Speeding up Kriging through fast estimation of the hyperparameters in the frequency-domain

  • Authors:

  • J. H. S. De Baar;R. P. Dwight;H. Bijl

  • Affiliations:

  • TU Delft, Department of Aerodynamics, Kluyverweg 2, 2629 HT Delft, The Netherlands;TU Delft, Department of Aerodynamics, Kluyverweg 2, 2629 HT Delft, The Netherlands;TU Delft, Department of Aerodynamics, Kluyverweg 2, 2629 HT Delft, The Netherlands

  • Venue:
  • Computers & Geosciences
  • Year:
  • 2013

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Abstract

Kriging is a widely applied data assimilation technique. The computational cost of a conventional Kriging analysis of N data points is dominated by the m iterations of the maximum likelihood estimate (MLE) optimization, resulting in a computational cost of O(mN^3). We propose two fast methods for estimating the hyperparameters in the frequency domain: frequency-domain maximum likelihood estimate (FMLE) and frequency-domain sample variogram (FSV), both of which reduce the cost of the optimization to O(N^2+mN) in the case of a regular Fourier transform (FT), and to O(NlnN+mN) in the case of a fast Fourier transform (FFT). In addition to this speed up, problems concerning positive definiteness of the gain matrix - which limit the robustness of the conventional approach - vanish in the proposed methods.