飞行器姿态确定的四元数约束滤波算法

Quaternion constrained filter algorithm for spacecraft attitude determination

摘要:

单位四元数作为姿态描述参数具有全局非奇异、运动学方程线性的优点,但其归一化约束必须精确保持．针对这一问题,提出一种飞行器姿态确定的非线性约束滤波算法．首先,通过比较四元数先验和后验估计值的范数大小,证明乘性扩展卡尔曼滤波算法难以获得姿态最优约束解．然后,将QUEST算法与乘性卡尔曼滤波算法有效结合起来,建立一个广义的二次约束优化目标函数; 状态预测阶段利用姿态及其方差传播模型来修正目标损失函数,测量更新阶段则通过求解特征值/特征矢量问题,全局显性保持了四元数的归一化约束,避免了扩展卡尔曼滤波的局部线性化近似．数学仿真对所提出算法的精度、稳定性和收敛性能进行了验证,并与乘性扩展卡尔曼滤波算法进行了比较．

Abstract:

A major advance of using the quaternion to describe body orientation is that the kinematics equation is linear and the quaternion is also globally nonsingular. However, the algebraic constraint of unit norm needs to be maintained. An improved nonlinear constrained filter algorithm is proposed for the spacecraft attitude estimation problem subject to a unit quaternion norm constraint. First,by comparing the quaternion norm of a priori and a posteriori estimate, it is proved that the Multiplicative Extended Kalman filter can not gain the optimal solution under nonlinear constraint. Then, a generalized quadratically constrained optimization object function is developed by effective combination of QUEST algorithm and Multiplicative Kalman filter. During the predicting state, the attitude and its covariance propagation models are used to modify the cost function. During the measurement update phase, the quaternion normalization is explicitly maintained in a globally optimal manner by solving the eigenvalue-eigenvector problem and therefore the local linearization is avoided. Compared with the Multiplicative Extended Kalman filter, numerical simulation result demonstrates the precision, stability and convergence of the presented algorithm.