泛协Kriging的数学模型

Due to its complexities in both mathematicM formulations and applications, universal co-kriging （UCK） has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporation of a polynomial variable trend is proposed in this paper. Estimators of the value and expectation of a regionMized vector taken in a point are obtained on the basis of cross-covaxiance and cross-vaxiogram, respectively. The complex expressions of co-kriging with trend are greatly simplified by introducing special matrix operations, such as Kronecker product, into the formulations. This simplification offers a feasible and easier approach for computer coding of the UCK, and helps the practitioners to use the UCK technique conveniently in real cases.

On the Mathematical Model of Universal Co-kriging

Due to its complexities in both mathematical formulations and applications, universal co-kriging (UCK) has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporation of a polynomial variable trend is proposed in this paper. Estimators of the value and expectation of a regionalized vector taken in a point are obtained on the basis of cross-covariance and cross-variogram, respectively. The complex expressions of co-kriging with trend are greatly simplified by introducing special matrix operations, such as Kronecker product, into the formulations. This simplification offers a feasible and easier approach for computer coding of the UCK, and helps the practitioners to use the UCK technique conveniently in real cases.