrse

per secondl)r on Neodbrniuur.yAG at 3;0*,Itz.o The receiven - parabolio refleoting ralirro4 which then passed to a

photo.mulbipfier.o Intenrax tirnihg eleoftonie - deteotir*g eentre of return putrse (20

nano seoon& - 6'rnefres) and memrering interval tinne to the orderlo.to seconds (-3crn)

o Tnaoking syster,rru - set of'axes controlfed by cornputer controlledsenvornotors, to aoqurate$ point the laser and traok tho satellite asit passes overhead.

Cunent SLR systen$ oan'measure range to a standard error as low aslOtnrn" althoughmost systenft are up to about five times worst than this(50nrm) The systerm ean work day or night, but need a clear sky (i.e.inable to peneffate cloud). SLR systern is equipped with saf€ty iui outdevice to proteet the eyes of the pu*sengers in aircraft who rross the laserpath.

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The sinap,lesg4losition:f,,xinguse,o-f laser.rangngls,totiravg' apqqlbel ofstations, op.eratut&simult o.ul.ly _If

slat1o-+ A, E Pdi C ar.e linowq weeae conr,, trtrate- satellite'p-osifrion S, i, 52, Si. Kno. wiqgj Sir, Sz, Ss, we ca-ni

oompute,: the posttrqnu F; ,the q4trgl 4l: station

. Thi,s, see,rys.- srpnle rg theory

brm &fficrlilt to aphieve cl* ln' practiS e b e c aus e simultanepus ob s er,Yatipn,

frory foum slations are,dififibultto:agange andrweathg,n is unlikely to be

clear at allrfoun stations.

Amore prac{ical,solution is,to,track a'satellite ftom.known-stations and'touse a geopotential,model,to help compute the satellite position when it isobserved,'from unkrtown stationi

2. Phase comparison,systemi

This system is similar to EDM'(e.g. Tellurometer MRA seriesinstrument): A ground'station sends, a carrier mictowave, modulated' tosay 500mi the satellite receives andire-fiansmits the signal:'(like a remoteTellurometer) and tlie phase shift is measuredi Measurements on variousmodirlhtion: frequencies'lbads' to, a distance.

Accuracies of about 5m (standard"error) in ground position can beachieved:

'l,. ::;l\1,/

._.3. trvfioro.vr-arre EqyEl:tiqre

This dii,,staoge rleasur. esig-nt system i s. use di in NAVSTA,R (GF S ) r Thesystem naaliing use of the travel time of a microwave signali

A satelillirte, and th9 grougdireceive4 both have a. clockp, ogremtingnomina.,[V on, the same time system. Ati acertain,pre4r.4anged*ep,gch asatelilfiitepuls acodb mar,!(en onthe miorpfvayeiignaliiGis,,lgntihuouslytrans-q-itliiqg, theltimp:of'eutivaltof,,the,code is,measure4andlhence thetravellti,me'Ar,, is know4i Trhe distance is, car, lbss:a;refiactibncorrqction,

trf 'the,oBer.ationisicasipdlouGsimultanrouslywithsigqaft

fr om,latilbastthreo satel*ites,whose,positioqs, are knolryq then the position of theobserver can'be simply gomputedi

e2A

For this,systern,to,be accurate, the sarellite clocks n..l"liS'l#'L1it"-rr,stable (tot"); drifterrors in the observer.s clbck can easily be determinedby making observation to fourth,satellites and:solving for the clock erroras fourth unknown

Satellite altimetrv

Altimetry is the tenn' used'to. describe the' direct,, measurement of theheighl,sf'a'satellite. The technique adoptbd'in thib system utilizes'radarpulse, which are emitted from the satellite carrying altimeter and thenmeasuring,the return signal travel time fiom the earthts surface.

Cunently, only water (sea'& lake) surfaces have given good qualityrefurns. However, returns have been received'from certain smooth,surfaces such as polar ice caps and dbserts,

;;i...,

The satellite ii* traoked' fromr ltno,rruq grcrmd stations_by Doppler aad lasermeasrrrement, so i1s -orbi& ts;haown. Xhe salelite in a well tracked onb'it

witrl contintrou.sn54 reoordb. rts heigfrl ab,ove m,eaq \ryaYe le,vel O4WL) of the

sea oveJ afr Neao,f ab-out nhur" inrnediiatety below lt. Ordinary waves are

av,eragpd out, but ng$ the:edfgcts o'f ti&siqor o-f'variations of cu- er:il >

tenrperattue, sqifieiliy, ot afinospfterio Prcssure This mean level isooineiidbs with the ggoiditorwithiqr tQ to3 meftes afr?r. aofrecting, &rtides" aBart ftonq errofiq in fracking tlie satetrltite-Thl.s teehnigrre qresdineo-t me-a-suse of'tfrE s-hape q,f the sea swf'aoe. The as.orirrasy is dependent

on tlie ltnowled[e of the or,,b*t (resotution o'f the aftiEreter]

