0273—1l7786S0.00-~50Adv. Space Res. Vol. 6, No. 9. pP. 205—209.1986 Copvri~hC© COSPARPrintedin GreatBritain. Alt rightsresersed. - -

SPACE-VLBI : POTENTIALAPPLICATIONS IN GEODYNAMICS

I. Fejes,” I. Almár,** J. Adám~’and Sz. Mihály*

*Satellite Geodetic Observatory, H-.1373 Budapest, Pf. 546,

Hungary**KOnkOly Observatory, 1-14525 Budapest, Pf 67, Hungary

ABSTRACT

A unique characteristic of space—VLSI for geodynamic studies is pointed out:space—VLSI provides a direct connection between the Conventional Inertial Re-ference System of extragalactic radio sources and geocentric reference systemsof extragalactic radio sources and geocentric reference systems defined bydynamical methods respectively. New satellite projects (Quasat, Radioastron)are in preparation requiring precise orbits; different satellite trackingmethods are discussed for this purpose.

INTRODUCTION

A common requirement for all geodynamic investigations is a welidefined coor-dinate system attached to the Earth— Conventional Terrestrial System (CTS) -

as well as a well—defined Conventional Inertial System (CIS) in which themotions of the terrestrial system can be monitored /1/. Inertial referencesystems may be defined kinematically i.e. through the position of extragalacticradio sources (EGRS), or dynamically i.e. through the geocentric motion ofsatellites (satellite—CIS) /2/. On the other hand satellite orbits are usedfor defining the origin of CTS.as -the mass center of the Earth.

The most accurate CIS is the one attached to ECRS by VLSI astrometry kinema-tically (radio source—CIS). Its long sought submilliarcsecond precision re-cently has been demonstrated /3/. Although the reliable connection of thissystem to the others defined by dynamical methods is very important, presentlyfew techniques exist for this purpose. Station co-location is used to connectsatellite laser and VLSI coordinate frames, but only a very few such co-loca-ted sites are available. VLSI is used for direct measurements of spacecraftangular distances from EGRS positions, but the scope of VLSI measurements isvery limited.

In this paper we would like to point out a new possibility provided by space--VLSI for a direct connection of these reference frames. A space—VLSI systemoffers a good opportunity to connect the CTS with two types of CIS: radiosource—CIS and satellite-CIS inherent in the space—VLSI system. The radiosource—CIS is based on observations performed by the network of VLSI stationson the Earth surface. This Earth based geodetic VLSI technique is a purelygeometric method and these measurements are independent from the mass centerof the Earth. A VL8I station in orbit, on the other hand, is an integralelement of this Earth based network but at the same time is tied dynamically(via its orbit) to the mass center of the Earth.The orbital plane of the VLSIsatellite defines the satellite—CIS. As this orbiting radio telescope willobserve EGRS with Eart)~-based VLBI networks as its integral element, geodeticevaluation of space—VLSI data provides a direct connection between frames ofsatellite—CIS and radio source—CIS. Moreover, through the EarTh-based VLSInetwork coordinates adopted in CTS, the relationships between frames of theCS and the two CIS’s inherent in the space—VLSI system can be established.It is to be noted, however, that the connection satellite system is suitablefor short—term work only (for the period of the satellite’s lifetime).

There are two important projects recently under consideration for space—VLSI:Quasat by ESA and NASA /4/, and Radioastron by the USSR and Intercosmos.Our suggestions are relevant to b&th projects.

MATHEMATICALMODEL

The final goal is to determine at an epoch t the ~ vector of ground stationsexpressed in the CIS. The X vector consists of ~ following parts: - the~ vector of ground stations

9 in the CTS;-9the Earth Rotation Parameters (ERP) at epoch t connecting the CIS with the

CTS, namely UT1 and polar motion (x~~yr).

205

206 1. Fejeseta!.

The above quantities are directly related by

~g= F(~g~precession, nutation, UT1, x~, y~, t) (1)

The proposal is based on using observations taken simultaneously from twoor more ground VLSI stations and the space VLSI station to EGRS. However,independent range and range—rate observations of ground stations to the or-biting VLSI are also suggested to cover the orbit with observations as fullyas possible.

