基于乘性四元数和约束滤波的飞行器姿态估计算法

以单位四元数作为姿态描述参数提出一种乘性约束姿态估计算法。四元数具有全局非奇异、运动学方程双线性的优点，但归一化约束条件必须精确保持。首先，比较了加性和乘性滤波算法在估计误差定义和校正方式上的差别，并从物理概念和估计精度上详细分析了无约束四元数估计算法的不足。然后，针对“矢量测量+陀螺”姿态观测模式，利用乘性约束滤波算法设计了姿态估计器。针对状态部分受约束的姿态估计问题，推导了状态和方差预测方程及状态受约束的最优增益矩阵，并将约束增益矩阵应用到姿态估计算法的测量更新过程。最后，通过数学仿真验证了算法在估计精度和收敛性能上的优越性。

Spacecraft attitude estimation algorithm based on multiplicative quaternion and constrained filter

A multiplicative constrained attitude estimation algorithm is proposed by using unit quaternion to describe the attitude. A major advantage of using the quaternion is that the kinematics equation is linear in the quaternion and is also free of singularities, but the normalization constraint condition must be preserved accurately. First, the differences in the definition of estimation errors and state correction modes between the additive and multiplicative filter algorithms are compared, and the disadvantages in the physical conception and estimation accuracy of the unconstrained quaternion estimation algorithm are also analyzed in detail. Then, an attitude estimator for the attitude measurement model composed of vector observation and gyros is designed by using the multiplicative constrained filter algorithm. According to the state part constrained attitude estimation problem, the state and covariance propagation equations and the optimal gain matrix subject to state normality constraint are derived. Subsequently the constrained gain matrix is applied to the measurement update phase of the attitude estimation algorithm. Finally, the numerical simulation result demonstrates the superiority in estimation accuracy and convergence property of the proposed algorithm.