Modified filter for mean elements estimation with state jumping

doi:10.23919/JSEE.2024.000081

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (4): 999-1012.doi: 10.23919/JSEE.2024.000081

• CONTROL THEORY AND APPLICATION • Previous Articles

Modified filter for mean elements estimation with state jumping

Yanjun YU¹(), Chengfei YUE²^,*(), Huayi LI¹(), Yunhua WU³(), Xueqin CHEN¹()

¹ Research Center of Satellite Technology, Harbin Institute of Technology, Harbin 150001, China
² Institute of Space Science and Applied Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
³ College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2023-03-14 Online:2024-08-18 Published:2024-08-06
Contact: Chengfei YUE E-mail:yuyanjun9511@163.com;yuechengfei@hit.edu.cn;lihuayi@hit.edu.cn;yunhuawu@nuaa.edu.cn;cxqhit@163.com
About author:
YU Yanjun was born in 1995. She received her B.S. and M.S. degrees from Harbin Institute of Technology, China, in 2018 and 2020, respectively. She is currently pursuing her Ph.D. degree with the School of Astronautics, Harbin Institute of Technology, China. She is also a visiting Ph.D. student in the Department of Aerospace Science and Technology of Politecnico di Milano. Her main research interests include orbital dynamics, navigation, constellation design, and constellation control. E-mail: yuyanjun9511@163.com

YUE Chengfei was born in 1989. He received his B.E. degree in spacecraft design and engineering from Harbin Institute of Technology, Harbin, China, in 2013, and Ph.D. degree in electrical and computer engineering from the National University of Singapore, Singapore, in 2019. He is currently a professor with Harbin Institute of Technology (Shenzhen) (HITSZ), Shenzhen, China, where he is also the director of the Advanced Space Application and Intelligent Control Lab. His main research interests include high-performance control and on-orbit service. E-mail: yuechengfei@hit.edu.cn

LI Huayi was born in 1978. He received his M.S. and Ph.D. degrees in control science and engineering from Harbin Institute of Technology, China, in 2004 and 2008, respectively. Currently, he is a full professor in spacecraft design with Harbin Institute of Technology, Harbin, China, and the director in Research Center of Satellite Technology with Harbin Institute of Technology, Harbin, China. His main research interests include autonomous distributed space systems, space remote sensing and satellite electronic testing. E-mail: lihuayi@hit.edu.cn

WU Yunhua was born in 1981. He received his B.S., M.S., and Ph.D. degrees in aerospace engineering from Harbin Institute of Technology, in 2004, 2006, and 2009, respectively. Since 2013, he has been a professor with the School of Astronautics, Nanjing University of Aeronautics and Astronautics. His main research interests include space vehicle design, mission analysis, space vehicle dynamics and control, and hardware-in-the-loop simulation. E-mail: yunhuawu@nuaa.edu.cn

CHEN Xueqin was born in 1982. She received her Ph.D. degree in control science and engineering from Harbin Institute of Technology, China, in 2008. She is currently a professor in aircraft design and engineering with Harbin Institute of Technology, Harbin, China. Her main research interests are fault diagnosis and fault-tolerant control. E-mail: cxqhit@163.com
Supported by:
This work was supported by National Natural Science Foundation of China (12372045) and Shanghai Aerospace Science and Technology Program (SAST2021-030).

Abstract

Abstract:

To investigate the real-time mean orbital elements (MOEs) estimation problem under the influence of state jumping caused by non-fatal spacecraft collision or protective orbit transfer, a modified augmented square-root unscented Kalman filter (MASUKF) is proposed. The MASUKF is composed of sigma points calculation, time update, modified state jumping detection, and measurement update. Compared with the filters used in the existing literature on MOEs estimation, it has three main characteristics. Firstly, the state vector is augmented from six to nine by the added thrust acceleration terms, which makes the filter additionally give the state-jumping-thrust-acceleration estimation. Secondly, the normalized innovation is used for state jumping detection to set detection threshold concisely and make the filter detect various state jumping with low latency. Thirdly, when sate jumping is detected, the covariance matrix inflation will be done, and then an extra time update process will be conducted at this time instance before measurement update. In this way, the relatively large estimation error at the detection moment can significantly decrease. Finally, typical simulations are performed to illustrated the effectiveness of the method.

Key words: unscented Kalman filter, mean orbital elements (MOEs) estimation, state jumping detection, nonlinear system

Yanjun YU, Chengfei YUE, Huayi LI, Yunhua WU, Xueqin CHEN. Modified filter for mean elements estimation with state jumping[J]. Journal of Systems Engineering and Electronics, 2024, 35(4): 999-1012.