Radar aXtiraeter operates at tr3.5 GHz QZnrnwavetrengthl or at reducedpower of 27.$GYJz. I-ong putrses are emitted at 30km (l00ps) in length,but measlmemenl is made at a modulated wavetrength of 3m (t0ns). Theradar pulse has 4" bearnwidth, and cover an af,ea of about 60hm diameterat sea level.

From direct measurement of satellite's height, OS, and sea surface(approximately the geoid), h,, geoidellipsoid separation,.I/, can be

directly determined from the fotrlowing:O,S=r*trf+M+ho+h,

Wherg the radius r cornes from ellipsoidal geometry, Ai (known as sea

surface topography) comes from oceanography, and ft, from tidal studies.

Note: nk and k, are difficult to determine and are often ignored.

This is t}le ranost aocurate tecliroigue avarilAbXe for detemninatiorr oj thegeoid at sea andformsiarar exfrenae$ im,gutaut data source modelsctrrrsnlly used fbr orhit prediirctibn and geoid deseription.

Saf e ltrif e - D,opqf,eri {np,Fq,F,,Ee ryqn:t

The princi,ple of sateliliite tracking eaplbying the Doppler ef,fbol is thatwhile the ransmiitter of the sdennite serldb a oorltinuous, unruoduilaledwave at a fxed ftequeuoy" the signal receivcd on the, grou,tld exibits aohasrgg in &egueney due tc relative vetrocirty o,f the satel$irtq asd thEobserv-img station. The received frequency is a ffirinetj,Ep of tlhe traqso&itted&eEreney; veloei8 of radio propogation, the rafe of'ehamge between the

satellite and the observer (i.e. radial veloaity, o ).

e- S.3 s^

The received and fransmit{ed &equency are related by:

U = .fo- S, where {f is known as Doppler Shift.

ril/here: fi : vmiable frequency received

fi : fransmitted frequeucy by the satellitet

_,r : rddisfrvenoeity of the satellitec: vetrooity of light in vasuo

Doppler measurernent consists of integrating the frequency differencesbetween the variable freguency received, f*, and the signal of frequencygenerated by the receiver, fo, arrtd counting the 'beat frequency' over

some interval (epoch) time. The number of cycles counted (IntegratedDoppler Count) between r, and rr(receiver time epoch) is given as:

n =*[,-:J *,.,,ii,

{ ;i:',\r!''

Nnz= f:,'V" - f^Vt,

where: Tt=tr+A/i, Tz=t'z+Lt2;

4r andi r, is, the satelil{te signa,l en*issiou time

Llence: Nrz= f:,:,:: W" - f*)-U^- t)Y,

Integrating thg, fiqst te@ and separatlng the seoogdit€@r becomes:

Nrz=Qfo- f,W,-"nFL,# r.*[i[ rrao

,' The secondlter,noi. cag be written as:

ii,-I t^oo=fn f,oo,

. Because the nunober of'cycles leavrngtlae satel,liite betiween

times, 4 andi r, nurst be thesame as,the numb'er arrivfuilrg at the

receiven betweenrtiiirrr,es 8r, +Asn and 4* Mr.

Substit'uting andt expanding the integra{s yielrd$:

N,z = Vo - f ,k r- r, )'_ fr\, - tr)+ f, {kr+ &, }- ft, + &, D,

Rearrangeg gives Nn = Vo - frYpr- ou)+ fr(Mr- Arr)

Assu'nring no,reftaotion effbats (i.e. fravel in vacuum), thg ffavel tirnes Ar,

and Ar, are equalito the respective ranges divided by the velocit5r of light,c. Hence, can be written as:

Rearranges to r, -r, = {i/,, -(f, - frk, - rr)\ %,

This equation is referred to the basic integrated Doppler count formul4 as

it retrates the difference in range (or range rate) to the basic Doppler countff*r, ffid the reoeiven tirnes for starting and stopping the cycle counting r,and r". Xt is a fundramenta'l equation of satellite Doppler positioning.

