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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%。
Aiming at the problem of space rendezvous based on angle measurement only, a method of rapid analysis of closed-loop control error using linear covariance is developed. An angular measurement-only navigation algorithm based on Square Root Unscented Kalman Filter (SRUKF) was established and the observational sensitivity matrix was derived. A closed-loop controlled linear covariance analysis model based on multi-pulse Hill guidance was constructed. The experimental results show that the proposed closed loop control covariance analysis is in good agreement with the Monte Carlo method. The proposed method is suitable for only angular measurement of navigation using Extended Kalman Filter (EKF) There is an eccentricity corresponding to the variance of the direction control error in the estimation of the track position. The long axis and the short axis of the error ellipse are respectively 24.68% and 20.56% larger than the estimation result based on the SRUKF. In addition, the SRUKF-based covariance model was calculated to be 10% faster than the EKF-based covariance model due to two efficient algebraic operations, QR decomposition and Cholesky factor update.