Generalized Inverse Distance Weighting Methodfor Spatial Interpolation
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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。Abstract: We propose a generalized inverse distance weighting method after discussing theproperties of the Taylor series expansion of the traditional inverse distance weighting func-tion.Our generalized inverse distance weighting method is established by a set of virtual ob-servation equations from the Taylor Series expansion of the spatial function.The probabilitymeasure,defined by the variance-covariance matrix,and the k-order partial derivatives esti-mation,is used to determine the weights for virtual observations.In order to optimally de-termine the parameter dimensions for the model,the criteria of BIC is introduced.The appli-cable conditions for the traditional inverse distance weighting average method are obtainedfrom the first-order generalized inverse distance weighting average method.At last,the pro-posed generalized method is applied to a GPS leveling fitting problem to verify the proposedmethod.
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