Local geoid determination in strip area projects by using polynomials, least-squares collocation and radial basis functions

Abstract

Orthometric heights are used in many engineering projects. However, the heights determined by the widely-used Global Navigation Satellite System (GNSS) are ellipsoid heights. Leveling measurements conducted with the purpose of determining the orthometric heights on points are quite arduous and time-consuming processes. To be able to use ellipsoid heights in engineering projects, their transformation to orthometric heights defined in the height datum of the region is necessary. Therefore, in terms of convenience and feasibility GNSS/levelling method is preferred in determining geoid heights. This method is based on the principle of transformation of ellipsoid heights to orthometric heights. In effect, the main purpose of the method can also be regarded as the estimation of geoid undulation values for the study area.During the estimation process, polynomial (surface, curve) models are generally used. Polynomial models produce meaningful results for points which are scattered uniformly on the study area. However, for strip areas where the points scatter along a route (road etc. projects), the accuracy of the geoid heights obtained from these models is low. Therefore, different estimation techniques have to be implemented in strip areas instead of polynomial models. In this study, interpolation methods used in determining the geoid undulation of a strip area were researched and the identification of the best suitable method for the area was examined. For this purpose, geoid undulation values were calculated with the help of least-squares collocation (LSC) and radial basis functions such as Multiquadric (MQ), Thin Plate Spline (TPS) along with polynomial models, and results were presented. According to the results, it was observed that TPS, MQ, LSC methods respectively yield better results compared to polynomial methods.