基于SRUKF仅测角导航的空间交会闭环控制协方差分析

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SRUKF (Square Root Unscented Kalman Filter) 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。经算例验证，本文提出的闭环控制协方差分析结果与Monte Carlo打靶结果能够很好吻合；该方法适用于采用传统Extended Kalman Filter (EKF)的仅测角导航问题，但其迹向位置的估计存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的估计结果大了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的协方差分析模型要比基于EKF的协方差分析模型在计算速度上快了10%。

Closed-Loop Covariance Analysis for Orbital Rendezvous using Square Root UKF based Angles-Only Navigation

A closed-loop linear covariance analysis method is proposed for orbital rendezvous using angles-only navigation (AON). The Square Root Unscented Kalman Filter (SRUKF) based AON algorithm is constructed and the observation sensitivity matrix is furtherly calculated. The multi-impulsive Hill guidance law is employed to derive the closed-loop linear covariance analysis model. Through numerical simulation, the closed-loop linear covariance analysis result fits the 1,000 times Monte Carlo shooting well. The covariance analysis method is applicable to traditional Extended Kalman Filter (EKF) based 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 covariance is about 24.68% and 20.56% longer than the SRUKF based error ellipse, respectively. Besides, SRUKF and EKF have same order computational burden for state estimation, but SRUKF is about 10% faster than the EKF due to using two powerful linear algebra techniques, QR decomposition and Cholesky factor updating.