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.
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.
Keywords
Least Squares Support Vector Machine (LS-SVM); Kernel Function, Local Geoid Model
