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


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.


Orbit modelling Efficient orbit determination Pseudo-stochastic parameters 


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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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