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

Abstract

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

CLC Number:

V448.2

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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References 36

1	WANG R Y , LIANG H , ZHAO H , et al. Deep space multi-file delivery protocol based on LT codes[J]. Journal of Systems Engineering and Electronics, 2016, 27 (3): 524- 530. doi: 10.1109/JSEE.2016.00055
2	TURAN E , SPERETTA S , GILL E . Autonomous navigation for deep space small satellites: scientific and technological advances[J]. Acta Astronautica, 2022, 193, 56- 74. doi: 10.1016/j.actaastro.2021.12.030
3	LIU J , MA J , TIAN J W . Pulsar/CNS integrated navigation based on federated UKF[J]. Journal of Systems Engineering and Electronics, 2010, 21 (4): 675- 681. doi: 10.3969/j.issn.1004-4132.2010.04.022
4	ZOCCARATO P , LARESE S , NALETTO G . Deep space navigation by optical pulsars[J]. Journal of Guidance, Control, and Dynamics, 2023, 46 (8): 1501- 1512.
5	WANG Y D , ZHENG W , ZHANG S N , et al. Review of X-ray pulsar spacecraft autonomous navigation[J]. Chinese Journal of Aeronautics, 2023, 36 (10): 44- 63. doi: 10.1016/j.cja.2023.03.002
6	MCLEMORE B , PSIAKI M L . Navigation using Doppler shift from LEO constellations and INS data[J]. IEEE Trans.on Aero- space and Electronic Systems, 2022, 58 (5): 4295- 4314. doi: 10.1109/TAES.2022.3162772
7	ADAMS D W , PECK C , MAJJI M . Doppler light detection and ranging-aided inertial navigation and trajectory recovery[J]. Journal of Guidance, Control, and Dynamics, 2023, 46 (9): 1689- 1707. doi: 10.2514/1.G007318
8	LIU J Z , XIANG Q , NING X L , et al. GGA-EMD-based inversion method of spectrum reflectance template for celestial Doppler difference navigation[J]. IEEE Trans.on Aerospace and Electronic Systems, 2024, 60 (1): 658- 674. doi: 10.1109/TAES.2023.3327226
9	刘付成, 朱庆华, 孙建党, 等. 基于图像边缘信息的火星探测器自主光学导航技术[J]. 中国科学: 技术科学, 2020, 50 (9): 1160- 1174.
	LIU F C , ZHU Q H , SUN J D , et al. Autonomous optical edge technology for Mars probe based on image edge information[J]. SCIENTIA SINICA Technologica, 2020, 50 (9): 1160- 1174.
10	朱庆华, 王卫华, 刘付成, 等. "天问一号"火星探测环绕器导航制导与控制技术[J]. 深空探测学报(中英文), 2023, 10 (1): 11- 18.
	ZHU Q H , WANG W H , LIU F C , et al. Navigation, gui-dance and control technology of Mars exploration orbiter Tianwen-1[J]. Journal of Deep Space Exploration, 2023, 10 (1): 11- 18.
11	孙建党, 刘宇, 谭天乐. 基于EM-EKF的深空光学自主导航系统光轴偏差补偿算法[J]. 上海航天(中英文), 2020, 37 (4): 25- 31.
	SUN J D , LIU Y , TAN T L . An optical axis deviation compensation algorithm based on EM-EKF for deep space optical autonomous navigation system[J]. Aerospace Shanghai (Chinese & English), 2020, 37 (4): 25- 31.
12	LI Y Y , ZHONG M Y . Fault detection filter design for linear discrete time-varying systems with multiplicative noise[J]. Journal of Systems Engineering and Electronics, 2011, 22 (6): 982- 990. doi: 10.3969/j.issn.1004-4132.2011.06.015
13	WANG S Y , WANG Z D , DONG H L , et al. Dynamic event-triggered quadratic nonfragile filtering for non-Gaussian systems: tackling multiplicative noises and missing measurements[J]. IEEE/CAA Journal of Automatica Sinica, 2024, 11 (5): 1127- 1138. doi: 10.1109/JAS.2024.124338
14	KALMAN R E . A new approach to linear filtering and prediction problems[J]. Journal of Basic Engineering, 1960, 82 (1): 35- 45. doi: 10.1115/1.3662552
15	ZHANG L F , WANG S P , SELEZNEVA M S , et al. A new adaptive Kalman filter for navigation systems of carrier-based aircraft[J]. Chinese Journal of Aeronautics, 2022, 35 (1): 416- 425. doi: 10.1016/j.cja.2021.04.014
16	FRASER C T , ULRICH S . Adaptive extended Kalman filtering strategies for spacecraft formation relative navigation[J]. Acta Astronautica, 2021, 178, 700- 721. doi: 10.1016/j.actaastro.2020.10.016
17	GUO Y H , VOUCH O , ZOCCA S , et al. Enhanced EKF-based time calibration for GNSS/UWB tight integration[J]. IEEE Sensors Journal, 2022, 23 (1): 552- 566.
