航姿参考系统中的三种简易四元数平均算法

Three simple quaternion averaging algorithms used in attitude and heading reference system

单位四元数平均运算通常被定义为求解约束最小化问题的最优解,在计算上很耗时。考虑到航姿参考系统中只有两个四元数进行加权平均运算,针对三种基于最小化的四元数平均算法,分别得出其用于求解两个四元数平均值的简易公式。数据分析指出利用这三种简易公式得到的平均四元数非常接近,其角距离小于0.04°。大角度机动实验证实三种四元数平均公式可用于基于四元数的航姿参考系统,为四元数平均算法在航姿参考系统及其他有关领域中的有效应用提供参考。

Unit quaternion averaging is normally defined as the optimal solution to a constrained minimization problem,which is computationally time-consuming.Considering that there are only two quaternions in an attitude and heading reference system(AHRS)for weighted averaging,three easy two-quaternion averaging formulas are obtained from each minimization-based quaternion averaging algorithm,respectively.The data analysis demonstrates that the quaternions obtained using the three easy two-quaternion averaging formulas are very close,and the angular distances between them are less than 0.04°.The large angle maneuver experiment confirms that the three two-quaternion averaging formulas can be used in the quaternion-based AHRS.The conclusions provide a reference for the effective application of quaternion averaging algorithm in AHRS and other related fields.