深空探测中考虑乘性噪声影响的自主导航滤波算法设计

doi:10.12305/j.issn.1001-506X.2025.01.29

摘要/Abstract

摘要：

针对深空探测任务中航天器的状态估计问题, 考虑到基于光学相机的自主导航系统在建立观测方程时所使用的坐标系转换矩阵含有由星敏感器引入的测量噪声, 该噪声与量测状态相互耦合, 属于乘性噪声, 建立带有乘性噪声的光学自主导航系统模型。针对系统存在乘性噪声时, 仅适用于处理加性噪声的传统滤波器估计误差增大的问题, 将乘性噪声矩阵引入高斯滤波算法的递推公式进行推导, 并结合混合阶球面单形-径向容积卡尔曼滤波器(mixed-order spherical simplex-radial cubature Kalman filter, MSSRCKF)的数值积分方法, 提出混合阶容积-乘性卡尔曼滤波器(mixed-order cubature-multiplicative Kalman filter, MC-MKF)。该滤波器能够对由星敏感器引入观测方程的高斯以及非高斯乘性噪声进行处理, 在不增加计算复杂度的情况下提升滤波器的估计精度。最后, 将MC-MKF应用于自主导航系统模型, 并与MSSRCKF进行比较分析。仿真结果表明, 当系统存在乘性噪声时, MC-MKF的估计精度明显优于MSSRCKF, 且计算量与MSSRCKF基本一致。

关键词: 深空探测, 光学自主导航, 乘性噪声, 非线性滤波

Abstract:

Regarding the state estimation problem of spacecraft in deep space detection mission, considering that the coordinate system transformation matrix used by the autonomous navigation system based on optical cameras in establishing observation equations contains measurement noise introduced by star sensors, which is coupled with the measurement state and belongs to multiplicative noise, a model of an optical autonomous navigation system with multiplicative noise is established. In response to the problem of increased estimation error in traditional filters that are only suitable for handling additive noise when there is multiplicative noise in the system, the multiplicative noise matrix is introduced into the recursive formula of the Gaussian filtering algorithm for derivation, and combined with the numerical integration method of the mixed-order spherical simplex-radial cubature Kalman filter (MSSRCKF), a mixed-order cubature multiplicative Kalman filter (MC-MKF) is proposed. This filter can process Gaussian and non-Gaussian multiplicative noise introduced into the observation equation by star sensors, improving the estimation accuracy of the filter without increasing computational complexity. Finally, MC-MKF is applied to the autonomous navigation system model and compared with MSSRCKF for analysis. The simulation results show that when there is multiplicative noise in the system, the estimation accuracy of MC-MKF is significantly better than MSSRCKF, and the computational complexity is basically the same as MSSRCKF.

Key words: deep space detection, optical autonomous navigation, multiplicative noise, nonlinear filtering

中图分类号:

V448.2

卢山, 张世源, 侯月阳, 张晓彤, 李晴. 深空探测中考虑乘性噪声影响的自主导航滤波算法设计[J]. 系统工程与电子技术, 2025, 47(1): 287-295.

Shan LU, Shiyuan ZHANG, Yueyang HOU, Xiaotong ZHANG, Qing LI. Filter algorithm design for autonomous navigation in deep space detection considering the influence of multiplicative noise[J]. Systems Engineering and Electronics, 2025, 47(1): 287-295.

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参数名称	参数值
初始位置/km	$\boldsymbol{r}_{P, 0}=\left[\begin{array}{ccc}300 & 310.894 & 7 \\156 & 742.357 \\88 & 204.615 & 25\end{array}\right]$
初始速度/(km·s^-1)	$\dot{\boldsymbol{r}}_{P, 0}=\left[\begin{array}{cc}-0.382\;\;\;235 \\0.557\;\;403 \\0.225 \;\; 564\end{array}\right]$

参数	MC-MKF	MSSRCKF
位置/km	7.162	8.468
速度/(m·s^-1)	0.154	0.219

参数	MC-MKF	MSSRCKF
位置/km	6.357	7.036
速度/(m·s^-1)	0.142	0.180

参数	MC-MKF	MSSRCKF
位置/km	7.216	8.635
速度/(m·s^-1)	0.156	0.224

计算时间	MC-MKF	MSSRCKF
t_mean	0.713	0.703