Kriging Interpolation Toolbox

The Kriging Interpolation Toolbox is a spatial interpolation tool based on geostatistical principles, primarily used for processing data with spatial autocorrelation. The Kriging interpolation method originated in mineral exploration, proposed by South African geologist Danie G. Krige and later refined by French mathematician Georges Matheron.

The toolbox analyzes spatial distribution patterns of sample points to effectively predict values at unknown locations while providing corresponding prediction error estimates. Unlike traditional interpolation methods, Kriging considers both distance relationships between sample points and quantifies spatial structure characteristics through variogram modeling, delivering more accurate interpolation results.

In practical implementations, the Kriging Interpolation Toolbox typically includes these core computational components:

Data Exploration and Preprocessing: Performs statistical analysis on input data, examines spatial distribution characteristics, and ensures data meets Kriging's fundamental assumptions through normality tests and trend removal algorithms.

Variogram Modeling: Fits experimental variograms and selects appropriate theoretical models (spherical, exponential, or Gaussian) using optimization algorithms like weighted least squares to characterize spatial correlation structures.

Interpolation Computation: Implements various Kriging algorithms (ordinary, simple, or universal Kriging) that solve systems of linear equations based on variogram models and sample data to generate prediction surfaces with error variance estimates.

Validation and Optimization: Employs cross-validation techniques to assess prediction accuracy and utilizes parameter tuning methods to optimize model performance through iterative refinement of variogram parameters.

The toolbox finds extensive applications in geological exploration, environmental science, agriculture, and meteorology, particularly for datasets with spatial heterogeneity. Through proper utilization of its computational functions, users can efficiently complete spatial data analysis tasks and obtain reliable predictions with quantified uncertainty measures.