Template-based smoothing functions for data smoothing in Geodesy

Abstract This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid. The method employed here is the local L 2 − semi-norm minimization, through Euler-Lagrange method, for the Beltrami operator. The method results in a weighted average of the surrounding points in a template based on the first order Taylor expansion of the unknown function under consideration. The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran, derived from the EGM2008 geopotential model.