基于LSTM神经网络的短期轨道预报

doi:10.12305/j.issn.1001-506X.2022.03.26

摘要/Abstract

摘要：

针对基于动力学模型的轨道预报方法对卫星自主轨道预报与大量非合作目标轨道预报中存在建模成本过高和缺少目标空间环境信息的问题, 提出一种基于误差数据驱动的神经网络轨道预报方法。该方法在解析法动力学模型的基础上, 使用长短期记忆神经网络对历史轨道预报的误差进行学习, 预测未来短期动力学模型的预报误差, 以此对预报结果进行修正。选用Ajisai卫星轨道数据和SGP4(simplified general perturbations)动力学模型对所提模型的有效性和性能进行仿真验证。实验结果表明, 所提方法对地心惯性坐标系下3个轴一天的预报误差分别下降到原来的16.87%、17.66%、19.58%, 显著提升了轨道预报精度。

关键词: 卫星轨道预报, 机器学习, 长短期记忆神经网络, 时间序列分析

Abstract:

Aiming at the problems of high modeling cost and lack of target space environment information in satellite autonomous orbit prediction and a large number of non cooperative target orbit prediction based on dynamic model, a neural network orbit prediction method driven by error data is proposed. Based on the analytical dynamic model, this method uses the long short-term memory neural network to learn the error of historical orbit prediction and predict the prediction error of future short-term dynamic model, so as to correct the prediction results. The ajisai satellite orbit data and SGP4 (simplified general pertubations) dynamic model are selected to verify the effectiveness and performance of the proposed model. The experimental results show that the one-day prediction errors of the three axes in the geocentric inertial coordinate system are reduced to 16.87%, 17.66% and 19.58% respectively, which significantly improves the orbit prediction accuracy.

Key words: satellite orbit forecast, machine learning, long short-term memory (LSTM) neural network, time series analysis

中图分类号:

V44
P228

张心宇, 刘源, 宋佳凝. 基于LSTM神经网络的短期轨道预报[J]. 系统工程与电子技术, 2022, 44(3): 939-947.

Xinyu ZHANG, Yuan LIU, Jianing SONG. Short-term orbit prediction based on LSTM neural network[J]. Systems Engineering and Electronics, 2022, 44(3): 939-947.