rlr'.r .:;i;i,i

Ile, ordbl {or coqpute,,thp positioro of groundls,tatioi} F- we rewri,.te the,rangerate ini te[,m] of the station andtsatelliite,coordinates as foliliows:

rz - rt. = &x, - x rY' + @6 - yr[ * @, -' z rB|1' - W o - x rF + (rr" - r,f + (2, - z,y{'

\feere; theltnouao; oooldinates,gf' s' aadt s, ate: ftx,,yr.,zrlam& @r,yr,z"hnespeo-fiiv,e}S. T'herrnknorypcoond,iaatesiof ggoundistationi ffifr (Xr,yp,zr\.Com.'bini,ng two range{ote equationsl wc,get the generalt obsbr,vationequationf orsateliliite,Dopplb===============rpOsif ionfu ry

ftu, - x r)? + (x, - r,)?' * (2, - z,YY' - ftt" - x,,F + (r, - y,)?' + (2, - z,)?t'' -fr,, -(fo - frYv,-r,)fot 7, --a'

Whene: l/,, is fhe observabtb; (Xr,Yr,Zr)iandr f, ffieunl(nown'

pararanetens: 6 is'considbredf unknown because the satellite oseillhton willihave &iftedtsince its calibratio4 whereas,the oscillator in the receiver(ftequenoy f) cnbe calibratedby connecting the receiven to afrequepoy standardi

To sotrVe for four unknown,parametem; we,il€edi tb: incllrd'e five, sateltitesposition (q,sr...sr)landfour ihtegratedlDoppl'en countsi (Nrr,Nrr"Nrn,dru),

to form*four equations to-solve for the unknowns

Doppler principle was extensively usedtinNavy Navigation SatelliteSystem'(NIIISSI or Transi$f for fixingthe subralarirlesposifior' .

Satellite to' sateliife naneine

The same Doppl'er principal describes previous$ call also be used tomeasure range dl'fferences between pairs of sateltite. In particuilar, it couldbo usedl'bef,ween' higtr and* lbw orbiting satelffites'.

The metllodis nof directly usefuil for positioning points on eartlil'ssurface, but imporfant in determinationr of the eartllr's gav$y field henoeindireotl! helps,with,position' f*ing beoause it helps to prediot thesatel{ite orbit

I

I.t,t:

tI

The idbaftsatellite to dbtermine the earthis gravity fieldiislbw (200lim)r

orbitingsatellite; which,has a shor.,hlife due to the, a&ct of'smalfivariationsrin earth" s; gavity fieldl T',racliing'this, sate-llite'ftoru a few(p o s si6ft geo -stationary), *rut re duce the nee d5' of, ' d'ens e tracking networ,lk

station andialso removedige effect atnospherio regactionl hence givingaccurate'measurements of orbitpei':tirlrbationi sver tffe wholb satellite or,bit

Verv lOne baseline interferometrv

VLBil is not asystemr ItinvolVes tht measur€ment of'the variation,inthearrivalrtirne ofradio,signal's,from'distantradis source or llUasars; ernittihgradlation' at atarger:ange of high'frequencies; at different observing radio,telescopes sites (separated,by thousandb of lhn' apart)' aroundr the worldl.

The interfer,omqter makes use of the interference pattern between thesignals received'at apat of,antennaiarrays. The distance betweentheantennas is smalltcompared.to the distance of the quasar. Data is record'ed

andlaccurately time tagged,at each, site, and,then cross-correl'atedJwith'similar d'ata,at:other sites: Extrerne$ precise relhtive position'andJearth,

rotation parameters can be detbnnined

t0

A andj E ar.e, two,gfouqdb, stations, sep,arated thswand$,hni ana$ AQr andB Qr poinfed the diiectio# of subistantial$ ffiitetyu distant radio, source-AF:is perpendicular to BQ; so ignoring ahgspheric delays, a quirarw&v€, front reaches: A and P" simultaneous$ and, reaclies Br aG Z seconds,Iaten. Thedistance BP is then Tc, where c is the,velocity of propagation.

Giver* sufEcientli accuate syncb,ronised,clocks aGA andi$ the delhy ?can be,measuredrandilbn$ of BP'can be obtained'i FqttliennorE, bylknowing the direction of the source,'ihe lbngtfi andJ Cirection ofi' ABi canalSo be computedt Given; suitably disti -huted observations; the relhtivedbolinations of different source, theii R 's andiother parameters,such as

the polar motion; can also be computedi

As with,SILR, the data contributes to IERS and,coordinate system,definition'. Relative positions can also be usedto study the defonnationsof the eartl,! due to continental,drift andrtidaliphenomena,

;1.,l rllr'

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