Figures/Tables 12

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References 34

1	CAO X, LI N, QIU S, et al Research on the method of searching and tracking of the time-sensitive target through the mega-constellation. Aerospace Science and Technology, 2023, 137, 108299.
2	INIGO D P, BRUCE G C, EDWARD F C A technical comparison of three low earth orbit satellite constellation systems to provide global broadband. Acta Astronautica, 2019, 159 (6): 123- 135.
3	TAO X F, LI Z, XU C, et al Track-to-object association algorithm based on TLE filtering. Advances in Space Research, 2021, 67 (8): 2304- 2318. doi: 10.1016/j.asr.2021.01.036
4	KUAI Z Z, CAO X L, SHEN H X, et al. Maneuver planning of geostationary satellites using mean orbital elements. Proc. of the Chinese Automation Congress, 2020: 6596−6600. (in Chinese)
5	PAN X, XU M, DONG Y F Low-thrust displaced orbits by weak Hamiltonian-structure-preserving control. Communications in Nonlinear Science and Numerical Simulation, 2018, 62 (9): 282- 306.
6	ASRAF A, SURAYUDA R H, RIBAH A Z, et al. Determination of mean orbital elements using GPS data for LAPAN satellite daily operation. Proc. of the IEEE International Conference on Aerospace Electronics and Remote Sensing Technology, 2021. DOI: 10.1109/ICARES53960.2021.9665177.
7	KOZAI Y The motion of a close Earth satellite. Astronomical Journal, 1959, 64 (11): 367- 377.
8	KOZAI Y Effect of precession and nutation on the orbital elements of a close earth satellite. Astronomical Journal, 1960, 65 (10): 621- 623.
9	BROUWER D Solution of the problem of artificial satellite theory without drag. Astronomical Journal, 1959, 64 (11): 378- 396.
10	CHEN H Y, WU H Y, ZHOU M J, et al. Orbit engineering application and STK simulation for micro-satellite. Beĳing: China Science Publishing & Media Ltd., 2016. (in Chinese)
11	SETTY S, CEFOLA P, MONTENBRUCK O, et al Application of semi-analytical satellite theory orbit propagator to orbit determination for space object catalog maintenance. Advances in Space Research, 2016, 57 (10): 2218- 2233. doi: 10.1016/j.asr.2016.02.028
12	DUTT P, ANILKUMAR A K. Orbit propagation using semi-analytical theory and its applications in space debris field. Astrophysics and Space Science, 2017, 362: 35.
13	LARA M, SAN J F, HAUTESSERRES D, et al. A mean elements orbit propagator program for highly elliptical orbits. CEAS Space Journal, 2018, 10(5): 3−23.
14	NIE T, GURFIL P. Reducing inter-satellite drift of low Earth orbit constellations using short-periodic corrections. Celestial Mechanics and Dynamical Astronomy, 2021, 133: 19.
15	VNIE T, GURFIL P. Long-term evolution of orbital inclination due to third-body inclination. Celestial Mechanics and Dynamical Astronomy, 2021, 133: 1.
16	JULIER S, UHLMANN J K, DURRANT-WHYTE H. A new approach for filtering nonlinear systems. Proc. of the American Control Conference, 1995: 1628−1632.
17	MERWE R, WAN E. The square-root unscented Kalman filter for state and parameter-estimation. Proc. of the IEEE International Conference on Acoustics, 2001: 3461−3464.
18	LI K Y, GUO Z K, ZHOU G J State estimation in range coordinate using range-only measurements. Journal of Systems Engineering and Electronics, 2022, 33 (3): 497- 510. doi: 10.23919/JSEE.2022.000050
19	GONG B C, WANG S, HAO M R, et al Range-based collaborative relative navigation for multiple unmanned aerial vehicles using consensus extended Kalman filter. Aerospace Science and Technology, 2021, 112, 106647.
20	WANG K, CHEN T, XU S J Determination and estimation of differential mean orbital elements for formation-flying missions. Journal of Guidance, Control, and Dynamics, 2014, 37 (1): 86- 97. doi: 10.2514/1.61623
21	WANG K, CHEN T, XU S J. A comparison of algorithms for computing differential mean orbital elements in formation flying missions. Proc. of the AIAA Guidance, Navigation, and Control Conference, 2013. DOI: 10.2514/6.2013-4542.
22	ZHONG W C, GURFIL P Mean orbital elements estimation for autonomous satellite guidance and orbit control. Journal of Guidance, Control, and Dynamics, 2013, 36 (6): 1624- 1641. doi: 10.2514/1.60701
23	LI L C, ZHANG J R, ZHAO S G, et al Autonomous onboard estimation of mean orbital elements for geostationary electric-propulsion satellites. Aerospace Science and Technology, 2019, 94, 105369.
24	ZHAI G, ZHAO H Y, WEN Q Q, et al Relative motion and thrust estimation of a non-cooperative maneuvering target with adaptive filter. Acta Astronautica, 2019, 162 (9): 98- 108.
25	WANG Y D, SUN S M, LI L Adaptively robust unscented Kalman filter for tracking a maneuvering vehicle. Journal of Guidance, Control, and Dynamics, 2014, 37 (5): 1696- 1701. doi: 10.2514/1.G000257
26	JIANG Y Z, BAOYIN H X, MA P B Augmented unbiased minimum-variance input and state estimation for tracking a maneuvering satellite. Acta Astronautica, 2019, 163, 96- 107.
27	KO H C, SCHEERES D J Orbit determination across unknown maneuvers using the essential thrust-Fourier-coefficients. Acta Astronautica, 2016, 118 (1/2): 90- 95.
28	ZHAI G, BI X Z, ZHAO H Y, et al Non-cooperative maneuvering spacecraft tracking via a variable structure estimator. Aerospace Science and Technology, 2018, 79 (8): 352- 363.
29	NASTASI K M, BLACK J T Adaptively tracking maneuvering spacecraft with a globally distributed, diversely populated surveillance network. Journal of Guidance, Control, and Dynamics, 2019, 42 (5): 1033- 1048. doi: 10.2514/1.G003743
30	YU Y J, YUE C F, LI N, et al Onboard estimation of mean orbital elements extended to state jumping case. Journal of Guidance, Control, and Dynamics, 2022, 45 (11): 1996- 2012. doi: 10.2514/1.G006468
31	LIU L, TANG J S. Satellite orbit theory and application. Beĳing: Publishing House of Electronics Industry, 2015. (in Chinese)
32	SCHAUB H, ALFRIEND K Impulsive feedback control to establish specific mean orbit elements of spacecraft formations. Journal of Guidance, Control, and Dynamics, 2001, 24 (4): 739- 745. doi: 10.2514/2.4774
33	BATTIN R. An introduction to the mathematics and methods of astrodynamics. Reston: AIAA Education Series, 1999.
34	JULIER S. The spherical simplex unscented transformation. Proc. of the American Control Conference, 2003: 2430−2434.

