Application of Robust Estimation in Polynomial Modelling

Polynomials are often used as a reference surface in modelling. In geodesy they are used to approximate geoid/quasi-geoid shape or to transform height datum especially for relatively small areas and if considered surface is regular, i.e. there are no local anomalies. When amount of points is greater than number of polynomial terms, surface modelling requires adjustment and accuracy analysis of obtained results. Besides the ordinary least squares adjustment, calculations can be carried out with the use of several methods based on robust estimation, e.g. Huber, Hampel, Danish, Ga?dzicki and other methods. The aim of the research was to indicate best method to determine best-fitted polynomial to geodetic network. The analyses were performed, based on Polish state geodetic height network for 9 areas, about 1200 km2 each. The set of points was numerically prepared and intentionally "contaminated" with a several inaccurate (outlying) values of the points.