Correction of Gravimetric Geoid Using Symbolic Regression

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 computing models (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).