Local geoid height approximation and interpolation using moving least squares approach

Abstract

In this paper an introduction of the moving least squares approach is presented in the context of data approximation and interpolation problems in Geodesy. An application of this method is presented for geoid height approximation and interpolation using different polynomial basis functions for the approximant and interpolant, respectively, in a regular grid of geoid height data in the region 16.0417∘≤ϕ≤47.9583∘ and 36.0417∘≤λ≤69.9582∘, with increment 0.0833∘ in both latitudal and longitudal directions. The results of approximation and interpolation are then compared with the geoid height data from GPS-Levelling approach. Using the standard deviation of the difference of the results, it is shown that the planar interpolant, with reciprocal of distance as weight function, is the best choice in this local approximation and interpolation problem. keywords: Approximation and interpolation points, GPS-Levelling, Moving Least Squares, Geoid height, Grid points