Determination of geoid surface by Artificial Neural Networks

Abstract

The height obtained by the GNSS (Global Navigation Satellite System) is merely mathematical. In most works the height should refer to the Geoid. With a sufficient number of Level References, it is almost always adjusted polynomials that allow the interpolation of geoidal undulations. Nevertheless, these polynomials are inefficient to extrapolate data that are not in the study area. The aim of this study is to present a new method to model the surface of a local Geoid based on the technique of Artificial Neural Networks. The study area is the metropolitan region of São Paulo, Brazil, and undulations data from the MAPGEO program were used for the neural network training. The program was developed by the Brazilian Institute of Geography and Statistics (IBGE) with an absolute error upper to 0.5 m. Even with such a big error, the data provided by MAPGEO2004 may be used in the training of a neural network due to its tolerance to errors and noises. The efficiency of the model was tested in 21 points with known undulations. In these points the model shows, by calculated discrepancies, a Root Mean Square error of 0.100 m. The study demonstrates that the method can be an alternative in modeling local and/or regional Geoid.

Key words: GPS, Artificial Neural Networks, geoidal undulation, MAPGEO, São Paulo, Brazil.