广义反距离加权空间推估法  

Generalized Inverse Distance Weighting Method for Spatial Interpolation

作　　者：薛树强[1,2] 杨元喜[3,4] 

机构地区：[1]长安大学地质工程与测绘学院,西安市雁塔路126号710054 [2]中国测绘科学研究院,北京市莲花池西路28号100830 [3]国家地理信息工程国家重点实验室,西安市雁塔路中段1号710054 [4]西安测绘研究所,西安市雁塔路中段1号710054

出　　处：《武汉大学学报（信息科学版）》2013年第12期1435-1439,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41020144004;41104018);国家863计划资助项目(2009AA121405);总装备部航天装备总体研究发展中心资助项目(GFZX0301040309)

摘　　要：提出了k阶广义反距离加权空间推估法。首先,估计空间函数在已知点处的各阶偏导数;然后,利用泰勒级数逼近原理计算待估点处的函数值,根据空间函数偏导数估值的方差协方差评价推估精度;最后,对待估点处的这些推估值进行最小二乘平差。引入了确定k阶广义反距离加权空间推估法阶次k的BIC准则,并以GPS水准推估为例进行了实验。We propose a generalized inverse distance weighting method after discussing the properties of the Taylor series expansion of the traditional inverse distance weighting function. Our generalized inverse distance weighting method is established by a set of virtual observation equations from the Taylor Series expansion of the spatial function. The probability measure, defined by the variance-covariance matrix, and the h-order partial derivatives estimation, is used to determine the weights for virtual observations. In order to optimally determine the parameter dimensions for the model, the criteria of BIC is introduced. The applicable conditions for the traditional inverse distance weighting average method are obtained from the first-order generalized inverse distance weighting average method. At last, the proposed generalized method is applied to a GPS leveling fitting problem to verify the proposed method.

关 键 词：空间推估 反距离加权 泰勒级数 概率测度 GPS水准拟合 

分 类 号：P207.1[天文地球—测绘科学与技术] P208