方向余弦矩阵中四元数提取算法比较

Comparison of algorithms for extracting quaternion from DCM

在捷联惯性导航系统姿态算法中,用四元数取代方向余弦阵来描述姿态变化具有计算量小、精度高、不存在奇异问题的优点。在实际工程应用中常常需要从方向余弦矩阵中提取对应的旋转四元数,但是经典的提取算法可能会出现平方根计算时根号内出现负值的情况,从而使四元数的提取失败。针对这一问题,总结了现有文献中提出的两种新算法,并从计算量和计算精度的角度对这几种算法进行了分析对比,通过比较发现基于特征值和特征向量的提取算法实现了计算量和精度的最佳组合,为工程应用提供了有价值的参考。

While describing the attitude changes in SINS algorithm, quaternion method is superior to direction cosine matrix because the former requires less computation, gives better accuracy and avoids singularity. Extracting the rotation quaternion from the direction cosine matrix is often needed in engineering applications, but the classical extracting algorithm has a fatal disadvantage which will result in an extraction failure when negative value appears in a square root computation. Aiming at this problem, two new algorithms from the literatures available was introduced and analyzed from the aspect of the computation complexity and the precision. The comparison of computation results shows that the algorithm based on eigenvalue and eigenvector performs the best combination of computation complexity with precision, which is valuable for the engineering application.