基于单位四元数的空间后方交会解算

介绍四元数的概念及运算性质,提出基于单位四元数的空间后方交会解算方法并给出计算公式。该方法利用单位四元数表示旋转,根据最小二乘原理,通过矩阵运算先求出单位四元数解析解,再获取旋转矩阵,得到角元素值;最后求出撮站点的坐标。此法不需提供外方位元素初始值,并且推导过程中不涉及共线条件方程的线性化。通过算例证明方法的正确性与可靠性。

A Solution to Space Resection Based on Unit Quaternion

Determining exterior orientation parameters of image is an important task in photogrammetiy, and various classic methods are in use. On consideration of some shortcomings in classic methods, a new, quaternion-based, closed-form solution is presented here. The concept of quaternion and its operation rules were introduced first, then formulae for space resection based on unit quaternion were deduced. The new method uses unit quaternion to represent rotation. Based on the least square principle, the closed-form solution to unit quaternion is solved out first. Then the rotation matrix is obtained, and angular elements are derived. lastly coordinates of projective centre is computed. The main advantages of the method are that initial values of exterior orientation parameters need not to be provided, and linearization for the collinearity equations is not involved in formula deduction, so iterative computing of exterior orientation parameters is avoided. The numerical experiments are done and results show the correctness and reliability of the method.