Using a least squares support vector machine to estimate a local geometric geoid model

Abstract

In this study, test-region global positioning system (GPS) control points exhibiting known first-order orthometric heights were employed to obtain the points of plane coordinates and ellipsoidal heights by using the real-time GPS kinematic measurement method. Plane-fitting, second-order curve-surface fitting, back-propagation (BP) neural networks, and least-squares support vector machine (LS-SVM) calculation methods were employed. The study includes a discussion on data integrity and localization, changing reference-point quantities and distributions to obtain an optimal solution. Furthermore, the LS-SVM was combined with local geoidal-undulation models that were established by researching and analyzing3 kernel functions. The results indicated that the overall precision of the local geometric geoidal-undulation values calculated using the radial basis function (RBF) and third-order polynomial kernel function was optimal and the root mean square error (RMSE) was approximately ± 1.5 cm. These findings demonstrated that the LS-SVM provides a rapid and practical method for determining orthometric heights and should serve as a valuable academic reference regarding local geoid models.