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.
Highlights
The gravimetric method is the technique most commonly used to precisely determine the local geoid
According to CHUNG (2008), the root mean square error (RMSE) could attain± 2.62 cm, ± 3.52 cm, and ± 2.62 cm by adopting the hyperbolic curve, 3power of distance, and squared distance methods, respectively
In this study, the RMSE was calculated for the same test region and fitting point conditions, using checkpoints that were not employed in model training
Summary
The gravimetric method is the technique most commonly used to precisely determine the local geoid. A gravimetric geoid model covering Taiwan was generated using gravity survey data, which are relatively difficult and timeconsuming to measure and often yield results that do not fit well with the local terrain. Gravimetric geoid results fit large rather than small areas. Because of the lack of gravity data in mountainous regions of Taiwan, this study was conducted to generate a regional geoid model that yields adequate accuracy regarding GPS-based leveling but does not require using a high-resolution gravimetric geoid model to evaluate a small area. After calculating the local geometric geoid heights at the points of interest, combining the GPS-derived ellipsoid heights and an accurate model provides a novel alternative method for determining orthometric height. A stand-alone geometrically derived geoid model must be constructed to transform the ellipsoid height h from the GPS to the orthometric height H in research or real-time situations
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