18	MARCOS R F , GIORGIO M M , YUSEF R C Z , et al. GNSS/MEMS-INS integration for drone navigation using EKF on lie groups[J]. IEEE Trans.on Aerospace and Electronic Systems, 2023, 59 (6): 7395- 7408.
19	ITO K , XIONG K . Gausian filters for nonlinear filtering pro-blems[J]. IEEE Trans.on Automatic Control, 2000, 45 (5): 910- 927.
20	JIA B , XIN M , CHENG Y . High-degree cubature Kalman filter[J]. Automatica, 2013, 49 (2): 510- 518.
21	CUI B B , WEI X H , CHEN X Y , et al. Improved high-degree cubature Kalman filter based on resampling-free sigma-point update framework and its application for inertial navigation system-based integrated navigation[J]. Aerospace Science and Technology, 2021, 117, 106905.
22	WANG S Y , FENG Y L , DUAN S K , et al. Mixed-degree spherical simplex-radial cubature Kalman filter[J]. Mathematical Problems in Engineering, 2017, 2017, 6969453.
23	LIU J K , WANG P F , ZHA F S , et al. A strong tracking mixed-degree cubature Kalman filter method and its application in a quadruped robot[J]. Sensors, 2020, 20 (8): 2251.
24	ARASARATNAM I , HAYKIN S . Cubature Kalman filters[J]. IEEE Trans.on Automatic Control, 2009, 54 (6): 1254- 1269.
25	SHI J , QI G Q , LI Y Y , et al. Stochastic convergence analysis of cubature Kalman filter with intermittent observations[J]. Journal of Systems Engineering and Electronics, 2018, 29 (4): 823- 833.
26	GAO B B , HU G G , ZHANG L , et al. Cubature Kalman filter with closed-loop covariance feedback control for integrated INS/GNSS navigation[J]. Chinese Journal of Aeronautics, 2023, 36 (5): 363- 376.
27	褚东升, 郭丽娜, 高守婉. 基于约当分解的带乘性噪声广义系统状态最优滤波算法[J]. 中国海洋大学学报(自然科学版), 2010, 40 (4): 115- 118.
	CHU D S , GUO L N , GAO S W . Optimal filtering for stochastic singular systems with multiplicative noise based on Jordan decomposition[J]. Periodical of Ocean University of China, 2010, 40 (4): 115- 118.
28	王炯琦, 矫媛媛, 周海银, 等. 适合处理乘性噪声估计卫星姿态的非线性迭代滤波算法[J]. 电子学报, 2011, 39 (6): 1417- 1422.
	WANG J Q , JIAO Y Y , ZHOU H Y . An iterative filter for nonlinear satellite attitude determination system with multiplicative stochastic matrix[J]. Acta Electronica Sinica, 2011, 39 (6): 1417- 1422.
29	LU X , WANG L L , WANG H X , et al. Kalman filtering for delayed singular systems with multiplicative noise[J]. IEEE/CAA Journal of Automatica Sinica, 2016, 3 (1): 51- 58.
30	LIU J , WANG P F , LI M T , et al. A multiplicative noises and additive correlated noises cubature Kalman filter and its application in quadruped robot[J]. IEEE Access, 2020, 8, 162290- 162301.
31	GE Q B , MA Z C , LI J L . Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise[J]. Chinese Journal of Aeronautics, 2022, 35 (5): 40- 52.
32	荆武兴, 高长生. 月球探测器精确相对动力学模型及其应用[J]. 中国科学: 物理学天文学力学, 2010, 40 (4): 462- 470.
	JING W X , GAO C S . Precise relative dynamics model of a lunar probe and its application[J]. SCIENTIA SINICA Physica, Mechanica & Astronomica, 2010, 40 (4): 462- 470.
33	KIM K H , JEE G J , PARK C G , et al. The stability analysis of the adaptive fading extended Kalman filter using the innovation covariance[J]. International Journal of Control, Automation and Systems, 2009, 7, 49- 56.
34	卢山, 张世源. 非合作航天器相对运动估计的混合滤波器设计方法[J]. 宇航学报, 2023, 44 (5): 764- 773.
	LU S , ZHANG S Y . Hybrid filter design for relative motion estimation of non-cooperative spacecraft[J]. Journal of Astronautics, 2023, 44 (5): 764- 773.
35	钱霙婧, 荆武兴, 刘玥, 等. 地月平动点拟周期轨道设计方法[J]. 系统工程与电子技术, 2014, 36 (8): 1586- 1594. doi: 10.3969/j.issn.1001-506X.2014.08.22
	QIAN Y J , JING W X , LIU Y , et al. Design of quasi-periodic orbit about the translunar libration point[J]. Systems Engineering and Electronics, 2014, 36 (8): 1586- 1594. doi: 10.3969/j.issn.1001-506X.2014.08.22
36	KAYAMA Y , HOWELL K C , BANDO M , et al. Low-thrust trajectory design with successive convex optimization for libration point orbits[J]. Journal of Guidance, Control, and Dynamics, 2022, 45 (4): 623- 637.

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

Filter algorithm design for autonomous navigation in deep space detection considering the influence of multiplicative noise

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