摘要：A spatial data interpolation algorithm is a method to transform scattered and sparse measurement data into regular and continuous applicable data. This algorithm can make the display results smooth and continuous without changing the data characteristics, which is closer to the real acquisition object. In response to the low interpolation accuracy of the inverse distance weighting (IDW) algorithm and the poor interpolation efficiency of the ordinary kriging (OK) algorithm, this study proposes a variational-weighted (VW) interpolation algorithm based on data fixed-frame sampling. By introducing the variational function of OK into IDW and taking different weight coefficients from OK, a new computational model is constructed to improve the interpolation accuracy and adapt to different types of data characteristics. In the whole interpolation process, the data are sampled in a fixed frame and a new sampling point search method is proposed to improve the computational efficiency. The study not only compares the accuracy and efficiency of the algorithm using two types of data but also tests the stability of the new algorithm for different data volumes. It is shown that VW based on a fixed-grid sampling of the data is more accurate than the inverse distance interpolation algorithm for both data types. The VW interpolation algorithm based on data lattice sampling improves the computational efficiency for featureless data and exhibits better performance in terms of accuracy and computational efficiency for data with features, compared to the common kriging interpolation algorithm. In addition, the VW interpolation algorithm based on a fixed-grid sampling of data has a more stable performance for different amounts of data.
