反距离加权插值函数性质及最优插值条件  

Applicable conditions to spatial interpolation of inverse distance weighting average

作　　者：薛树强[1] 杨文龙 李保金 XUE Shuqiang;YANG Wenlong;LI Baojin(Chinese Academy of Surveying and Mapping,Beijing 100036,China)

机构地区：[1]中国测绘科学研究院,北京100036

出　　处：《测绘科学》2022年第10期1-7,65,共8页Science of Surveying and Mapping

基　　金：国家重点研发计划项目(2020YFB0505802)

摘　　要：针对反距离加权插值存在的“牛眼”问题,该文研究了反距离加权插值函数的微分性质及适用条件,给出了反距离加权插值的已知点最佳分布条件。反距离加权插值要求空间函数无趋势性信号,而对称设计和均匀设计是抵偿系统误差、提高反距离加权插值精度的重要途径。该文利用反距离加权插值方法对5 m分辨率数字高程模型(DEM)和海洋温度进行插值,结果表明,基于最佳控制点构型条件可提高插值精度,在保证插值控制点构型对称的前提下,选取尽量小的窗口进行插值,能获得较高的插值精度。Aiming at the“bull’s eye”problem of inverse distance weighted interpolation,the differential properties and applicable conditions of inverse distance weighted interpolation function were studied in this paper,and the optimal distribution conditions of known points of inverse distance weighted interpolation were given.Inverse distance weighted interpolation requires that the spatial function has no trend signal,and symmetric design and uniform design are important ways to compensate for the systematic error and improve the accuracy of inverse distance weighted interpolation.The inverse distance weighted interpolation method was used to interpolate the 5-meter resolution digital elevation model(DEM)and ocean temperature.The results showed that the interpolation accuracy could be improved based on the optimal control point configuration conditions.On the premise of ensuring the symmetry of the interpolation control point configuration,selecting the smallest window for interpolation could obtain higher interpolation accuracy.

关 键 词：空间推估 反距离加权 泰勒级数 最佳构型 DEM插值 

分 类 号：P207[天文地球—测绘科学与技术]