Abstract
The determination of the orthometric height from geometric leveling has practical difficulties that, despite a number of scientific and technological advances, passed a century without substantial modifications or advances. Currently, the Global Navigation Satellite System (GNSS) has been used with reasonable success for orthometric height determination. With a sufficient number of benchmarks with known horizontal and vertical coordinates, it is often possible to adjust using the least squares method mathematical expressions that allow interpolation of geoid heights. The objective of this study is to present an alternative method to interpolate geoid heights based on the technique of Artificial Neural Networks (ANNs). The study area is the Brazilian state of São Paulo, and for training the ANN the authors have used geoid height information from the EGM08 gravity model with a grid spacing of 10 minutes of arc. The efficiency of the model was tested at 157 points with known geoid heights distributed across the study area. The results were also compared with the Brazilian Geoid Model (MAPGEO2004). Based on those 157 benchmarks it was possible to verify that the model generated by ANNs provided a mean absolute error of 0.24 m in obtaining a geoid height value. Statistical tests have shown that there was no difference between the means from known geoid heights and geoid heights provided by the neural model for a significance level of 5%. It was also found that ANNs provided an improvement of 2.7 times in geoid height estimates when compared with the MAPGEO2004 geoid model.
Highlights
Artificial Neural Networks (ANNs) are clusters of processing units interconnected and structured, whose operation is analogous to a neural structure from intelligent organisms [1]
The operation of ANNs is inspired by the human brain [2]; though ANNs have been used successfully in a variety of different application areas
For [1], the major advantage of ANNs over conventional methods is that there is no need to know the intrinsic theory of the problem, nor the necessity to analyze the relationships that are not fully known among the variables involved in modeling
Summary
Artificial Neural Networks (ANNs) are clusters of processing units (known as neurons or nodes) interconnected and structured, whose operation is analogous to a neural structure from intelligent organisms [1]. ANNs derive their computing power from their distributed massively parallel structure and their ability to learn and generalize, making possible the resolution of complex problems in different knowledge areas [2]. For [1], the major advantage of ANNs over conventional methods is that there is no need to know the intrinsic theory of the problem, nor the necessity to analyze the relationships that are not fully known among the variables involved in modeling. ANNs have been used to model complex phenomena involving variables difficult to obtain. Some ANN applications involve obtainable variables for the solution of problems, but which are usually difficult to solve using conventional mathematical methods. In the case of GPS, for example, a neural model to estimate the L1 and L2 carrier waves using as input information pseudorange data from the RBMC (Brazilian Network for Continuous Monitoring) was proposed [21]; and ANNs have been used to estimate the value of TEC (Total Electron Content) using data from continuous monitoring GPS stations [22]
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