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Journal of Geodesy

, Volume 80, Issue 7, pp 353–372 | Cite as

Efficient satellite orbit modelling using pseudo-stochastic parameters

  • G. BeutlerEmail author
  • A. Jäggi
  • U. Hugentobler
  • L. Mervart
Original Article

Abstract

If the force field acting on an artificial Earth satellite is not known a priori with sufficient accuracy to represent its observations on their accuracy level, one may introduce so-called pseudo-stochastic parameters into an orbit determination process, e.g. instantaneous velocity changes at user-defined epochs or piecewise constant accelerations in user-defined adjacent time subintervals or piecewise linear and continuous accelerations in adjacent time subintervals. The procedures, based on standard least-squares, associated with such parameterizations are well established, but they become inefficient (slow) if the number of pseudo-stochastic parameters becomes large. We develop two efficient methods to solve the orbit determination problem in the presence of pseudo-stochastic parameters. The results of the methods are identical to those obtained with conventional least-squares algorithms. The first efficient algorithm also provides the full variance–covariance matrix; the second, even more efficient algorithm, only parts of it.

Keywords

Orbit modelling Efficient orbit determination Pseudo-stochastic parameters 

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References

  1. Beutler G (2005) Methods of celestial mechanics. Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M, Verdun A (1994) Extended orbit modeling techniques at the CODE processing center of the international GPS service for geodynamics (IGS): theory and initial results. Manuscr Geod 19:367–386Google Scholar
  3. Colombo OL (1989) The dynamics of global positioning orbits and the determination of precise ephemerides. J Geophys Res 94(B7):9167–9182Google Scholar
  4. Dow JM, Neilan RE, Gendt G (2005) The international GPS service: Celebrating the 10th anniversary and looking to the next decade. ASR 36(3):320–326Google Scholar
  5. Hugentobler U, Schaer S, Beutler G, Bock H, Dach R, Jäggi A, Meindl M, Urschl C, Mervart L, Rothacher M, Wild U, Wiget A, Brockmann E, Weber G, Habrich H, Boucher C (2003) In: Gowey K (ed) CODE IGS Analysis Center technical report 2002. IGS Central Bureau, Jet Propulsion Laboratory, PasadenaGoogle Scholar
  6. Hugentobler, U, Dach R, Fridez P (2005) Bernese GPS software, version 5.0. Printing Office, University of BernGoogle Scholar
  7. Jäggi A, Hugentobler U, Beutler G (2004) Efficient stochastic orbit modeling techniques using least squares estimators. In: Sansó F (ed) A window on the future of geodesy. Springer, Berlin Heidelberg New York, pp 175–180Google Scholar
  8. Jäggi A, Hugentobler U, Beutler G (2006) Pseudo-stochastic orbit modeling techniques for low Earth orbiters. J Geod 80(1):47–60CrossRefGoogle Scholar
  9. Press WH, Teukolsky A, Vetterling WT, Flannery BP (1996) Numerical recipes in Fortran 77—the art of scientific computing, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  10. Strang G, Borre K (1997) Linear algebra, geodesy, and GPS. Wellesley, CambridgeGoogle Scholar
  11. Švehla D, Rothacher M (2002) Kinematic orbit determination of LEOs based on zero- or double-difference algorithms using simulated and real SST GPS data. In: Ádam J, Schwarz K-P (eds) Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New YorkGoogle Scholar
  12. Švehla D, Rothacher M (2003) CHAMP double-difference kinematic POD with ambiguity resolution. In: Reigber C, Lühr H, P (eds) First CHAMP mission results for gravity, magnetic and atmospheric studies. Springer, Berlin Heidelberg New YorkGoogle Scholar
  13. Teunissen PJG, Kleusberg A (eds) (1998) GPS for geodesy. Springer, Berlin Heidelberg New YorkGoogle Scholar
  14. Visser PNAM, van den IJssel J (2003) Aiming at a 1-cm orbit for low Earth orbiters: reduced-dynamic and kinematic precise orbit determination. Space sciences series of ISSI. Earth gravity field from space—from sensors to Earth sciences. Kluwer, DordrechtGoogle Scholar
  15. Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • G. Beutler
    • 1
    Email author
  • A. Jäggi
    • 1
  • U. Hugentobler
    • 1
  • L. Mervart
    • 2
  1. 1.Astronomical InstituteUniversity of BernBernSwitzerland
  2. 2.Institute of Advanced GeodesyCzech Technical UniversityPrague 6-DejviceCzech Republic

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