三维坐标转换参数估计的平方根矩阵法

A square root matrix method for three-dimensional coordinate transformation

针对三维坐标转换模型参数估计的核心是旋转矩阵的表示方法这一客观事实,该文通过对现有三维坐标转换模型中不同旋转矩阵的表示方法进行研究,依据任何一个方阵都可以惟一地分解为一个对称矩阵与一个反对称矩阵之和的矩阵理论,提出了一种使用反对称矩阵表示旋转矩阵的新方法,并详细推导了基于布尔莎模型的三维坐标转换算法——平方根矩阵法;最后,根据文献算例对该方法进行实验分析。实验结果表明,该算法适用于大旋转角,且相较于方向余弦法、罗德里格矩阵法和单位四元数法具有计算收敛速度快、精确度高的优点。

Through the study of different representations of rotation matrix in exisiting three-dimensional coordinate transformation models,this article introduced a new method using antisymmetric matrix to express rotational matrix based on the theory that any square martrix can be only deconposed into a symmetrical matrix and a antisymmetric matrix,and then derived in detail the three-dimensional coordinate transformation algorithm based on Bursa model——square root matrix method.Finally,simulated and practical experiments showed that the new method proposed in this article was suitable in coordinate transformation with big rotation angle.Besides,the method had faster convergence rate and higher accuracy comparing with direction cosine,unit quaternion and Rodrigues.