Quaternion-Based Iterative Solution of Three-Dimensional Coordinate Transformation Problem

Three-dimensional coordinate transformation problem is the most frequent problem in photogrammetry, geodesy, mapping, geographical information science (GIS), and computer vision. To overcome the drawback that traditional solution of the problem based on rotation angles depends strongly on initial value of parameter, which makes the method ineffective in the case of super-large rotation angle, the paper adopts an unit quaternion to represent three-dimensional rotation matrix, then puts forward a quaternion-based iterative solution of the problem. The cases study shows that the quaternion-based solution has no dependence on the initial value of parameter and desirable result with fast speed. Thus it is valid for three-dimensional coordinate transformation of any rotation angle.