一种基于李群表征的空间后方交会新方法

A new space resection method based on Lie group representation

经典的空间后方交会使用欧拉角或四元数对摄影测量姿态进行表征。基于欧拉角表征的旋转变换存在计算复杂、方向锁定等弱点,四元数表征无法正确反映姿态几何特性,且两者都存在姿态奇异值问题。为解决摄影测量姿态无奇异值表征难题,提升摄影测量平差定位效率,本文首先提出了一种基于李群表征的空间后方交会新方法,其次推导了采用李代数的外方位元素系数矩阵,相较于经典欧拉角和四元数,该算法结构简明清晰、易于实现,最后经模拟和实际数据验证,算法正}有效。

Euler angles or quaternions are used te represent the attitude of photogrammetry in classic space resection.The method based on Euler angles is complicated and with gimbal lock and the geometric characteristics of attitude cannot be reflected by the quaternions correctly.Both methods have attitude singular values.In order te solve the representation problem of photogrammetric attitude without singular ralue and cnprove the efficiency of photogrammetry adjustment and positioning,a new method of space resection based on Lie group representation is proposed in this paper,and the coefficient matric is derived by Lie algebra.Compared with Euler angles and quaternions,the alaorithm is concise in structure,easy to implement,and proved to be accurate and effcient through simulated and actual data verification.