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The A-optimal regularization parameter in uniform Tykhonov-Phillips regularization — α-weighted BLE-

  • Conference paper
V Hotine-Marussi Symposium on Mathematical Geodesy

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 127))

Abstract

Numerical tests have documented that the estimate \(\hat \xi \) of type BLUUE of the parameter vector ξ within a linear Gauss-Markov model {Aξ=E{y}, Σ y = D{y}} is not robust against outliers in the stochastic observation vector y. It is for this reason that we give up the postulate of unbiasedness, but keeping the set-up of a linear estimation \(\hat \xi = Ly\) of homogeneous type. Grafarend and Schaffrin (1993) as well as Schaffrin (2000) have systematically derived the best linear estimators of type homBLE (Best homogeneously Linear Estimation), S-homBLE and α-homBLE of the fixed effects ξ, which turn out to enhance the best linear uniformly unbiased estimator of type BLUUE, but suffer from the effect being biased. Here the regularization parameter in uniform Tykhonov-Phillips regularization (α-weighted BLE) is determined by minimizing the trace of the Mean Square Error matrix MSE α,s {\(\hat \xi \)} (A-optimal design) in the general case. In lieu of a case study, both model and estimators are tested and analyzed with numerical results computed from simulated direct observations of a random tensor of type strain rate.

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Author information

Authors and Affiliations

  1. Department of Geodesy and GeoInformatics, University of Stuttgart, Geschwister-Scholl-Str. 24, D-70174, Stuttgart, Germany

    Jianqing Cai & Erik W. Grafarend

  2. Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, Ohio, USA

    Burkhard Schaffrin

Authors
  1. Jianqing Cai
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  2. Erik W. Grafarend
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  3. Burkhard Schaffrin
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Editors and Affiliations

  1. Polytechnic of Milan, D.I.I.A.R. — Surveying Section, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy

    Fernando Sansò

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Cai, J., Grafarend, E.W., Schaffrin, B. (2004). The A-optimal regularization parameter in uniform Tykhonov-Phillips regularization — α-weighted BLE-. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_41

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  • DOI: https://doi.org/10.1007/978-3-662-10735-5_41

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