Kinematic Precise Orbit Determination for Gravity Field Determination

  • D. Švehla
  • M. Rothacher
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 128)


In this paper we first present approaches and results in precise orbit determination (POD) for satellites in Low Earth Orbit (LEO) based on one or two frequency GPS measurements and, secondly, we focus on the relations between kinematic POD and gravity field determination. Using GPS measurements of the CHAMP satellite we show that it is possible to estimate kinematic positions of a LEO satellite with the same level of accuracy (≈ 1–3 cm w.r.t. SLR) as with the widely applied reduced-dynamic or dynamic approaches. Kinematic precise orbit determination (POD) as presented here is based on GPS phase measurements and is independent of satellite dynamics (e.g. gravity field, air-drag, etc.) and orbit characteristics (e.g. orbit height, eccentricity, etc.). We also looked at the LEO POD based on GPS measurements from only one frequency, where we make use of what we call the LP linear combination. We show that with this linear combination LEO POD can be performed with one frequency at the 10 cm level. In the second part of the paper the use of kinematic POD is discussed in the framework of the CHAMP, GRACE and GOCE gravity missions. With simulated GPS measurements we studied the impact of ambiguity resolution for the kinematic baseline between the two GRACE satellites. At the end of the paper we present an alternative approach in gravity field determination by measuring the gravitational frequency shift between (optical) atomic clocks in space. In this approach we require very accurate clocks positions, which may be obtained from kinematic POD.


