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Correction of Gravimetric Geoid Using Symbolic Regression

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Joseph Awange
Organization: Curtin University of Technology
Department: Spatial Sciences, Division of Resource and Environmental
Lajos Völgyesi
Organization: Budapest University of Technology and Economics
Department: Department of Geodesy and Surveying
Journal / Anthology

Mathematical Geosciences
Year: 2015
Volume: 47
Issue: 7
Page range: 867-883

In this study, the problem of geoid correction based on GPS ellipsoidal height measurements is solved via symbolic regression (SR). In this case, when the quality of the approximation is overriding, SR employing Keijzer expansion to generate initial trial function population can supersede traditional techniques, such as parametric models and soft computingmodels (e.g., artificial neural network approach with different activation functions). To demonstrate these features, numerical computations for correction of the Hungarian geoid have been carried out using the DataModeler package of Mathematica. Although the proposed SR method could reduce the average error to a level of 1–2 cm, it has two handicaps. The first one is the required high computation power, which can be eased by the employment of parallel computation via multicore processor. The second one is the proper selection of the initial population of the trial functions. This problem may be solved via intelligent generation technique of this population (e.g., Keijzer-expansion).

*Science > Geology and Geophysics