The VLSI observations are the fringe phase ~ and the fringe rate ~ . Twotypes of them are considered: ~ and ~Sson the ground—to—space b~seline,as well as and on the g~ound—to-~round baseline. The ranges p orthe range—rates ô ate measured from the ground stations to the orbitingVLSI. The following relations are valid (5):

= F1 (~, E~, ~g’ UT1, x~, ~, precession, nutation, t) (2)

= F~(~, ~, UT1, x~, ~, precession, nutation, t) (3)

p F5 ( E1, ~g’ UT1, x~, y~, precession, nutation, t) (4)

where ~ represents the EGRS coordinates in vectorial form and E.(i~l,2,...6)are the orbital elements of the VLSI satellite at epoch t. The~e functionsand similar relations for ~ , ~ and j help to determine ~g’ UT1, x~and ~.

A practical approach will now be given for the case of fringe phase observa-tions on a •ground—to-space baseline:

1. The orbital elements E. are to be computed at epoch t selecting a compre-hensive set of very ac~urate parameters ~k (k 1, 2,..., at, . ..n) providingthe gravitational and non—gravitational perturbations by analytical ornumerical integration. Special attention must be paid to the problem ofthe geocenter /6/ and on non-gravitational parameters P.(j=m+l,...n) forradiation pressure, albedo, atmospheric drag etc. These

3parameters must becarefully modeled and, in addition, corrected in an adjustment.

2. The calculated value of fringe phase ~ is to be obtained using ~ andE. by means of function F

1 and substituting the best available estim0ations

O~ ~ UT1, ~ ~ in equation (2).

3. After correlating the VLSI observations the observed value of fringe phaseis available.

4. The difference between calculated and observed fringe phases ~ - ~fs~ooccurs mainly because of the approximations in E. , x , UT1, x , ~ a~well as errors in modeling and observing. Correc+ions9dE. , d~~dUTf, dxdy , dP. can be estimated in a least squares adjustment èompo~edof thenfo~lowi~g observation equations

6~F, ~F ~F ~F ~F n 3F2: 0 l_ 1 1 1 1 ——

— dE. + — dx ÷ dUTl + -—— dx ÷————dy+ ——— dP.+ L’~V1 ~E1 1 ~ g ~UTl ~ ~ ~ ~ m+l ~P3 ~

where T is the vector of differences ~95,C - .~5’0,ar~ V is the vector of

residuals. The procedure is similar in case relations for ~s ,•ag f.5f,JJ andp

The observation equations coming from all types of measurements are treatedin a common system which — besides other advantages — presumably decreasesthe systematic errors of individual types of measurements. The above procedureleads to an Earth—based realization of the geocentric CIS through ~ stationcoordinates and UT1, ~ ~ ERPs determined inherently in one syste~.

THE PROBLEM OF ORBIT DETERMINATION

Solar radiation mismodelling is the dominating error source in orbit determina-tion of ~LSI satellites. In the case of Quasat the effective spacecraft areais 314 m , the surface being totally ref~ecting

2 The perturbing accelerationdue to solar radiation is about 0.35 10 km s . If the modelling uncertain-ty is 10% then its effect on Quasat orbit determination equals the total ef-fect of radiation pressure on the ERS-l satellite.Primary Tracking

Under the term “primary tracking” we understand the tracking network naviga-tion and, in addition, the positional and kinematic information of the space—

Space-VLBI 207

craft which can be obtained by VLSI processing of the science data itself.Primary tracking is carried out during the standard operation of a space—VLSIsystem without additional equipment or observing.

The Tracking Network Navigation is performed by the mission control networkand science data acquisition network. These stations can provide rather accu-rate spacecraft range and/or range rate data for orbit determination. To beable to process the science data at the VLSI processing centres the orbitaccuracy requirements are not very stringent. For instanc~, in the case ofQuasat, o~bit ~rrors of less than 100 m in position, l0 rn/s in velocityand 2.10 rn/s in acceleration are acceptable. These requirements can easilybe met using the data provided by the tracking network /4/.