Kinematic orbit LEO POD space clock 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Balmino G, Perosanz F, Rummel R, Sneeuw N, Sünkel H, 1999. CHAMP, GRACE and GOCE: mission concepts and simulations. Bolletino di Geofisica Teorica ed Applicata. Vol. 40, 309–319.Google Scholar
  2. Bertiger W, Bar-Sever Y, Christensen E, Davis E, Guinn J, Haines B, Ibanez-Meier R, Jee J, Lichten S, Melbourne W, Muellerschoen R, Munson T, Vigue Y, Wu S, Yunck T, Schutz B, Abusali P, Rim H, Watkins M, Willis P, 1994. GPS precise tracking of TOPEX/POSEIDON: results and implication. J Geophys Res 99,C12: 24449–24464.CrossRefGoogle Scholar
  3. Bertiger W, Wu SC, 1996. Single frequency GPS orbit determination for low earth orbiters, ION National Technical Meeting, Jan., 1996.Google Scholar
  4. Byun SH, 2003. Satellite orbit determination using triple-differene GPS carrier phase in pure kinematic mode, J. of Geodesy 76: 569–585.CrossRefGoogle Scholar
  5. Bock H, 2003. Effiient Methods for Determining Precise Orbits of Low Earth Orbiters Using the Global Positioning System. PhD thesis. Astronomial Institute University of Berne, Berne, Schwitzerland.Google Scholar
  6. Colombo OL, Luthcke SB, Rowlands DD, Chin DS, Poulouse S, 2002. Filtering Errors in LEO Trajectories Obtained by Kinematic GPS with Floating Ambiguities. Presented at The ION Symposium ”GPS 2002”, Sept. 24–27, 2002, Portland Oregon.Google Scholar
  7. Földváry L, Gerlach Ch, Švehla D, Frommknecht B, Gruber Th, Peters Th, Rothacher M, Rummel R, Sneeuw N, Steigenberger P, 2003. Determination of the Gravity Field From CHAMP Measurements Considering the Energy Integral. IUGG 2003, General Assembly, June 30–July 11 2003, Sapporo, Japan.Google Scholar
  8. Gerlach Ch, Földváry L, Švehla D, Gruber Th, Wermuth M, Rothacher M, Rummel R, Sneeuw N, Frommknecht B, Peters Th, Steigenberger P, 2003. A CHAMP only Gravity Field Model From Kinematic Orbits Using the Energy Integral. Geoph. Res. Letters, 30(20), 2037, doi: 10. 1029/2003GL01 8025.CrossRefGoogle Scholar
  9. Melbourne WG, 1985. The Case for Ranging in GPS Based Geodetic Systems. First International Symposium on Precise Positioning with the GPS, C. Goad (Ed), U.S. Department of Commerce, Rockville, Maryland, pp. 373–386.Google Scholar
  10. Reigber Ch, Schwintzer P, Neumayer K-H, Barthelmes F, König R, Förste Ch, Balmino G, Biancale R, Lemoine J-M, Loyer S, Bruinsma S, Perosanz F, Fayard T, 2003. The CHAMP-only Earth Gravity Field Model EIGEN-2. Adv. in Space Research, 31(8), 1883–1888, 2003, doi: 10. 1016/S0273-1177(03)00162-5.CrossRefGoogle Scholar
  11. Rim HJ, Ries JC, Yoon S, Webb CE, Bettadpur S, Schutz BE, 2003. Gravity model development for ICESAT precision orbit determination. IUGG 2003, General Assembly, June 30–July 11 2003, Sapporo, Japan.Google Scholar
  12. Salomon C, Dimarcq N, Abgrall M, Clairon A, Laurent P, Lemonde P, Santarelli G, Uhrich P, Bernier LG, Busca G, Jornod A, Thomann P, Samain E, Wolf P, Gonzalez F, Guillemot P, Léon S, Nouel F, Sirmain C, Feltham S, 2001. Cold Atoms in Space and Atomic Clocks: ACES. C.R. Acad.Sci. Paris, T2 Série 4, 1313.Google Scholar
  13. Švehla D, Rothacher M, 2002a. Kinematic Orbit Determination of LEOs Based on Zero-or Double-Difference Algorithms Using Simulated and Real SST Data. IAG 2001 Scientific Assembly, Budapest, Vistas for Geodesy in the New Millenium, Adam J, Schwarz KP (Eds), Springer IAG Vol. 125, pp. 322–328.Google Scholar
  14. Švehla D, Rothacher M, 2003b. CHAMP double-difference kinematic orbit with ambiguity resolution. 1st CHAMP Science Meeting, Potsdam, Germany. First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, Reigber Ch, Lühr H, Schwintzer P (Eds), Springer, pp. 70–77.Google Scholar
  15. Švehla D, Rothacher M, 2003c. Kinematic and Reduced-Dynamic Precise Orbit Determination of Low Earth Orbiters. EGSXXVII General Assembly 2002, Nice, France. Advances in Geosciences 1, 47–56. ( Scholar
  16. Švehla D, Rothacher M, 2003d. Kinematic and Reduced-Dynamic Precise Orbit Determination of CHAMP satellite over one year using zero-differences. Poster presented at EGS-AGU-EUG Joint Assembly 06–11 April 2003, Nice, France. ( Scholar
  17. Tapley BD, Ries JC, Davis GW, Eanes RJ, Schutz BE, Shum CK, Watkins MM, Marshall JA, Nerem RS, Putney BH, Klosko SM, Luthcke SB, Pavlis D, Williamson RG, Zelensky NP, 1994. Precision orbit determination for TOPEX/POSEIDON. J Geophys Res 99,C12: 24383–24404.CrossRefGoogle Scholar
  18. Udem Th, Holzwarth R, Hänsh TW, 2002. Optical frequency metrology. Nature, Vol. 416, 233–237.CrossRefGoogle Scholar
  19. Yunck T, Bertiger W, Wu S, Bar-Sever Y, Chris-tensen E, Haines B, Lichten S, Muellerschoen R, Vigue Y, Willis P, 1994. First assessment of GPS-based reduced dynamic orbit determination on TOPEX/POSEIDON. Geophys Res Letters 21:541–544.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • D. Švehla
    • 1
  • M. Rothacher
    • 1
  1. 1.Forschungseinrichtung Satellitengeodäsie, Institut für Astronomische und Physikalische GeodäsieTechnical University of MunichMunichGermany

Personalised recommendations