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参考文献 30

1	杨瑞红. 卫星轨道预报的快速算法研究[D]. 西安: 西安理工大学, 2017.
	YANG R H. Research on the fast algorithm of satellite orbit prediction[D]. Xi'an: Xi'an University of Technology, 2017.
2	MONTENBRUCK O . Numerical integration methods for orbital motion[J]. Celestial Mechanics and Dynamical Astronomy, 1992, 53 (1): 59- 69.
3	KIM H K , HAN C Y . Analytical and numerical approaches of a solar array thermal analysis in a low-earth orbit satellite[J]. Advances in Space Research, 2010, 46 (11): 1427- 1439. doi: 10.1016/j.asr.2010.08.023
4	王海红, 陈忠贵, 初海彬, 等. 导航卫星星载自主轨道预报技术[J]. 宇航学报, 2012, 33 (8): 1019- 1026. doi: 10.3873/j.issn.1000-1328.2012.08.004
	WANG H H , CHEN Z G , CHU H B , et al. Autonomous orbit prediction technology for navigation satellites on board[J]. Acta Astronautics, 2012, 33 (8): 1019- 1026. doi: 10.3873/j.issn.1000-1328.2012.08.004
5	PENG H , BAI X L . Artificial neural network-based machine learning approach to improve orbit prediction accuracy[J]. Journal of Spacecraft and Rockets, 2018, 55 (5): 1248- 1260. doi: 10.2514/1.A34171
6	PENG H , BAI X L . Improving orbit prediction accuracy through supervised machine learning[J]. Advances in Space Research, 2018, 61 (10): 2628- 2646. doi: 10.1016/j.asr.2018.03.001
7	PENG H , BAI X L . Exploring capability of support vector machine for improving satellite orbit prediction accuracy[J]. Journal of Aerospace Information Systems, 2018, 15 (6): 366- 381. doi: 10.2514/1.I010616
8	PENG H, BAI X L. Obtain confidence interval for the machine learning approach to improve orbit prediction accuracy[C]// Proc. of the AAS/AIAA Astrodynamics Specialist Conference, 2018.
9	PENG H , BAI X L . Gaussian processes for improving orbit prediction accuracy[J]. Acta Astronautica, 2019, 161 (8): 44- 56.
10	PENG H , BAI X L . Comparative evaluation of three machine learning algorithms on improving orbit prediction accuracy[J]. Astrodynamics, 2019, 3 (4): 325- 343. doi: 10.1007/s42064-018-0055-4
11	PENG H, BAI X L. Limits of machine learning approach on improving orbit prediction accuracy using support vector machine[C]//Proc. of the Advanced Maui Optical and Space Surveillance Techno-logies Conference, 2017.
12	LI B , HUANG J , FENG Y M , et al. A machine learning-based approach for improved orbit predictions of LEO space debris with sparse tracking data from a single station[J]. IEEE Trans.on Aerospace and Electronic Systems, 2020, 56 (6): 4253- 4268. doi: 10.1109/TAES.2020.2989067
13	李晓杰, 潘玲, 郭睿, 等. 基于补偿波形调整的导航卫星轨道预报方法[J]. 武汉大学学报(信息科学版), 2017, 42 (8): 1061- 1067.
	LI X J , PAN L , GUO R , et al. Navigation satellite orbit prediction method based on compensation waveform adjustment[J]. Journal of Wuhan University (Information Science Edition), 2017, 42 (8): 1061- 1067.
14	曹磊. 基于深度神经网络补偿模型的轨道预报技术[D]. 南京: 南京航空航天大学, 2014.
	CAO L. Orbit prediction technology based on deep neural network compensation model[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2014.
15	杨先睿. 基于深度学习的卫星轨道预报算法研究[D]. 哈尔滨: 哈尔滨工业大学, 2019.
	YANG X R. Research on satellite orbit prediction algorithm based on deep learning[D]. Harbin: Harbin Institute of Technology, 2019.
16	朱俊鹏, 赵洪利, 杜鑫, 等. 长短时记忆神经网络在卫星轨道预报中的研究[J]. 兵器装备工程学报, 2017, 38 (10): 127- 132. doi: 10.11809/scbgxb2017.10.026
	ZHU J P , ZHAO H L , DU X , et al. Research on long and short-term memory neural network in satellite orbit prediction[J]. Chinese Journal of Ordnance Equipment Engineering, 2017, 38 (10): 127- 132. doi: 10.11809/scbgxb2017.10.026
