Skip to main content
Springer Nature Link
Log in

Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

  • Original Article
  • Published:
Journal of Geodesy Aims and scope Submit manuscript

Abstract

The Earth’s non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2 cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30 s.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bertiger WI, Bar-Sever YE, Christensen EJ, Davis ES, Guinn JR, Haines BJ, Ibanez-Meier RW, Jee JR, Lichten SM, Melbourne WG, Muellerschoen RJ, Munson TN, Vigue Y, Wu SC, Yunck TP, Schutz BE, Abusali PAM, Rim HJ, Watkins MM, Willis P (1994) GPS precise tracking of TOPEX/POSEIDON: results and implication. J Geophys Res 99(C12):24449–24464

    Article  ADS  Google Scholar 

  • Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M (1994) Extended orbit modeling techniques at the CODE processing center of the international GPS service for geodynamics (IGS): theory and initial results. Manuscripta Geodetica 19:367–386

    Google Scholar 

  • Beutler G (2004) Methods of celestial mechanics. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Bock H, Hugentobler U, Springer TA, Beutler G (2002) Efficient precise orbit determination of LEO satellites using GPS. Adv Space Res 30(2):295–300

    Article  Google Scholar 

  • Boomkamp H (2003) The CHAMP orbit comparison campaign. In: Reigber C, Lühr H, Schwintzer P (eds) First CHAMP mission results for gravity, magnetic and atmospheric studies. Springer, Berlin Heidelberg New York, pp 53–58

    Google Scholar 

  • CSR ocean tide model from Schwiderski (1995) ftp://ftp.csr.utexas.edu/pub/tide/oldfiles/spharm_schwid+

  • Eanes RJ, Bettadpur SV (1995) The CSR 3.0 global ocean tide model. Technical Memorandum 95-06, Center for Space Research University of Texas, Austin

    Google Scholar 

  • European Space Agency ESA (1999) The Four Candidate Earth Explorer Core Missions: Gravity Field and Steady-State Ocean Circulation Mission. ESA SP-1233 (1)

  • Földváry L, Švehla D, Gerlach C, Wermuth M, Gruber T, Rummel R, Rothacher M, Frommknecht B, Peters T, Steigenberger P (2004) Gravity model TUM-2Sp based on the energy balance approach and kinematic CHAMP orbits. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observation with CHAMP, results from three years in orbit. Springer, Berlin Heidelberg New York, pp 13–18

    Google Scholar 

  • Fu L, Christensen EJ, Yamarone CA, Lefebvre M, Ménard Y, Dorrer M, Escudier P (1994) TOPEX/POSEIDON mission overview. J Geophys Res 99(C12):24369–24381

    Article  ADS  Google Scholar 

  • Gerlach C, Földváry L, Švehla D, Gruber T, Wermuth M, Sneeuw N, Frommknecht B, Oberndorfer H, Peters T, Rothacher M, Rummel R, Steigenberger P (2003) A CHAMP-only gravity field model from kinematic orbits using the energy integral. Geophys Res Lett 30(20):2037 DOI 10.1029/2003GL018025

    Article  ADS  Google Scholar 

  • Hugentobler U, Schaer S, Fridez P (2001) Bernese GPS Software Version 4.2. Documentation. Astronomical Institute University of Berne, Berne

    Google Scholar 

  • van den IJssel J, Visser PNAM, Patiño Rodriguez E (2003) CHAMP precise orbit determination using GPS data. Adv Space Res 31(8):1889–1895

    Article  ADS  Google Scholar 

  • van den IJssel J, Visser PNAM (2005) Determination of non-conservative accelerations from GPS satellite-to-satellite tracking of CHAMP. Adv Space Res 36(3):418–423

    Article  ADS  Google Scholar 

  • Jäggi A, Beutler G, Hugentobler U (2004a) Efficient stochastic orbit modeling techniques using least squares estimators. In: Sansò F (eds) A window on the future of geodesy. Springer, Berlin Heidelberg New York, pp 175–180

    Google Scholar 

  • Jäggi A, Bock H, Hugentobler U, Beutler G (2004b) Comparison of different stochastic orbit modeling techniques. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observation with CHAMP, results from three years in orbit. Springer, Berlin Heidelberg New York, pp 89–94

