广义反距离加权空间推估法

Generalized Inverse Distance Weighting Method for Spatial Interpolation

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.