Kriging Interpolation With Neighborhood Constraints

Kriging interpolation method,as a representative algorithm of geostatistics,is a regression algorithm for spatial modeling and interpolation of random field according to covariance function.It can realize the optimal interpolation of spatial autocovariance and is widely used in many fields.Kriging interpolation method is a prediction algorithm for limited areas.In actual interpolation,it is necessary to select appropriate neighborhood for each point to be interpolated as an effective calculation area.However,when using neighborhood for regional fitting,due to the differences in the spatial distribution laws of different local regions,the step problem of discontinuous attribute values of interpolation results will appear when the selection of neighborhood is unreasonable.In addition,Kriging interpolation is a geostatistical algorithm based on random field hypothesis,which may lead to the problem that the attribute value of the interpolation result is out of bounds.When the attribute value of the research object has strict range constraints,this out of bounds is not allowed.Aiming at the above problems of Kriging interpolation method,this paper carries out the research in the following two aspects:(1)Aiming at the attribute value step problem caused by unreasonable selection of neighborhood in the process of Kriging interpolation,a Kriging interpolation neighborhood selection method reflecting the proximity and directionality of natural attribute distribution is proposed,so that the neighborhood points can better fit the local region.(2)Aiming at the possible out of bounds problem of attribute value in Kriging interpolation results,a method of auxiliary sampling point generation based on the influence domain of sampling points is proposed,and then Kriging interpolation in the specified attribute value domain is realized through sampling points and auxiliary sampling points.Experiments show that the neighborhood constrained Kriging interpolation method proposed in this paper can obtain a more reasonable neighborhood distribution in the interpolation process,realize the effective constraint of the value range of interpolation results,and improve the effect and accuracy of Kriging interpolation method.