The VLSI post processing. The mutual positional and kinematic properties ofthe VLSI stations and the observed EGRS are inherent of the science data. Byprocessing these data, very precise fringe phase (delay) and fringe rate valuescan be obtained for those baselines where the source was actually detected.The accuracy of these values can be 2 to 3 orders of magnitude higher thanthe a priori values obtained by preliminary orbit modelling. Tang Guoqianghas pointed out that this data—type can be used to further improve the com-puted orbit /5/. The measurement accuracy of the space baselines could bebetter than 10 cm at 22 0Hz or better than 40 cm at 5 0Hz. We would like tostress that just these processed VLSI data implicitly represent the instanta-neous geometric configuration between the source and the polyhedron of theobserving stations as well as the orbit model of the space—VLBI at the sametime. The analysis of the residual fringe phase and fringe rates togetherwith the applied orbit model provides valuable information for geodynamics.Figure 1 schematically illustrates the concept.

Space VLBI Tracking

raw data network data

VLBI processor VLBI-satellite

orbit model

residual delay,

L delay rate

______ ______ ~1~ _______________

VLBI network improve J improve model

and source k ground based parameters

geometry network

J Unified celestial

and terrestrial frame

Fig. 1. Unification of celestial and terrestrial frames using space—VLSI.

~VLBI is a tracking method where the angular distance and its time derivati-ve between a spacecraft and a natural radio source is determined with highaccuracy by using VLSI. Jacobi et al. studied the achievable Quasat navigationaccuracy by processing ~VLBI type tracking data /7/. The assumed noise of thesimulation data was ~l5 cm with a bias of 20 cia. It has been demonstrated,that the 4VLBI tracking data may yield submeter positional accuracy and0.03 cm s velocity accuracy. The quality of the results deteriorates howeverwhen the number of baselines is reduced. The realization of a VLSI trackingconcept seems to be difficult.

208 I. Fejes el a!.

Secondary Tracking

Laser ranging has many advantages for high accuracy orbit determination.From a technical point of view the reflectors are passive elements and requireno additional power and data transmission capability. Fejes suggested to putlaser reflectors on the Quasat satellite /4/ and to call in the satellite la-ser ranging network for tracking Quasat during geodetic experiments. On rela-tively short arcs laser ranging can improve orbit determination accuracy sig-nificantly. In the ERS—l orbit determination study Wakker et al. assumed 10 cmlaser ranging errors and the same value for individual station coordinates /8/.By using 14 laser ranging stations the simulated orbit errors were 0.6 m radialand cross—tracR and 2.4 m along—track. Because of the 900 km altitude of theERS—l satellite the gravity model errors were significant. Assuming similarconditions for the Quasat satellite, an orbit accuracy of 1—2 at seems realis-tic even at higher~altitudes. Laser ranging can be used for orbit determination(origin) and also for scaling. The laser observations - combined with VLSIdata — can. connect the system defined by LAGEOS with that of Quasat and withEarth—based VLSI stations as a “higher order co—location”.

PRARE is a very precise microwave range and range-rate system for satellitetracking developed at the Institut für Navigation,Stuttgart, which operatesas a two-way space based system /9/. The transceiver (2 and 8 0Hz) and datamemory are on board the satellite, while the regenerative transponders (7 0Hz)are on ground. All operation instructions are broadcast from the spacebornetransmitter to the ground stations and all information returned by the ground——based transponder and measured on board is collected, processed and stored onboard. Once or twice a day, this worldwide collected data be dumped on commandto a master ground station for further evaluation. The concept allows that upto 4 ground stations can be operated simultaneously; in principle many groundstations can share the satellite. It is possible to determine the preciseorbit at the control center very effectively once or twice daily. The rangingsignal consists of 1 s periodic PM s~quences. This makes t possible to measureunambiguously any range up to 1.5 10 km (one way). The ranging accuracy isexpected to be in the interval of 4-15 cm for a single 1 s measurement.

DORIS isanew system for accurate orbit determination developed at CMES. It isbased upon the measurements by a spaceborne receiver of the Doppler shift onradio signals transmitted from the ground during a satellite pass above thebeacons. The initial positions of the beacons should be known to within sometens of cm. The orbit determination beacon network provides the accurate orbitof the satellite, the expected accuracy being about 10 cm (after an initialperiod of six months). The selection of a spaceborne Doppler system offerssome advantages: simple equipment, centralized measurements, no timetaggingproblems /10/.

