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

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(mN3)O(mN3). 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(N2+mN)O(N2+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.

► We propose a fast estimate for the Kriging correlation range.
► We compare this estimate to results from a conventional MLE.
► We apply this estimate to uniformly as well as randomly sampled data.
► We apply this approach to three large data sets.