A new method for obtaining geoidal undulations through Artificial Neural Networks

Maurício Roberto Veronez 1, Adriane Brill Thum 1 and Genival Côrrea de Souza 2
1 Graduate Program in Geology - Vale do Rio dos Sinos University
Avenida Unisinos, 950, São Leopoldo/RS, Brazil – CEP: 93022-000
Tel.: + 55 (51) 3591-1100 – Ramal 1769; Fax: + 55 (51) 3590-8177
veronez@unisinos.br
2 Graduate Program in Civil and Environmental Engineering. Feira de Santana State University
Feira de Santana/BA Brazil. Br 116 - Km 03 , Campus Universitário – CEP:44031-460 
Tel.: +55(75)3224-8240; Fax: +55(75)3224-8056

Abstract
The height supplied by the GPS system is merely mathematics. In most studies the height shall be referred to the Geoid. With a sufficient number of Level References with known horizontal and vertical coordinates, it is almost always adjusted by polynomials of Least Squares Method that allow the interpolation of geoidal undulations. These polynomials  are inefficient when extrapolating the data outside the  study area. Thus the aim of this work is to present a new method for modeling the surface of Local Geoid based on the technique of Artificial Neural Networks. The study area is the Hydrological Basin of Rio dos Sinos which is located in Rio Grande do Sul State – Brazil and for the training of the neural network undulations data supplied by the MAPGEO2004 program was used. The program was developed by the Instituto Brasileiro de Geografia e Estatística (Brazilian Institute of Geography and Statistics) with an absolute error band bigger than 0.5 meter. Even with such a big error, the data supplied by MAPGEO2004 can be used in the training of a neural network, because it is tolerant to errors and noises. The efficiency of  the model was tested in 8 points with known undulations and distributed throughout the study area. On these points the model has presented, through calculated discrepancies, a root mean square error of 0.170 meter, approximately. The study shows that this method can be an alternative in modeling local and/or regional Geoid.

Keywords: GPS, artificial neural networks, geoidal undulation, MAPGEO2004

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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