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 ( 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 ( N ln N + 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.