测绘学报

• 学术论文 •    

一种基于四元数的空间后方交会全局收敛算法

龚辉,江刚武,姜挺,陈密密   

  1. 信息工程大学测绘学院
  • 收稿日期:2009-07-20 修回日期:2009-10-16 出版日期:2011-10-25 发布日期:2011-10-25
  • 通讯作者: 龚辉

A Globally Convergent Algorithm of Space Resection Based on Quaternion

  • Received:2009-07-20 Revised:2009-10-16 Online:2011-10-25 Published:2011-10-25

摘要: 摄影测量学中传统的空间后方交会解法是对共线条件方程按泰勒公式展开进行线性化,并按最小二乘原理求解,其求解的精度与外方位元素的初值具有很大关系。为从理论上彻底解决空间后方交会对初值的依赖问题,结合四元数在摄影测量中的良好应用,提出了一种基于四元数的空间后方交会全局收敛算法。该算法利用四元数描述影像姿态,采用绝对定向和正交投影两种变换来代替中心投影的共线条件方程,再利用非线性方程直接迭代的方法进行求解,从而无需进行线性化,最后从理论上对算法的全局收敛性进行了证明。实验结果表明该算法正确可靠,对外方位元素初值没有要求,真正做到无初值依赖空间后方交会,具有很好的稳定性和适应性。

Abstract: The traditional solution of space resection in photogrammetry is expanding the collinear equation according to Taylor formula to obtain the linear equations, and then the linear equation is solved iteratively by the least square principle. The precision of the solution is greatly related to the initial value of exterior orientation elements. In order to solve this problem in theory, a globally convergent algorithm of space resection based on quaternion is presented by combining good application of quaternion in photogrammetry. Firstly the unit quaternion is used to describe the attitude of the image in this algorithm, and absolute orientation equation and orthogonal projection formula are used to replace the collinear equation. Then the iterative solution of nonlinear equation is used to solve this problem. So that, the linearization of collinear equation is needless. Lastly the globally convergent property of this algorithm is proved in theory. Experimental results indicate that this algorithm, which is a real space resection solution independent of initial values, is right, stable and adaptive, and have no requirement for initial values of exterior orientation elements.