Estimativa de alturas geoidais para o estado de São Paulo baseada em redes neurais artificiais

Abstract

ABSTRACT. The information of height provided by the GNSS (Global Navigation Satellite System) is purely geometrical, and in most engineering papers, the height must be referenced to the geoid. Provided we have a sufficient number of Bench Marks (BMs) with known horizontal and vertical coordinates, it is nearly always possible to adjust mathematical expressions that allow for the interpolation of geoidal heights. The aim of this paper is to evaluate the efficiency of Artificial Neural Network (ANN) in the process of predicting geoidal heights, having the State of São Paulo as the area of study. The information used is based on a set of 157 BMs, evenly distributed all across the State. The horizontal coordinates (latitude and longitude) and the vertical coordinates (geometrical, orthometrical and geoidal heights) of these BMs are known. From the 157 BMs, 115 were used for the training of RNA and 42 in the process of simulation to assess the efficiency of the model proposed. Efficiency is based in determining the discrepancies (error) between known geoidal heights and those which were obtained by the neural model. As a contribution to this research, we have compared the values simulated with the Earth Gravitational Model 2008 (EGM2008) and with the MAPGEO2004 as well. In terms of results, the RNA produced a mean absolute error of 0.19 m ± 0.14 m and a strong correlation (R 2 = 0.9871) with the values taken as true. Statistically, the tests showed that there was no difference between known geoidal heights and those which were provided by the neural model for a level of significance of 5%. When we compare these results with the EGM2008 and MAPGEO2004, the RNA has an error reduction of 0.07 and 0.44 m, respectively. Keywords: GPS, MAPGEO2004, EGM2008, artificial neural networks, geoidal height. RESUMO.A informação da altitude fornecida pelo sistema GNSS (Global Navigation Satellite System )é puramente geométrica, e na maioria dos trabalhos de engenharia a altitude deve estar referenciada ao geóide. Com um número suficiente de Referências de nível (Rn's) com coordenadas horizontais e verticais conhecidas, quase sempre,é possível ajustar-se, pelo Método dos Mínimos Quadrados, expressões matemáticas que permitem interpolar as alturas geoidais. O objetivo deste trabalho foi avaliar a eficiência das Redes Neurais Artificiais (RNAs) no processo de predição de alturas geoidais tendo comoárea de estudo o Estado de São Paulo. As informações utilizadas basearam-se em um conjunto de 157 Referências de nível (Rn's) distribuídas uniformemente em todo Estado. Para estas Rn's são conhecidas suas coordenadas horizontais (latitude e longitude) e verticais (altitudes geométrica e ortométrica e altura geoidal). Das 157 Rn's, 115 foram utilizadas para o treinamento da RNA e 42 no processo de simulação para avaliar a eficiência do modelo proposto. A eficiência baseou-se em determinar as discrepâncias (erro) entres as alturas geoidais conhecidas e as obtidas pelo modelo neural. Como contribuição da pesquisa comparou-se também os valores...

Regional Mapping of the Geoid Using GNSS (GPS) Measurements and an Artificial Neural Network

“…However, when an analysis is made of the differences between the known geoid heights and the ones obtained by MAPGEO2004 it can be seen that the Sum of Squared Differences (SQR) has increased compared to the model of the ANNs. This fact can be explained because MAPGEO2004 has been found to have a systematic error in all Brazilian regions [8,26,31]. This fact can also be confirmed from the linear regression plot in Figure 9.…”

“…In general, the best results were obtained with the values normalized between [0;1] and consequently with the logistic sigmoid activation function (Equation (3)) that assumes values between 0 and 1. The sigmoid activation function is the most commonly employed in geoid modeling studies [8,26,29,31], and is usually associated with training algorithms of the back-propagation type [8].…”

“…Training by Levenberg-Marquardt results in the network being slower to perform more calculations, but with a reduction in the number of iterations [8,26,31].…”