Abstract
This paper aims at a comparative study of several measures to compensate for gross errors in kinematic orbit data. It starts with a simulation study on the influence of a single outlier in the orbit data on the gravity field solution. It is shown that even a single outlier can degrade the resulting gravity field solution considerably. To compensate for outliers, two different strategies are investigated: wavelet filters, which detect and eliminate gross errors, and robust estimators, which due to an iterative downweighting gradually ignore those observations that lead to large residuals. Both methods are applied in the scope of the analysis of a 2-year kinematic CHAMP (challenging minisatellite payload) orbit data set. In various real data studies, robust estimators outperform wavelet filters in terms of resolution of the derived gravity field solution. This superior performance is at the cost of computational load, as robust estimators are implemented iteratively and require the solution of large sets of linear equations several times.
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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: Ádám J, Schwarz K-P (eds) Vistas for geodesy in the new millennium International Association of Geodesy Symposia 125. Springer, Berlin Heidelberg New York
Beaton A, Tukey J (1974) The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics 16: 147–192
Caspary W (1988) Fehlerverteilungen, Methode der kleinsten Quadrate und robuste Alternativen. Z Vermess 113(3):123–133
Chang XW, Guo Y (2005) Huber’s M-estimation in relative GPS positioning: computational aspects. J Geod 79(6–7):351–362. DOI 10.1007/s00190-005-0473-y
Ditmar P, van Eck van der Sluijs AA (2004) A technique for modelling the Earth’s gravity field on the basis of satellite accelerations. J Geod 78(1–2):12–33. DOI 10.1007/s00190-003-0362-1
Földvary 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 C, Lühr H, Schwintzer P, Wickert J (eds) Earth observations with CHAMP – results from three years in orbit. Springer, Berlin Heidelberg New York, pp 13–18
Gerlach C, Sneeuw N, Visser P, Švehla D (2003) CHAMP gravity field recovery with the energy balance approach: first results. In: Reigber C, Lühr H, Schwintzer P (eds) First CHAMP mission results for gravity, magnetic and atmospheric studies. Springer, Berlin Heidelberg New York, pp 134–139
Hampel FR (1974) The influence curve and its role in robust estimation. J Am Stat Assoc 62:1179–1186
Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35:73–101
Huber PJ (1981) Robust statistics. Wiley, New York
Ilk KH, Mayer-Gürr T, Feuchtinger M (2005) Gravity field recovery by analysis of short arcs of CHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observations with CHAMP – results from three years in orbit. Springer, Berlin Heidelberg New York, pp 25–30
Kargoll B (2005). Comparison of some robust parameter estimation techniques for outlier analysis applied to simulated GOCE mission data. In: Jekeli C, Bastos L, Fernandes J (eds) gravity, geoid and space missions. International Association of Geodesy Symposia 129. Springer, Berlin Heidelberg New York
Keller W (2004) Wavelets in geodesy and geodynamics. Walter de Gruyter Verlag, Berlin
Kern M, Allesch M (2003) GOCE DAPC Graz. WP Ia-3: pre-processing. Final Report, Phase Ia, Technical University of Graz
Kern M, Preimesberger T, Allesch M, Pail R, Bouman J, Koop R (2005) Outlier detection algorithms and their performance in GOCE gravity field processing. J Geod 78(9):509–519. DOI 10.1007/s00190-004-0419-9
Koch KR (1996) Robuste Parameterschaetzung. Allg Vermess Nachricht 103(1):1–18
Lemoine FG et al (1988) The development of the Joint NASA GSFC and National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA technical report, NASA/TP-1996\8-206861
Reigber C, Schmidt R, Flechtner F, König R, Meyer U, Neumayer KH, Schwintzer P, Zhu SY (2004) An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J Geodyn 39(1):1–10
Reigber C, Jochmann H, Wünsch J, Petrovic S, Schwintzer P, Barthelmes F, Neumayer KH, König R, Foerste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Perosanz F (2005) Earth gravity field and seasonal variability from CHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observations with CHAMP – results from three years in orbit. Springer, Berlin Heidelberg New York, pp 25–30
Reubelt T, Austen G, Grafarend EW (2003a) Harmonic analysis of the Earth’s gravitational field by means of semi-continuous ephemerides of a low Earth orbiting GPS-tracked satellite. Case study: CHAMP. J Geod 77(5–6):257–278. DOI 10.1007/s00190-003-0322-9
Reubelt T, Austen G, Grafarend EW (2003b) Space gravity spectroscopy – determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris; case studies on dynamic (CHAMP rapid science orbits) and kinematic orbits. Adv Geosci 1:127–135
Scales JA, Gersztenkorn A (1988) Robust methods in inverse theory. Inverse Probl 4:1071–1091
Schlossmacher EJ (1973) An iterative technique for absolute deviations curve fitting. J Am Stat Assoc 68:857–859
Schmidt M (2001) Grundprinzipien der Wavelet-Analyse und Anwendungen in der Geodäsie. Shaker Verlag, Aachen
Somogyi J, Zavoti J (1993) Robust estimation with iteratively reweighted least-squares method. Acta Geod Geoph Mont Hung 28(3–4):413–420
Švehla D, Rothacher M (2003) Kinematic and reduced-dynamic precise orbit determination of low Earth orbiters. Adv Geosci 1:47–56
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 6. ISSN:1029-7006
Xu P (1989) On robust estimation with correlated observations. Bull Géod 63:237–252
Xu P (2005) Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness. J Geod 79(1–3):146–159. DOI 10.1007/s00190-005-0454-1
Yang Y, Song L, Xu T (2002) Robust estimator for correlated observations based on bifactor equivalent weights. J Geod 76(6–7):353–358. DOI 10.1007/s00190-002-0256-7
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Götzelmann, M., Keller, W. & Reubelt, T. Gross Error Compensation for Gravity Field Analysis Based on Kinematic Orbit Data. J Geodesy 80, 184–198 (2006). https://doi.org/10.1007/s00190-006-0061-9
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DOI: https://doi.org/10.1007/s00190-006-0061-9