Enfoques de Aprendizaje Automático para Predecir las Ondulaciones del Geoide y Mejorar la Determinación de Alturas Ortométricas en Regiones con Escasez de Datos

Résumé

This study investigates the use of machine learning algorithms for geoid undulation modelling in data-sparse environments, using Ibadan, Nigeria as a case study. A total of 207 control points were utilized, with 70% allocated for training and 30% for testing. Six algorithms were assessed: Multiple Linear Regression (MLR), Random Forest (RF), Gradient Boosted Regression (GBR), Decision Tree (DT), Support Vector Regression (SVR), and K-Nearest Neighbors (KNN). Model evaluation was conducted using root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²), and 5-fold cross-validation to ensure robustness. Among the models tested, GBR and SVR yielded superior performance. The GBR model achieved a test RMSE of 0.047 m with an R² of 0.9785, whereas the SVR model demonstrated a lower test RMSE of 0.026 m and a higher R² of 0.9934. Cross-validation results were consistent, with GBR yielding an RMSE of 0.043 m and R² of 0.9828, compared to SVR’s RMSE of 0.056 m and R² of 0.9719. These results highlight the strong generalization ability and practical applicability of both models. Additionally, the GBR model was applied to derive orthometric heights from GNSS-based ellipsoidal heights, and the output was validated against GNSS-derived orthometric heights, yielding an RMSE of 0.047 m. The study concludes that machine learning, particularly GBR and SVR, provides an effective complementary approach for geoid prediction and vertical height transformation in regions with limited access to gravimetric data, with important implications for geodetic infrastructure development, surveying, and vertical referencing improvement in developing regions.

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