Inverse Distance Weighting (IDW) Spatial Interpolation

Inverse Distance Weighting (IDW) is a widely used spatial interpolation method extensively applied in spatial data analysis, particularly valuable in fields such as Geographic Information Systems (GIS), meteorology, and environmental science. The method operates on an intuitive assumption: the value at an unknown point is influenced by neighboring known points, with this influence diminishing as distance increases.

The core concept of IDW involves assigning weights to each known sample point based on the inverse of its distance to the interpolation target point. Closer points receive higher weights, thus exerting greater influence on the interpolation result. The estimated value for the target point is obtained by calculating the weighted average of all neighboring points.

When implementing IDW interpolation in MATLAB, key steps typically include: First, identifying neighboring points around the target interpolation point (constrained by search radius or k-nearest neighbors parameters). Second, computing Euclidean distances between each neighbor and the target point using vectorized operations like pdist2. Finally, applying normalization through weight formulas and calculating weighted averages, often implemented via matrix operations for efficiency.

The method's advantages lie in computational simplicity and ease of interpretation, performing well with uniformly distributed data. However, note that IDW is sensitive to power parameter selection (controlling weight decay rate) and may exhibit "bull's-eye effects" with sparse or unevenly distributed data. Optimization strategies include adaptive power parameter adjustment or hybrid approaches combining other spatial statistics methods.

MATLAB-based implementations can be extended with functionalities such as multi-dimensional data interpolation, parallel computing acceleration using parfor loops, and integration with visualization tools like scatter3 or contourf for intuitive result display.