Abstract：In this paper, to solve the parameter of the three-dimensional spatial coordinate transformation model, quaternion is introduced to construct a rotation matrix. This paper proves that the coordinate transformation rotation matrix is equivalent to the orthogonal transformation of quaternion. Using unit quaternion theory derivates a direct algorithm for solving spatial coordinate transformations. A simulation test using analogue data and numerical examples show that the method is feasible and simple, does need not linearization, and can adapt to arbitrary rotation angle rotation transformations.
