Investigation of the methods used to derive indirectly orthometric height from GPS measurements

The widespread use of GPS in today's engineering applications and the ability to measure the ellipsoidal heights acquired via GPS easier, faster and more economically compared to levelling brought the necessity to transform the ellipsoidal heights to orthometric heights. The Large Scale Map and Map Information Production Regulation (LSMMIPR) offer various suggestions regarding the measurement and calculation methods to carry out this transformation. One of the suggested approaches is calculating the geoid model using the GPS measurements at the points in a local area of known orthometric heights and then providing the solution for the height transformation problem. In this study, local GPS/levelling geoids were formed in three different test areas for different point distributions using the polynomials, radial basis functions and flexible calculation methods and the performance of these methods were assessed. The importance level of reference point density in determining the local GPS/Nivelman geoid was examined in the studied areas (Rize, Kayseri and Karaman) by selecting different point densities: a) an reference point per each 2.5 km2, b) the minimum number of reference points according to LSMMIPR and c) an reference point per each 20 km2. Polynomials, radial basis functions, artificial neural networks and adaptive network based fuzzy inference system (ANFIS) methods were used for calculating the GPS/levelling geoids. The differences between the actual geoid heights of the test points and the geoid heights acquired by different models were calculated and the contributions of these methods to map production and engineering studies were evaluated statistically. As a result it was concluded that the flexible calculation methods are better suited for determining the local GPS/Nivelman geoids compared to the other methods based on the attained findings.