Stochastic model validation of satellite gravity data: A test with CHAMP pseudo-observations

  • J.P. van Loon
  • J. Kusche
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 129)


The energy balance approach is used for a statistical assessment of CHAMP orbits, data and gravity models. It is known that the quality of GPS-derived orbits varies and that CHAMP accelerometer errors are difficult to model. The stochastic model of the in-situ potential values from the energy balance is therefore heterogeneous and it is unclear if it can be described accurately using a priori information. We have estimated parameters of this stochastic model in an iterative variance-component estimation procedure, combined with an outlier rejection method. This means we solve simultaneously for a spherical harmonic model, for polynomial coefficients absorbing accelerometer drift, for sub-daily noise variance components, and for a variance parameter that controls the influence of an a-priori gravity model (EGM96). We develop here, for the first time, a fast Monte Carlo variant of the Minimum Norm Quadratic Unbiased Estimator (MINQUE) as an alternative for the fast Monte Carlo Maximum Likelihood VCE that we have introduced earlier. In this way, spurious data sets could be indicated and downweighted in the least-squares estimation of the unknown parameters. Using only 299 days of CHAMP kinematic orbit data, the quality of the estimated global gravity model was found com-parable to the EIGEN-3P model. Monte Carlo Variance Components Estimation appears to be a valid method to estimate the stochastic model of satellite gravity data and thus improves the least squares solution considerably.


CHAMP energy balance approach statistical assessment variance components 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Gerlach C, Földvary L, Švehla D, Gruber Th, Wermuth M, Sneeuw N, Frommknecht B, Oberndorfer H, Peters Th, Rothacher M, Rummel R, Steigenberger P (2003). A CHAMP-only gravity field model from kinematic orbits using the energy integral GRL 30(20), 2037, doi:10.1029/2003GL018025CrossRefGoogle Scholar
  2. Grafarend EG, Schaffrin B (1993) Ausgleichungsrechnung in linearen Modellen. BI Verlag, MannheimGoogle Scholar
  3. Howe E, Stenseng L, Tscherning CC (2003) Analysis of one month of state vector and accelerometer data for the recovery of the gravity potential. Adv Geosciences 1:1–4.Google Scholar
  4. Jekeli C (1999) The determination of gravitational potential differences from satellite-to-satellite tracking. Cel Mech Dyn Astr 75: 85–100.CrossRefGoogle Scholar
  5. Koch K-R, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geodesy 76: 259–268.CrossRefGoogle Scholar
  6. Kusche J (2003) A Monte-Carlo technique for weight estimation in satellite geodesy. J Geodesy 76: 641–652.CrossRefGoogle Scholar
  7. Kusche J, van Loon JP (2004) Statistical assessment of CHAMP data and models using the energy balance approach., in Reigber et al., Earth observation with CHAMP, results from three years in orbit, Springer.Google Scholar
  8. Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olsen TR (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. NASA/TP-1998-206861, NASA-GSFC, Greenbelt MDGoogle Scholar
  9. Löcher A, Ilk KH (2004) Energy balance relations for validation of gravity field models and orbit determination, in Reigber et al., Earth observation with CHAMP, results from three years in orbit, Springer.Google Scholar
  10. Lucas JR (1985) A variance component estimation method for sparse matrix applications NOAA Technical Report NOS 111 NGS 33, National Geodetic Survey, RockvilleGoogle Scholar
  11. Mayer-Gürr T, Ilk KH, Eicker A, Feuchtinger M (in press) ITG-CHAMP01: A CHAMP gravitiy field model from short kinematical arcs of a one-year observation period, accepted for J GeodesyGoogle Scholar
  12. Rao CR, Kleffe J (1988) Estimation of variance components and applications. North-Holland, AmsterdamGoogle Scholar
  13. Ray RD (1999) A global ocean tide model from TOPEX / POSEIDON altimetry: GOT99.2, NASA/TM-1999-209478, NASA-GSFC, Greenbelt, MDGoogle Scholar
  14. Reigber C, Schmidt R, Flechtner F, König R, Meyer U, Neumayer KH, Schwintzer P, Zhu SY EIGEN gravity field model to degree and order 150 from GRACE Mission data only, submitted to Journal of Geodynamics.Google Scholar
  15. Reigber C, Jochman H, Wünsch J, Petrovic S, Schwintzer P, Barthelmes F, Neumayer K-H, König R, Förste C, Balmino G, Biancale R, Lemoine J-M, Loyer S, Perosanz F (2004) Earth gravity field and seasonal variability from CHAMP, in Reigber et al., Earth Observation with CHAMP, results from three years in orbit, Springer.Google Scholar
  16. Švehla D, Rothacher M (2003) Kinematic and reduced-dynamic precise orbit determination of low earth orbiters. Adv Geosciences 1: 47–56.Google Scholar
  17. Sjöberg LE (1983) Unbiased estimation of variance-covariance components in condition adjustment with unknowns-A MINQUE approach. Zeitschrift fur Vermessungswesen 108:9, p. 382–387Google Scholar
  18. Visser P, Sneeuw N, Gerlach C (2003) Energy integral method for gravity field determination from satellite orbit coordinates. J Geodesy 77: 207–216.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J.P. van Loon
    • 1
  • J. Kusche
    • 1
  1. 1.DEOSTU DelftDelftThe Netherlands

Personalised recommendations