Summary
Based on very accurate kinematic CHAMP orbits, a new CHAMP gravitational field model was computed by means of a (point-wise) acceleration approach. In order to implement such an acceleration approach, the satellite’s acceleration has to be derived from the kinematic CHAMP orbits by means of interpolation and subsequent numerical differentiation. The iterative method of preconditioned conjugate gradients is implemented to solve the large linear system of equations for the spherical harmonic coefficients. If appropriate preconditioning is applied, convergence can be reached within 7 – 15 iterations. An important topic concerning the accuracy of the gravity field solutions is the detection and filtering or down-weighting of spikes, jumps, outliers and inaccurate data in the kinematic orbits. These problems are adressed by data-preprocessing or robust estimation. Different gravity field solutions up to degree and order 90 were computed, where validation exhibits a signal-to-noise (S/N) ratio per degree of S/N ≥ 1 for coefficients up to degree 80 and S/N ≥ 2 for coefficients up to degree 70. Comparisons to different CHAMP-models, which were obtained by application of alternative algorithms, prove that the acceleration approach can compete with other methods of gravity field determination.
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References
Austen G, Grafarend EW, Reubelt T (2002) Analysis of the Earth’s Gravitational Field from Semi-Continuous Ephemeris of a Low Earth Orbiting GPS-Tracked Satellite of Type CHAMP, GRACE or GOCE. In: International Association of Geodesy Symposia, Vol. 125, Vistas for Geodesy in the New Millennium, J. Adam and K. P. Schwarz (Editors), Axel Springer Verlag.
Ditmar P, Klees R (2002) A method to compute the Earth’s gravity field from SGG/SST data to be aquired by the GOCE satellite. Delft University Press, Delft, 2002.
Ditmar P, van Eck van der Sluijs AA (2004) A technique for modelling the Earth’s gravity field on the basis of satellite accelerations. Journal of Geodesy, Vol. 78, 1–2: 12–33.
Engeln-Müllges G, Reutter F (1987) Numerische Mathematik für Ingenieure. 5th revised edition, BI Wissenschaftsverlag, Mannheim, Wien, Zürich.
Földváry L, Švehla D, Gerlach C, Wermuth M, Gruber T, Rummel R, Rothacher M, Frommknecht B, Peters T, Steigenberger P (2005) Gravity model TUM-2Sp based on the energy balance approach and kinematic CHAMP orbits. In: Reigber Ch, Lühr H, Schwintzer P, Wickert J (Eds.), Earth Observation with CHAMP-Results from Three Years in Orbit, Springer, Berlin, 13–16, 2005.
Götzelmann M, Keller W, Reubelt T (submitted) Gross error compensation for gravity field analysis based on kinematic orbit data. Journal of Geodesy.
Huber PJ (1981) Robust statistics. Wiley, New York, 1981.
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, Olson TR (1998) The development of the joint NASA Goddard Space Flight Center and the National Imagery and Mapping Agency (NIMA) geopotential Model EGM96. NASA/TP-1998-206861, Greenbelt, Maryland, USA, 1998.
Koch KR (1996) Robuste Parameterschätzung. Allgemeine Vermessungsnachrichten AVN 1/1996, 103: 1–18, Wichmann, 1996.
Mayer-Gürr T, Ilk KH, Eicker A, Feuchtinger M (2005) ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period. Journal of Geodesy (2005) Vol. 78, Issue 7–8: 462–480.
Reigber C (1989) Gravity field recovery from satellite tracking data. In: Sanso F, Rummel R (Eds.), Theory of satellite geodesy and gravity field determination, Springer Verlag, Berlin, Heidelberg, New York 1989, pp. 197–234.
Reigber C, Balmino G, Schwintzer P, Biancale R, Bode A, Lemoine JM, König R, Loyer S, Neumayer H, Marty JC, Barthelmes KH, Perosanz F, Zhu SY (2002) A high quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophysical Research Letters, 29(14), 10.1029/2002GL015064, 2002.
Reigber C, Schwintzer P, Neumayer H, Barthelmes KH, König R, Förste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Bruinsma S, Perosanz F, Fayard T (2003) The CHAMP-only Earth Gravity Field Model EIGEN-2. Advances in Space Research 31(8): 1883–1888, 2003 (doi:10.1016/S0273-1177(03)00162-5).
Reigber C, Schmidt R, Flechtner F, König R, Meyer U, Neumayer KH, Schwintzer P, Zhu SY (2005a) An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. Journal of Geodynamics 39(1):1–10.
Reigber C, Jochmann H, Wünsch J, Petrovic S, Schwintzer P, Barthelmes F, Neumayer KH, König R, Förste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Perosanz F (2005b) Earth Gravity Field and Seasonal Variability from CHAMP. In: Reigber Ch, Lühr H, Schwintzer P, Wickert J (Eds.), Earth Observation with CHAMP-Results from Three Years in Orbit, Springer, Berlin, 25–30, 2005.
Reubelt T, Austen G, Grafarend EW (2003a) Harmonic analysis of the Earth’s gravitational field by means of semi-continous ephemerides of a low Earth orbiting GPS-tracked satellite. Case study: CHAMP. J Geod 77: 257–278.
Reubelt T, Austen G, Grafarend EW (2003b) Space Gravity Spectroscopydetermination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris; case studies on dynamic (CHAMP Rapid Science Orbit) and kinematic orbits. Advances in Geosciences, 1: 127–135, European Geosciences Union 2003.
Reubelt T, Götzelmann M, Grafarend EW (submitted) A new CHAMP gravitational field model based on the GIS acceleration approach and two years of kinematic CHAMP data. In Reigber C, Tapley B (Eds.): New Satellite Mission Results for the Geopotential Fields and Their Variations, special issue of Advances in Geosciences, EGU.
Švehla D, Rothacher M (2003) Kinematic and Reduced-Dynamic Precise Orbit Determination of Low Earth Orbiters. Advances in Geosciences, 1: 47–56, EGU, 2003.
Švehla D, Rothacher M (2004) Two years of CHAMP kinematic orbits for Geosciences. EGU, 1st General Assembly, Nice, France. Geophysical Research Abstracts, European Geophysical Society Vol. 6. ISSN: 1029–7006, 2004.
Weigelt M, Sneeuw N (submitted) Numerical Velocity determination and Calibration Methods for CHAMP Using the Energy Balance Approach. Proceedings of the 4th Meeting of the International Gravity and Geoid Commission “Gravity, Geoid and Space Missions — GGSM2004”, Aug. 30–Sept. 3, 2004, Porto, Portugal.
Xu P (1989) On robust estimation with correlated observations. Bull. Geod., 63: 237–252.
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Reubelt, T., Götzelmann, M., Grafarend, E.W. (2006). Harmonic Analysis of the Earth’s Gravitational Field from Kinematic CHAMP Orbits based on Numerically Derived Satellite Accelerations. In: Flury, J., Rummel, R., Reigber, C., Rothacher, M., Boedecker, G., Schreiber, U. (eds) Observation of the Earth System from Space. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29522-4_3
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