Implementation of the dual quaternion algorithm for 3D similarity-based coordinate transformation between Ghana’s local geodetic datum and WGS84

Abstract

Modern surveying practice has embraced the use of Global Navigation Satellite System (GNSS) technology due to its attainable precision and uncomplicated functionality. The adoption of this technology has therefore necessitated the transformation of coordinates between satellite-based and classical geodetic reference datums. It is known that the 3D similarity-based transformation models are the most widely used in the literature. However, one major limitation of such models is the representation of point rotations in space using Euler angles connected to X, Y, and Z-axes, which often leads to matrix singularities. To overcome this mathematical inconvenience, the dual quaternion is proposed. This paper implements the dual quaternion algorithm to transform coordinates between the World Geodetic System 1984 (WGS84) and Ghana War Office 1926. To perform the transformation, 31 common points were divided into two parts: reference and check points. The reference points, consisting of 24 common points that are evenly distributed across Ghana, were used to derive the transformation parameters. The remaining 7 points were used to evaluate the derived transformation parameters. The results confirmed that the coordinates transformed by the dual quaternion algorithm are in average agreement with the measured coordinates, with precision and accuracy levels of about 0.580 m and 1.023 m. The obtained results follow the Bursa-Wolf model that is already used by the Ghana Survey and Mapping Division to perform 3D transformations. Hence, the results satisfy cadastral applications, geographic information works, reconnaissance, land information system works and small-scale topographic surveys in Ghana.