17	刁宁辉, 刘建强, 孙从容, 等. 基于SGP4模型的卫星轨道计算[J]. 遥感信息, 2012, 27 (4): 64- 70. doi: 10.3969/j.issn.1000-3177.2012.04.011
	DIAO N H , LIU J Q , SUN C R , et al. Satellite orbit calculation based on SGP4 model[J]. Remote Sensing Information, 2012, 27 (4): 64- 70. doi: 10.3969/j.issn.1000-3177.2012.04.011
18	MORSELLI A , ARMELLIN R , DI LIZIA P , et al. A high order method for orbital conjunctions analysis: sensitivity to initial uncertainties[J]. Advances in space Research, 2014, 53 (3): 490- 508. doi: 10.1016/j.asr.2013.11.038
19	韦栋, 赵长印. SGP4/SDP4模型精度分析[J]. 天文学报, 2009, 50 (3): 332- 339. doi: 10.3321/j.issn:0001-5245.2009.03.010
	WEI D , ZHAO C Y . Accuracy analysis of SGP4/SDP4 model[J]. Acta Astronomica, 2009, 50 (3): 332- 339. doi: 10.3321/j.issn:0001-5245.2009.03.010
20	XU X L , XIONG Y Q . Study on the orbit prediction errors of space objects based on historical TLE data-science direct[J]. Chinese Astronomy and Astrophysics, 2019, 43 (4): 563- 578. doi: 10.1016/j.chinastron.2019.11.007
21	刘卫, 王荣兰, 刘四清, 等. TLE预报精度改进及碰撞预警中的应用[J]. 空间科学学报, 2014, 34 (4): 449- 459.
	LIU W , WANG R L , LIU S Q , et al. Improvement of TLE forecast accuracy and its application in collision warning[J]. Journal of Space Science, 2014, 34 (4): 449- 459.
22	高兴龙, 陈钦, 李志辉, 等. 大型航天器无控飞行轨道衰降预报初步研究[J]. 飞行力学, 2020, (6): 70- 76.
	GAO X L , CHEN Q , LI Z H , et al. Preliminary study on the prediction of uncontrolled flight orbit decline of large spacecraft[J]. Flight Dynamics, 2020, (6): 70- 76.
23	VALLADO D, CRAWFORD P, HUJSAK R, et al. Revisiting spacetrack report #3[C]//Proc. of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2006.
24	LEE B S , PARK J W . Estimation of the SGP4 drag term from two osculating orbit states[J]. Journal of Astronomy & Space Sciences, 2003, 20 (1): 11- 20.
25	许晓丽, 熊永清. 双行根数编目体系轨道误差研究[J]. 天文学报, 2018, 59 (3): 31- 38.
	XU X L , XIONG Y Q . Study on the orbit error of the double-row root number cataloging system[J]. Acta Astronomica, 2018, 59 (3): 31- 38.
26	SANG J , BENNETT J C . Achievable debris orbit prediction accuracy using laser ranging data from a single station[J]. Advances in Space Research, 2014, 54 (1): 119- 124. doi: 10.1016/j.asr.2014.03.012
27	陈国平, 何冰, 张志斌, 等. CPF星历精度分析[J]. 中国科学院上海天文台年刊, 2010, (1): 35- 44.
	CHEN G P , HE B , ZHANG Z B , et al. Accuracy analysis of CPF ephemeris[J]. Annual of Shanghai Observatory Academica sinica, 2010, (1): 35- 44.
28	HOCHREITERS , SCHMIDHUBER J . Long short-term memory[J]. Neural Computation, 1997, 9 (8): 1735- 1780. doi: 10.1162/neco.1997.9.8.1735
29	GRAVES A , SCHMIDHUBER J . Framewise phoneme classification with bidirectional LSTM and other neural network architectures[J]. Neural Networks, 2005, 18 (5-6): 602- 610. doi: 10.1016/j.neunet.2005.06.042
30	BENGIO Y , SIMARD P , FRASCONI P . Learning long-term dependencies with gradient descent is difficult[J]. IEEE Trans.on Neural Networks, 1994, 5 (2): 157- 166. doi: 10.1109/72.279181

NORAD ID	轨道周期/min	轨道倾角/(°)	轨道偏心率	近地点km
16 908	116	50.0	0.001	1 485.9

卫星形状	质量/kg	卫星直径/m	有无动力	远地点/km
球形	685	2.15	无	1 503.7

输入序列步长	输入向量大小	网络层数	神经元个数	预测时长/min	X轴Pml(x)/%	Y轴Pml(y)/%	Z轴Pml(z)/%
150	450	2	650	400	10.26	9.52	9.30
220	660	2	950	800	11.96	13.25	12.36
360	1 080	2	1 500	1 440	16.87	17.66	19.58

输入序列步长	Pml(x)/%	输入序列步长	Pml(x)/%
270	43.13	400	29.81
300	38.10	450	28.79
360	30.45	—	—

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