An Expanded Dual Quaternion Algorithm for 3D Helmert Transformation and Determination of the VCV Matrix of the Transformation's Parameters

Abstract

3D coordinate transformation is a problem frequently encountered in many different fields, for example, computer graphics, robotics, aeronautics and computer vision, in addition, in surveying, datum transformation and the transformation of lidar point cloud. This study aims to introduce a completely new expanded dual quaternion method that performs 3D coordinate transformation, which can also calculate the variance-covariance (VCV) matrix of the transformation parameters. The new dual quaternion algorithm (DQA) presented here will be given with two numerical examples as simply and clearly as possible.