A 3D coordinate transformation algorithm

3D coordinate transformation is usually encountered issue in geodesy, photogrammetry, geographical information science (GIS) and computer vision. This paper simplifies the mathematical model of 3D similarity transformation by optimization process, which finally only has the parameter of rotation matrix. According to the orthogonality of rotation matrix, the paper uses Rodrigues matrix to represent it, instead of classical rotation angle form. Making full use of the properties of Rodrigues matrix, we carry out the linearization of observation equations; further get the least squares solution of the model parameters. The case study shows that the proposed algorithm is valid and fast, regardless of whether rotation angles are large or small, and almost does not depends on the initial values of the parameter.