Kriging Interpolation Program and Inverse Distance Weighting Interpolation with Nearest Neighbors Program

The document discusses two distinct interpolation programs: a MATLAB-based Kriging interpolation implementation and an inverse distance weighting method utilizing nearest neighbor points. Kriging interpolation employs a geostatistical approach that models spatial correlation through variogram analysis, where the 'krig' function in MATLAB typically handles covariance structure estimation and optimal weight calculation for unbiased predictions. This method excels in quantifying uncertainty through variance estimation but requires careful variogram modeling. The inverse distance weighting algorithm calculates interpolated values by averaging neighboring points weighted by the inverse of their distances (often using power parameters like IDW^p). The MATLAB implementation generally involves distance matrix computation using 'pdist2' or similar functions, followed by weight normalization. While computationally efficient, this method may exhibit bull's-eye effects around data points. Both techniques serve distinct purposes in spatial estimation: Kriging provides statistically optimal predictions with error quantification, whereas inverse distance weighting offers straightforward implementation for rapid approximations. These tools are fundamental in geostatistical analysis for processing spatially correlated data in fields like environmental monitoring and resource mapping.