    Google Scholar 

  • Jäggi A, Beutler G, Hugentobler U (2005) Reduced-dynamic orbit determination and the use of accelerometer data. Adv Space Res 36(3):438–444

    Article  ADS  Google Scholar 

  • Jazwinski AH (1970) Stochastic processes and filtering theories. Academic, New York

    Google Scholar 

  • König R, Michalak G, Neumayer KH, Schmidt R, Zhu SY, Meixner H, Reigber C (2004) Recent developments in CHAMP orbit determination at GFZ. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observation with CHAMP, results from three years in orbit. Springer, Berlin Heidelberg New York, pp 65–70

    Google Scholar 

  • Kursinski ER, Hajj GA, Schofield JT, Linfield RP, Hardy KR (1997) Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J Geophys Res 102(D19):23429–23465

    Article  ADS  Google Scholar 

  • Mayer-Gürr T, Ilk KH, Eicker A, Feuchtinger M (2004) ITG-CHAMP01: a CHAMP gravity field model from short kinematical arcs of a one-year observation period. J Geod 78:462–480

    Article  ADS  Google Scholar 

  • O’Keefe JA (1957) An application of Jacobi’s integral to the motion of an Earth satellite. Astron J 62(1252):265–266

    Article  ADS  Google Scholar 

  • Reigber C (1989) Gravity field recovery from satellite tracking data. In: Sansò F, Rummel R (eds) Theory of satellite geodesy and gravity field determination. Springer, Berlin Heidelberg New York, pp 197–234

    Google Scholar 

  • Reigber C, Balmino G, Schwintzer P, Biancale R, Bode A, Lemoine JM, Koenig R, Loyer S, Neumayer H, Marty JC, Barthelmes F, Perosanz F, Zhu SY (2002) A high quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophys Res Lett 29(14):37–1 DOI 10.1029/2002GL015064

    Article  Google Scholar 

  • Reigber C, Schwintzer P, Neumayer KH, Barthelmes F, König R, Förste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Bruinsma S, Perosanz F, Fayard T (2003) The CHAMP-only Earth Gravity Field Model EIGEN-2. Adv Space Res 31(8):1883–1888

    Article  ADS  Google Scholar 

  • Reigber C, Jochmann H, Wünsch J, Petrovic S, Schwintzer P, Barthelmes F, Neumayer KH, König R, Förste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Perosanz F (2004) Earth gravity field and seasonal variability from CHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observation with CHAMP, results from three years in orbit. Springer, Berlin Heidelberg New York, pp 89–94

    Google Scholar 

  • Švehla D, Rothacher M (2002) Kinematic and reduced-dynamic precise orbit determination of low Earth orbiters. Adv Geosci 1:47–56

    Google Scholar 

  • Švehla D, Rothacher M (2004) Kinematic precise orbit determination for gravity field determination. In: Sansò F (eds) A window on the future of geodesy. Springer, Berlin Heidelberg New York, pp 181–188

    Google Scholar 

  • Touboul P, Willemenot E, Foulon B, Josselin V (1999) Accelerometers for CHAMP, GRACE and GOCE space missions: synergy and evolution. Boll Geof Teor Appl 40:321–327

    Google Scholar 

  • Visser PNAM, van den IJssel J (2003a) Aiming at a 1-cm orbit for low Earth orbiters: reduced-dynamic and kinematic precise orbit determination. In: Beutler G, Rummel R, Drinkwater MR, von Steiger R (eds) Earth gravity field from space - from sensors to Earth sciences. Kluwer, Dordrecht, pp 27–36

    Google Scholar 

  • Visser PNAM, Sneeuw N, Gerlach C (2003b) Energy integral method for gravity field determination from satellite orbit coordinates. J Geod 77:207–216

    Article  MATH  ADS  Google Scholar 

  • Wu SC, Yunck TP, Thornton CL (1991) Reduced-dynamic technique for precise orbit determination of low Earth satellites. J Guid Control Dyn 14(1):24–30

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Astronomical Institute, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    A. Jäggi, U. Hugentobler & G. Beutler

Authors
  1. A. Jäggi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Hugentobler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Beutler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Jäggi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jäggi, A., Hugentobler, U. & Beutler, G. Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters. J Geodesy 80, 47–60 (2006). https://doi.org/10.1007/s00190-006-0029-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00190-006-0029-9

Keywords

Search

Navigation