Accelerometer. The VLSI—satellite might incorporate a disturbance compensationsystem (DISCOS) which was first used by the TRIAD navigation satellite in1972, and later by the new “drag free” satellites of the Transit series —NO\h

1A~/11/. DISCOS counteracts along—track surface forces to a level of about 10 gor better. The range difference navigation residuals of passes used in theorbit determination process of NOVA—l are 40% smaller than the correspondingOSCAR residuals (13 and 22 cm respectively). Similar DISCOS systems mightbalance a VLSI-satellite between two consecutive sessions of accurate orbitmeasurements by laser. It could compensate drag forces like neutral or chargedrag, solar radiation pressure etc. demonstrated by the orbital variations ofLAGEOS /12/. Similar microaccelerometric measurements are suitable to analyseand separate different drag forces.

Characteristic features of the different orbit determination methods aresummarized in Table 1.

TABLE 1 Tracking Techniques

Coverage PrecisionTracking network navigation 3 - 5 partial —‘10 rnVLBI post processing 3 — 10 partial 5 — 40 cm~VLBI 2— 3 very limited 15 — 20 cm

Laser ranging “20 limited 3 — 6 cmPRARE or DORIS 4 — 50 full 10 — 20 cmAccelerometer (DISCOS) on board full —

Space-VLBI 209

RECOMMENDATION

Our recommendation is to use one of the suggested space-VLSI projects to es-tablish a direct connection between CT5, radio source-CIS and satellite-CISframes inherent in the space-VLSI system. For this purpose a high precisionorbit determination procedure of the VLSI-satellite is needed. In practiceVLSI post processing of combined ground and space data would necessarily haveto be complemented by some state—of—the—art range and/or range-rate trackingdata. The orbit determination accuracy would improve considerably with amicroaccelerometer on board.

REFERENCES

1. J.Kovalevsky and T. Mueller, Comments on Conventional Terrestrial andQuasi—Inertial Reference Systems, in: Reference Coordinate Systems forEarth Dynamics, ed. E.M.Gaposchkin, B.Kojaczek, Reidel (1981)

2. 1.1. Mueller, Reference coordinate systems for Earth dynamics, in: Refe-ET1 w480 563 m505 563 lSBTrence Coordinate Systems for Earth Dynamics, ed. E.M.Gaposchkin, B.Kolaczek,Reidel (1981)

3. O.S. Robertson, F.W. Fallon and W.E. Carter, Celestial reference coordina-te systems: submilliarcsecond precision demonstrated with VLSI observati-ons, Astron.3. 91, lt~56 (1986)

4. DUASAT, a Space VLSI Satellite. Assessment Study, ESA SCI 5 (1985)

5. T. Guoqiang, A short note on the high—precision navigation of Quasat,

ESA SP213 p. 185 (1984)6. J. Zielinski, Origin and scale of coordinate systems in satellite geodesy,

in: Reference Coordinate Systems for Earth Dynamics, ed. E.M.Gaposchkin,S. Kolaczek, Reidel (1981)

7. N. Jacobi, C.S. Christensen andM.C. Hanna, Study of navigation accuracyfor the proposed Quasat mission, AIAA 85-0290 preprint (1985)

8. K.F. Wakker, S.A.C Ambrosius and L. Aardom, Precise orbit determinationfor ERS—l, ESOC Contract Report, Delft (1983)

9. P. Hartl, The Precise Range and Range Rate Equipment (PRARE) and itspossible support to the radar altimeter measurements for ERS—l,ESA SP221 (1984)

10. N. Dorrer and M. Lefebre, Doppler Orbitography and RadiopositioningIntegrated by Satellite: DORIS, CSTG Bulletin 8, (1985)

11. A. Eisner, S.M. Yionoulis, J.A. Platt, R.E. Jenkins, J.C. Ray andL.L. Pryor, NOVA—i the newest Transit satellite (status report), preprint(1983)

12. G.Afonso, F. Barlier, C. Berger, F. Migrard and J.J. Waich, Reassessmentof the charge and neutral drag of LAGEDS and its geophysical implications,JGR 90, 811, 9281 (1985)