利用四元数改进大旋转角坐标变换模型

大旋转角坐标变换模型的迭代解法依赖于初值的确定。用四元数构造旋转矩阵,建立了三维坐标变换的牛顿迭代公式,并提出了一种初值构造算法。利用实测数据和模拟数据对该算法进行了验证,并与其他算法进行比较。结果表明,该初值构造算法使得基于四元数的大旋转角坐标变换模型更加稳健。

Improvement of a Three-dimensional Coordinate Transformation Model Adapted to Big Rotation Angle Based on Quaternion

In geometrics, machine vision and other fields, the large rotation angle three-dimensional coordinate transformation often need to be applied based on the two corresponding point sets. The solvingmethods of the large rotation angle three-dimensional coordinate transformationare broadly divided into iterative methods and analytical methods. The iterative methods can obtain higher transformation accuracy. However, these methods depend on the initial value. In this contribution, quaternion is used to construct rotation matrix, a large rotation angle three-dimensional coordinate transformation formulae based on Newton iterative method is established, and a method which is widely used in guidance and control field for initial value calculation is given. Simulated and real data are used to validate the proposed algorithm, and the results are compared with those of other algorithms. The results show that the proposed algorithm makes the large rotation angle coordinate transformation model based on quaternion more robust. So the proposed algorithm is practically valuable for its stability of results, reliable accuracy and fast convergence.