Alternative methods of determining translation parameters for Geocentric Translation Model Applications

Abstract

Several studies have been reported in geodetic sciences on the application of geocentric translation model (GTM) for coordinate transformation. The most commonly used method for estimating GTM parameters has been the simple averaging approach popularly known as the arithmetic mean. However, to the best of our knowledge, little or no alternative techniques have been fully explored for estimating GTM parameters. Therefore, the present study is focused on testing the capability and applicability of alternative mean estimation methods of median, geometric mean, harmonic mean and quadratic mean; by comparing with the arithmetic mean. In view of these developments, the methods were applied in Ghana’s geodetic reference network to transform Global Navigation Satellite System acquired data to the two local datums (Accra and Leigon) used in Ghana. The suitability of the mean estimation methods for coordinate transformation between local datums was also carried out. In determining the GTM parameters, the Vaníček and Steeves concept (VSC) was also applied for the first time as part of the GTM coordinate transformation process. The performance of the mean estimation approaches were assessed based on standard deviation, root mean square error, mean absolute error, minimum and maximum horizontal errors and horizontal positional errors. On the basis of the results, it was clearly revealed that the strength of a mean estimation method depends on whether it is applied for: global to local coordinate transformation; only local coordinate transformation, and the type of reference ellipsoids used in the transformation process. This study will therefore serve as a contribution to the dynamics in the implementation of GTM for surveying and mapping purposes in Ghana.