ANALYTICAL INTERPRETATION TO KRIGING ESTIMATION AND ALGEBRAIC DETERMINATION OF COVARIANCE FUNCTION'S PARAMETER

The analytical interpretation to Kriging estimation and the algebraic determination of a covariance function's parameter are presented. This paper first introduces the concept of function approximation using a rotating surface as a basic function. Then it is demonstrated that the universal Kriging may be expressed as the traditional weighted least square fitting and as the function approximation with a rotating surface as a basic function. It is also demonstrated that the parameter of a covariance function (i.e. a rotating surface) can be determined by the mathematical analysis on a certain condition (i.e. a highly continuous lump goldree effect in a random field). Finally, this paper presents two principles for the determination of a covariance function's parameter with the Gaussian function as an example: one is formulated through analysis of the linear combinations of the shifted Gaussian functions, and the other is derived from the equivalence between Bplines and Gaussian functions.