平方根无迹卡尔曼滤波仅测角导航的空间交会闭环协方差分析方法

摘要

A closed-loop linear covariance analysis method was proposed for orbital rendezvous using AON (angles-only navigation).The SRUKF (square root unscented Kalman filter) based on AON algorithm was constructed and the observation sensitivity matrix was further calculated.The multi-impulsive Hill guidance law was employed to derive the closed-loop linear covariance analysis model.The results of the numerical simulation indicate that the closed-loop linear covariance analysis result fits the 1000 times Monte Carlo shooting well.The covariance analysis method is applicable to the traditional EKF (extended Kalman filter) based on the AON method, but has an estimation bias along downrange, which is equivalent to the variance of trajectory dispersion.The major axis and minor axis of error ellipse achieved with EKF based on covariance respectively are about 24.68% and 20.56% longer than the results from SRUKF based error ellipse.Besides, SRUKF and EKF have the same order computational burden for the state estimation, but the SRUKF is about 10% faster than the EKF due to using two powerful linear algebra techniques, QR decomposition and Cholesky factor updating.%针对基于仅测角导航的空间交会问题,开展了采用线性协方差进行闭环控制误差快速分析方法的研究.建立了基于平方根无迹卡尔曼滤波(Square Root Unscented Kalman Filter,SRUKF) 的仅测角导航算法并推导了观测敏感矩阵,构建了基于多脉冲Hill制导的闭环控制线性协方差分析模型.算例验证结果表明:提出的闭环控制协方差分析结果与Monte Carlo打靶结果能够很好地吻合;该方法适用于采用传统扩展卡尔曼滤波(Extended Kalman Filter,EKF)的仅测角导航问题,但其迹向位置的估计存在一个与该方向控制误差方差相当的偏心,其误差椭圆的长轴和短轴分别比基于SRUKF的估计结果大24.68%和20.56%.此外,由于采用了QR分解和Cholesky 因子更新两种高效的代数运算,基于SRUKF的协方差分析模型的计算速度要比基于EKF的协方差分析模型的大10%.