用四元数状态切换无迹卡尔曼曼滤滤波器估计的飞行器姿态

Aircraft attitude estimation based on quaternion state-switching unscented Kalman filter

在较大初始姿态误差角下,针对捷联惯导/CCD星敏感器(strap-intertial navigation system/CCD star sensor,SINS/CCD)姿态估计系统扩展卡尔曼滤波(extended Kalman filter,EKF)算法精度下降的问题,提出了基于四元数的状态切换无迹卡尔曼滤波算法.通过状态实时切换降低了全维无迹卡尔曼滤波(unscented Kalman filter,UKF)的维数,减小了计算复杂度,提高了系统的实时性.文中采用基于特征向量求解的代价函数法计算四元数均值避免了UKF算法中四元数规范化的限制;利用乘性误差四元数表示姿态更新点与估计点之间的距离,解决了四元数协方差阵奇异性问题.仿真实验结果表明:与EKF相比,该算法在精度上有较大提高;与全维UKF算法和修正罗德里格斯参数UKF算法相比,该算法精度相当但估计时间均有不同程度的减少.

To deal with the divergence phenomenon of extended Kalman filter （EKF） in SINS/CCD attitude estimation, we put forward a stateswitching unscented Kalman filter （UKF） based on quaternion （QSUKF）. By switching the states in realtime, the dimensions of the fulldimension UKF algorithm are effectively reduced, the computation complexity is decreased and the timeliness is improved. To avoid the quaternion normalization limitation in UKF algorithm, a cost function based on the eigenvector resolution is derived to compute the average quaternion. To deal with the singularity of the quaternion covariance, we employ the multiplicative quaternion error to represent the distance between quaternion update points and the estimation points. The simulation results show that the proposed algorithm provides higher estimation precision than the EKF algorithm, and achieves almost the same estimation precision as the fulldimension UKF and Modified Rodrigues parameter UKF. Furthermore, this algorithm needs shorter estimation time than all other algorithms mentioned above.