A new analytical solution of nonlinear geodetic datum transformation

Nonlinear geodetic datum transformation is particular suitable for the case of large rotation angles, and has been an active area of research in recent years. In this paper, we propose a new analytical solution. The method expresses the scale parameter and translation parameters as the function of rotation matrix, through the derivation process. Then, according to the orthogonality of rotation matrix, the method adopts Rodrigues matrix to represent it. Using the relative formula of Rodrigues matrix with anti-symmetric matrix which is formed by a rotation vector, we derive the solution formula of the rotation vector. Finally, we obtain the analytical solution to the seven parameters. The case studies indicate that the proposed method is valid, regardless of whether the coordinates are polluted by noise or not, and whether rotation angles are big or small.