对偶四元数绝对定向迭代解法

An absolute orientaion iterative solution method based on dual quaternion

针对传统的欧拉角表述的绝对定向迭代解法存在的局限性问题,该文将对偶四元数应用到解析绝对定向中,提出一种利用对偶四元数描述的绝对定向迭代解法。该方法根据最小二乘原理求出尺度因子;顾及到模型点坐标含有误差,将模型点坐标作为观测值,对绝对定向方程进行线性化;在对偶四元数单位性和正交性的限制条件下,进行间接平差,求解出七个绝对定向元素。试验结果表明:该解法正确可靠,能够适用于大倾角和大尺度,且与传统欧拉角迭代法相比,具有无须计算初值、线性化程度高、迭代次数少、能够避免繁琐的三角函数运算、解更加稳定等优势,且该方法在一定程度上丰富了绝对定向的解法。

In view of the limitations of the traditional euler angle iterative method,the dual quaternion is applied to absolute orientation in this paper,and an iterative method of absolute orientation described by dual quaternion is proposed. Firstly,the scale factor is determined by using the principle of least squares in this method. Then,with respect to coordinate errors of model points,model point coordinates are as observation and the absolute orientation equations are linearized. Finally,seven absolute orientation elements can be calculated by indirect adjustment under restriction conditions of the unit and orthogonality. The test results show that the solution is correct and reliable,can be suitable for the situation of large angles and large scales;comparing with the traditional euler angle iterative method,the solution has the advantage of not calculating the initial value,high degree of linearization,less number of iterations,avoiding the tedious trigonometric function calculations,more stable results and high calculation accuracy. This method enriches the absolute orientation solution to a certain extent.