Locally Homogeneous and Isotropic Gaussian Fields in Kriging

Abstract

The paper deals with the application of the theory of locally homogeneous and isotropic Gaussian fields (LHIGF) to probabilistic modelling of multivariate data structures. An asymptotic model is also studied, when the correlation function parameter of the Gaussian field tends to infinity. The kriging procedure is developed which presents a simple extrapolator by means of a matrix of degrees of the distances between pairs of the points of measurement. The resulting model is rather simple and can be defined only by the mean and variance parameters, efficiently evaluated by maximal likelihood method. The results of application of the extrapolation method developed for two analytically computed surfaces and estimation of the position of the spacecraft re-entering the atmosphere are given.