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 ( 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(N2+mN) 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.
kriging fast hyperparameter fmle fsv nufft