Analytical solution to and error analysis of the quaternion based similarity transformation considering measurement errors in both frames
Analytical solution to and error analysis of the quaternion based similarity transformation considering measurement errors in both frames
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考虑两帧测量误差的基于四元数的相似变换的解析解和误差分析
DOI：
10.1016/j.measurement.2017.06.013
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发表时间：
2017
期刊：
影响因子：
5.6
通讯作者：
Liu Ming
中科院分区：
文献类型：
--
作者：
Chang Guobin;Xu Tianhe;Wang Qianxin;Liu Ming
两个坐标系之间的相似变换，在科学和工程中得到了广泛的应用。使用两个帧中的一组公共点的坐标确定来估计变换参数。用四元数表示旋转变换，定义一个3×1的误差向量来表示四元数估计误差。假设两个帧中的坐标确定都有噪声。给出了一个解析最小二乘解，其中四元数估计是一个4×4对称矩阵的最大特征值对应的特征向量.结果表明，只要存在一个有实际意义的四元数估计，最大本征值必然是单一的。详细分析了该解的误差分析，其中最大特征值-特征向量对的误差分析起着关键作用。进行了蒙特卡罗实验，结果验证了所提出的误差分析的一致性。
The similarity transformation between two coordinate frames, is widely adopted in science and engineering. The transformation parameters are estimated using coordinate determinations of a set of common points in both frames. The quaternion is employed to represent the rotation transformation; and a 3 × 1 error vector is defined to represent the quaternion estimation error. Coordinate determinations in both frames are assumed noisy. An analytical least-squares solution is derived in which the quaternion estimate is the eigenvector of a 4 × 4 symmetric matrix corresponding to its largest eigenvalue. It is found that as long as a practically meaningful quaternion estimate exists, the largest eigenvalue must be single. Error analysis of this solution is investigated in detail in which the error analysis of the largest eigenvalue-eigenvector pair plays a pivotal role. Monte Carlo experiments are conducted and the results validate the consistency of the developed error analysis.