Generalized Inverse Distance Weighting Methodfor Spatial Interpolation

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.