Testing frame-transformation, gridding and filtering of GOCE gradiometer data by Least-Squares Collocation using simulated data

  • C.C. Tscherning
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 128)


Least-squares collocation (LSC) has been used to test frame transformation, filtering and gridding of GOCE gradiometer data. Initially the function of the GRAVSOFT program GEOCOL was checked by using noise-free data with 5 s sampling provided by IAG along a 1 month realistic orbit. Data in a 2° × 2° area was used. For these data it was verified that 0.1° frame transformation and gridding in an interior 1° × 1° area of one quantity from the same quantity could be done with an error below 5 % of the signal standard deviation. If several components of the gravity gradient were used, the error decreased slightly.

Noise with standard deviations of 0.050 and 0.150 Eötvös Units (E=10−9/s2), respectively, and a 1 s correlation distance was generated and added to the data. For the 0.050 E noise the result of the gridding was as for the data without noise, when 1 s sampling was used. For the 0.150 E data, the use of totally 2 months of simulated data and all 3 diagonal components of the gradient matrix were necessary in order to obtain a result below 10 % of the signal standard deviation. Further improvements are possible if data from a larger area or from the planned second measurement phase of GOCE are used.


Gravity Gradient Geopotential Model Noise Standard Deviation Spherical Distance Covariance Expression 
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  1. Bouman, J., R. Koop, R. Haagmans, J. Mueller, N. Sneuw, C.C. Tscherning and P. Visser: Calibration and Validation of GOCE Gravity Gradients. Poster prepared for IUGG/IAG General Assembly, Sapporo, 2003.Google Scholar
  2. ESA: Gravity Field and Steady-State Ocean Circulation Mission, ESA SP-1233, 1999.Google Scholar
  3. Lemoine, F.G., S.C. Kenyon, J.K. Factor, R.G. Trimmer, N.K. Pavlis, D.S. Chinn, C.M. Cox, S.M. Klosko, S.B. Luthcke, M.H. Torrence, Y.M. Wang, R.G. Williamson, E.C. Pavlis, R.H. Rapp, and T.R. Olson, The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, MD, July, 1998.Google Scholar
  4. Moritz, H,: Advanced Physical Geodesy. H. Wichmann Verlag, Karlsruhe, 1980.Google Scholar
  5. Reguzzoni, M.: From the time-wise to the space-wise GOCE observables. Como, 2002.Google Scholar
  6. Sanso’, F. and C.C. Tscheming: Fast spherical collocation: A General Implementation. IAG Symposia, Vol. 125, pp. 131–137, Springer Verlag, 2002.Google Scholar
  7. Tscherning, C.C.: A FORTRAN IV Program for the Determination of the Anomalous Potential Using Stepwise Least Squares Collocation. Reports of the Department of Geodetic Science No. 212, The Ohio State University, Columbus, Ohio, 1974.Google Scholar
  8. Tscherning, C.C.: Covariance Expressions for Second and Lower Order Derivatives of the Anomalous Potential. Reports of the Department of Geodetic Science No. 225, The Ohio State University, Columbus, Ohio, 1976.Google Scholar
  9. Tscherning, C.C.: Computation of covariances of derivatives of the anomalous gravity potential in a rotated reference frame. Manuscripta Geodaetica, Vol. 18, no. 3, pp. 115–123, 1993.Google Scholar
  10. Tscherning, C.C. and D. Arabelos: Computation of a geopotential model from GOCE data using Fast Spherical collocation — a simulation study. Prepared for IUGG/IAG General Assembly, G03, Sapporo, 2003.Google Scholar
  11. Tscherning, C.C., R. Forsberg and P. Knudsen: The GRAVSOFT package for geoid determination. Proc. 1. Continental Workshop on the Geoid in Europe, Prague, May 1992, pp. 327–334, Research Institute of Geodesy, Topography and Cartography, Prague, 1992.Google Scholar

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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • C.C. Tscherning
    • 1
  1. 1.Department of GeophysicsUniversity of CopenhagenCopenhagen ØDenmark

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