Kriging Interpolation Source Code

Kriging interpolation is a spatial interpolation method based on geostatistics, widely used in geographic information systems, environmental science, and mining engineering. This method optimizes prediction results by accounting for spatial autocorrelation, making it particularly suitable for processing data with spatial continuity.

In the MATLAB environment, EasyKrig 3.0 is a commonly used Kriging interpolation toolkit that provides user-friendly interfaces for implementing variants such as Ordinary Kriging, Simple Kriging, and Universal Kriging. The core algorithm logic can be divided into the following implementation steps:

Variogram Modeling: The first step involves calculating the semi-variogram from sample points and fitting a theoretical model (such as spherical, exponential, or Gaussian models) to quantify spatial correlation. In code implementation, this typically uses optimization algorithms to minimize the difference between empirical and theoretical variograms.

Weight Matrix Construction: Through the Kriging equation system, combined with the variogram model, the optimal weights for known sample points around the prediction location are calculated to ensure unbiased estimates with minimum variance. This involves solving a linear system where the covariance matrix is constructed based on the fitted variogram model.

Interpolation Execution: The prediction values are generated using linear combinations of known points with the calculated weights, while simultaneously providing variance estimates for prediction errors. The implementation typically involves vectorized operations for efficient computation across multiple prediction points.

The advantage of EasyKrig 3.0 lies in its simplified parameter configuration process, featuring automatic optimization of variogram parameters and support for cross-validation to assess interpolation accuracy. For users requiring greater flexibility, the source code can be modified to adjust interpolation strategies or integrate custom variogram models through MATLAB's object-oriented programming capabilities.

Note: Practical applications must ensure input data satisfies Kriging assumptions (such as stationarity), otherwise data transformation or alternative interpolation methods may be required. The code includes diagnostic functions to check these assumptions before performing interpolation.