顾及距离的最小叉熵克里金负权系数改正  

Correction of Kriging negative-weight based on minimum cross-entropy for considering distance

作　　者：杨卫聪 陈天伟 欧阳心如 YANG Weicong;CHEN Tianwei;OUYANG Xinru(College of Geomatics and Geoinformation,Guilin University of Technology,Guilin 541006,China)

机构地区：[1]桂林理工大学测绘地理信息学院,广西桂林541006

出　　处：《海洋测绘》2024年第2期78-82,共5页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(41861050);广西省自然科学基金(2017GXNSFAA198308)。

摘　　要：针对克里金法在解算权系数时存在负值现象的问题,提出一种基于克里金负权系数改正的克里金改进方法。该方法考虑到参考点间的空间相关性和结构性,首先通过距离加权解算出主观权系数,然后通过叉熵最小化解算出客观权系数,最后结合主、客观权系数得到改正权系数。用日喀则市、上饶市和长春市三块实验区域内的格网高程数据对本文方法进行有效性验证。结果表明:该方法消除了负权系数,权系数的大小与参考点的点位相适应。在实验区域内本文方法的插值精度和成图效果优于克里金法和反距离加权法,平均绝对误差分别可达到0.1161m,0.4893m和0.0132m。因此,研究方法可为插值权系数的改正提供有益参考。A modified method is proposed to address the issue of negative-weight in the Kriging.This method takes into account the spatial correlation and structure between reference points.Firstly,the subjective weight is calculated through distance weighting.Then the objective weight is calculated through cross-entropy minimization.Finally,the correction weight is obtained by combining the subjective and objective weight.The validity of the method is verified by grid elevation data of three experimental areas including Shigatse,Shangrao and Changchun.The results show that the method eliminates the negative-weight,and the weight is adapted to the position of the reference point.In the experimental areas,the interpolation accuracy and mapping effect of the method are better than that of the Kriging algorithm and the inverse distance weighted algorithm,with the mean absolute error of 0.1161 m,0.4893 m and 0.0132 m respectively.Therefore,this method can provide useful reference for the correction of interpolation weight.

关 键 词：数字高程模型 负权系数改正 最小叉熵 克里金法 反距离加权法 格网高程数据 

分 类 号：P208.1[天文地球—地图制图学与地理信息工程]