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基于视线测量的航天器相对导航精度会受到相对轨迹形状和滤波算法设计等因素的共同影响。以低轨卫星近距离编队飞行为任务背景,设计了环航飞行、共面漂移和共线保持3种不同轨迹的相对运动模式。对3种模式建立了基于星间非线性相对运动模型的系统状态方程,并引入了J2项地球非球形摄动力的影响;建立了基于视线测量的观测方程,观测量包括星间相对距离、相对俯仰角和相对航向角。结合系统模型和观测模型均为高斯分布的非平稳随机过程的特点,分别在上述3种模式下设计了基于扩展卡尔曼滤波(extended Kalman filter,EKF)和无迹卡尔曼滤波(unscented Kalman filter,UKF)的相对导航滤波算法,对各自的相对运动轨迹进行了数值仿真,并在半物理硬件环境下进行了验证,分析了不同模式下EKF和UKF对于高斯非平稳随机过程的估计精度和稳定性,并结合EKF和UKF的运算复杂度,提出了3种相对运动模式下的滤波器优选方案,对工程设计提供了理论参考。
The relative navigation precision of the spacecraft based on line of sight measurement will be affected by the relative track shape and the design of the filter algorithm. Taking the low-altitude orbiting satellites flying in close range as the mission background, the relative motion patterns of three kinds of trajectories, namely cyclic flight, coplanar drift and collinearity, are designed. The system state equations based on non-linear relative motion between stars are established for the three modes, and the influence of the non-spherical perturbation of the earth J2 is introduced. The observation equation based on the line of sight measurement is established, including the relative distance between stars, Pitch angle and relative course angle. Combining the characteristics of both the system model and the observational model being nonstationary random processes with Gaussian distribution, an extended Kalman filter (EKF) and an unscented Kalman filter UKF) relative navigation and filtering algorithm, the relative motion trajectory of each is numerically simulated and verified in semi-physical hardware environment. The accuracy and stability of EKF and UKF for Gaussian nonstationary stochastic processes under different modes are analyzed , And combined with the computational complexity of EKF and UKF, the paper presents three filter options in relative motion mode, which provides a theoretical reference for engineering design.