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From Kinematic Orbit Determination to Derivation of Satellite Velocity and Gravity Field

  • Dražen Švehla
  • Lóránt Földváry

Summary

After an overview of approaches and results in precise orbit determination (POD) for the CHAMP satellite in the Low Earth Orbit (LEO) we focus on the relations between kinematic POD and gravity field determination. We discuss determination of kinematic velocities out of kinematic positions that enter the gravity field determination in the form of kinetic orbital energy. After testing several numerical differentiation techniques, we selected conceptually two alternative methods, the Newton-Gregory interpolation and the smoothing cubic spline function. Finally, performance of numerical differentiation techniques for the CHAMP orbit is presented based on the gravity field determination.

Key words

CHAMP precise orbit determination kinematic orbit GPS numerical differentiation gravity 

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References

  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: 309–319Google 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: 24449–24464CrossRefGoogle Scholar
  3. Byun SH (2003) Satellite orbit determination using triple-differene GPS carrier phase in pure kinematic mode. J. of Geodesy 76: 569–585CrossRefGoogle Scholar
  4. Bock H (2003) Efficient Methods for Determining Precise Orbits of Low Earth Orbiters Using the Global Positioning System. PhD thesis. Astronomical Institute University of Berne, Berne, SwitzerlandGoogle Scholar
  5. 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 OregonGoogle Scholar
  6. Ditmar P, Kuznetsov V, Van Eck van der Sluijs A, Schrama E, Klees R (2004) DEOS_CHAMP-01C_70: a new model of the Earth’s gravity field derived from the CHAMP satellite data by means of the acceleration approach. Paper presented at the Joint CHAMP GRACE Science Meeting, GFZ Potsdam, Germay, 5–8 July 2004Google 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. In: Earth Observation with CHAMP-Results from Three Years in Orbit (eds) Reigber Ch, Lühr H, Schwintzer P, Wickert J, pp. 13–18, Springer VerlagGoogle 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:10.1029/2003GL018025CrossRefGoogle Scholar
  9. Greville TNE (1969) Theory and Applications of Spline Functions. Proceedings of an Advanced Seminar Conducted by the Mathematic Research Center, United States Army, at the University of Wisconsin, Madison October 7–9, 1968. Academic Press, New York, LondonGoogle Scholar
  10. König R, Baustert G, Neumayer KH, Meixner H, Schweiger V, Zhu S, Reigber C (2001) Precise orbit determination for CHAMP. Paper presented at EGS XXVI General Assembly, Nice, FranceGoogle Scholar
  11. Mayer-Gürr T, Ilk KH, Eicker A, Feuchtinger M (2005) ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period. J. of Geodesy, 78,(7–8): 462–480. doi 10.1007/s00190-004-0413-2CrossRefGoogle Scholar
  12. 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. 373–386Google Scholar
  13. 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)00162-5CrossRefGoogle Scholar
  14. Reubelt T, Goetzelmann M, Grafarend EW (2004) A new CHAMP gravity field model based on the GIS acceleration approach and two years of kinematic CHAMP data. Paper presented at the Joint CHAMP GRACE Science Meeting, GFZ Potsdam, Germany, 5–8 July 2004Google Scholar
  15. Rothacher M, Schmid R, Steigenberger P, Svehla D, Thaller D (2004) Combination of the Space Geodetic Techniques for Monitoring the Earth’s System. AGU Fall Meeting, San Francisco, 13–17 December 2004Google Scholar
  16. Rummel R (2003) How to Climb the Gravity Wall. In: Beutler G, Rummel R, Drinkwater MR, Steiger R (Eds): Earth Gravity Field From Space — From Sensors to Earth Sciences, Proceedings of an ISSI Workshop 11–15 March 2002, Bern Switzerland. Space Science Reviews, 108,(1–2): pp. 1–14Google Scholar
  17. Švehla D, Rothacher M (2002) Kinematic Orbit Determination of LEOs Based on Zero-or Double-Difference Algorithms Using Simulated and Real SST Data. In: Adam J, Schwarz KP (Eds): Vistas for Geodesy in the New Millenium, Proceedings of the IAG 2001 Scientific Assembly, Budapest. Springer IAG Vol. 125, pp. 322–328. (http://tau.fesg.tu-muenchen.de/~drazen/)Google Scholar
  18. Švehla D, Rothacher M (2003a) CHAMP double-difference kinematic orbit with ambiguity resolution. In: Reigber Ch, Lühr H, Schwintzer P (Eds): First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, Springer, pp. 70–77. (http://tau.fesg.tu-muenchen.de/~drazen/)Google Scholar
  19. Švehla D, Rothacher M (2003b) Kinematic and Reduced-Dynamic Precise Orbit Determination of Low Earth Orbiters. EGSXXVII General Assembly 2002, Nice, France. Advances in Geosciences 1: 47–56 (http://www.copernicus.org/EGU/adgeo/published_papers.htm)Google Scholar
  20. Švehla D, Rothacher M (2003c) 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 (http://tau.fesg.tu-muenchen.de/~drazen/)Google Scholar
  21. Švehla D, Rothacher M (2003d) Report on Validation of SRON SST Simulator. Support to End-to-End Simulations for the GOCE mission, Alenia Contract no. GO-SC-SRON-0322, Munich, GermanyGoogle Scholar
  22. Švehla D, Rothacher M, (2004b) Two Years of CHAMP Kinematic Orbits for Geosciences. Geophysical Research Abstracts, European Geophysical Society Vol. 6. ISSN:1029-7006 (http://tau.fesg.tu-muenchen.de/~drazen/)Google Scholar
  23. Švehla D, Rothacher M (2004a) Kinematic Precise Orbit Determination for Gravity Field Determination. Proceedings of the International Association of Geodesy: A Window on the Future of Geodesy. Eds. F. Sanso. Springer Verlag, IAG Vol 126. pp 181–188Google Scholar
  24. Švehla D, Rothacher M (2005) Kinematic positioning of LEO and GPS satellites and IGS stations on the ground. Advances in Space Research, doi:10.1016/j.asr.2005.04.066Google Scholar
  25. 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: 24383–24404CrossRefGoogle Scholar
  26. Yunck T, Bertiger W, Wu S, Bar-Sever Y, Christensen 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: 541–544CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dražen Švehla
    • 1
  • Lóránt Földváry
    • 1
    • 2
  1. 1.Institute of Astronomical and Physical GeodesyTechnical University of MunichMunichGermany
  2. 2.Now at the MTA-BME Research Group for Physical Geodesy and Geodynamics, Department of Geodesy and SurveyingBudapest University of Technology and EconomicsBudapestHungary

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