Numerical Velocity Determination and Calibration Methods for champ Using the Energy Balance Approach

  • M. Weigelt
  • N. Sneeuw
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 129)


More than two years of data of the champ satellite mission is available and the usage of the energy balance approach for global gravity field recovery has been successfully implemented by several groups around the world. This paper addresses two important aspects of the data processing. First, high-quality gravity recovery requires numerical differentiation of kinematic positions. Two methods are investigated using simulated and real dynamic data. It is shown that a third order Taylor differentiator is sufficient to reach good results. Second, drift due to the accelerometer bias has to be corrected. Two possible approaches are discussed: cross-over calibration on the one hand, calibration w.r.t. a reference model on the other hand. Currently the crossover calibration fails due to the insufficient accuracy of the crossover determination whereas the calibration w.r.t. a reference model gives good results.


champ energy balance fft Taylor differentiator high-pass filter crossover calibration 


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  1. Antoniou, A. (1993), Digital filters: Analysis, design and applications, New York: McGraw-Hill.Google Scholar
  2. Bruton, A., C. Glennie, and K. P. Schwarz (1999), Differentiation for high-precision GPS velocity and acceleration determination, GPS Solutions, 2(4), 7–21.CrossRefGoogle Scholar
  3. Gerlach, C, N. Sneeuw, P. Visser, and D. Švehla (2003a), champ gravity field recovery with the energy balance approach: first results, In: C. Reigber, H. Lühr, and P. Schwintzer (eds), First champ Mission Results for Gravity, Magnetic and Atmospheric Studies, Springer, pp. 134–139.Google Scholar
  4. Gerlach, C, N. Sneeuw, P. Visser, and D. Švehla (2003b), champ gravity field recovery using the energy balance approach, Adv. Geosciences, 1, 73–80.Google Scholar
  5. Han, S., C. Jekeli, and C. Shum (2002), Efficient gravity field recovery using in situ disturbing potential observabels from champ, Geophys. Res. Lett., 29(16), 1789, doi:10.1029/2002GL015180.CrossRefGoogle Scholar
  6. Ilk, K. H. (2001), Special commission SC7, gravity field determination by satellite gravity gradiometry, Scholar
  7. Khan, I., and R. Ohba (1999), Closed-form expressions for the finite difference approximations of first and higher derivatives based on taylor series, Journal of Computational and Applied Mathematics, 46, doi:10.1049/ipvis:19990380.Google Scholar
  8. Lyons, R. (2001), Understanding Digital Signal Processing, Prentice Hall PTR.Google Scholar
  9. Schneider, M. (1992), Grundlagen und Determinierung, vol. I of Himmelsmechanik, BI-Wissenschaftsverlag, (In German).Google Scholar
  10. Sneeuw, N., C. Gerlach, D. Švehla, and C. Gruber (2003), A first attempt at time-variable gravity recovery from champ using the energy balance approach, In: I. Tziavos (ed), Gravity and Geoid 2002, pp. 237–242.Google Scholar
  11. Švehla, D., and M. Rothacher (2004), Two years of champ kinematic orbits for geosciences, Geophysical Research Abstracts, 6, 06645, SRef-ID:1607-7962/gra/EGU04-A-06645.Google Scholar
  12. Wermuth, M., D. Švehla, L. Földvary, C. Gerlach, T. Gruber, B. Frommknecht, T. Peters, M. Rothacher, R. Rummel, and P. Steigenberger (2004), A gravity field model from two years of champ kinematic orbits using the energy balance approach, Geophysical Research Abstracts, 6, 03843, SRef-ID:1607-7962/gra/EGU04-A-03843.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M. Weigelt
    • 1
  • N. Sneeuw
    • 1
  1. 1.Department of Geomatics EngineeringUniversity of CalgaryCalgary

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