Parameter	Value
Semi-major axis/km	6878.14
Eccentricity	0.02
Inclination/(°)	45
RAAN/(°)	20
Argument of the periapsis/(°)	20
Mean anomaly/(°)	20

ARMSE parameter	Method
ARMSE parameter	MASUKF	DM
Semi-major axis/m	2.855	104.1
Eccentricity	2.439×10⁻⁷	1.421×10⁻⁵
Inclination/(°)	6.110×10⁻⁶	4.292×10⁻⁴
RAAN/(°)	8.797×10⁻⁶	6.311×10⁻⁴
Argument of the periapsis/(°)	6.703×10⁻⁴	3.677×10⁻²
Mean anomaly/(°)	7.027×10⁻⁴	0.9551

ARMSE parameter	Method
ARMSE parameter	MASUKF	DM
Semi-major axis/m	3.655	127.3
Eccentricity	3.529×10⁻⁷	1.747×10⁻⁵
Inclination/(°)	9.440×10⁻⁶	5.167×10⁻⁴
RAAN/(°)	1.415×10⁻⁵	7.648×10⁻⁴
Argument of periapsis/(°)	1.050×10⁻³	6.480×10⁻²
Mean anomaly/(°)	1.105×10⁻⁴	1.210

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[7]	Abdollah AZIZI, Mehdi FOROUZANFAR. Stabilizing controller design for nonlinear fractional order systems with time varying delays [J]. Journal of Systems Engineering and Electronics, 2021, 32(3): 681-689.
[8]	Muhammad WASIM, Ahsan ALI. Airship aerodynamic model estimation using unscented Kalman filter [J]. Journal of Systems Engineering and Electronics, 2020, 31(6): 1318-1329.
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[11]	Ligang GONG, Qing WANG, Chaoyang DONG. Switching disturbance rejection attitude control of near space vehicles with variable structure [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 167-179.
[12]	Jianguo GUO, Yuchao LIU, Jun ZHOU. Integral terminal sliding mode control for nonlinear systems [J]. Journal of Systems Engineering and Electronics, 2018, 29(3): 571-579.
[13]	Yongfang NIE, Tao ZHANG. Scaling parameters selection principle for the scaled unscented Kalman filter [J]. Journal of Systems Engineering and Electronics, 2018, 29(3): 601-610.
[14]	Guifang LI, CHEN Ye-Hwa. Controller design for stochastic nonlinear systems with matched conditions [J]. Journal of Systems Engineering and Electronics, 2018, 29(1): 160-165.
[15]	Bomin Huang, Lingmei Chen, and Weiyao Lan. Global robust output regulation for a class of affine singular nonlinear systems [J]. Systems Engineering and Electronics, 2017, 28(4): 745-.

Modified filter for mean elements estimation with state jumping

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