基于天基光学测量的空间目标轨道确定及其精度分析
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摘要
天基观测相对于地基观测具有更好的覆盖性和实时性,光学测量由于设备质量轻、体积和功耗小且测量精度高,在天基测量中具有很广的应用前景。本文基于天基光学测量,系统分析空间目标轨道确定的问题。
首先,为了直接描述空间目标相对于天基光学平台的运动,基于拉格朗日方程,建立考虑地球J2摄动影响的非线性相对动力学模型,用于空间目标的轨道微分改进和轨道预报。与考虑同样摄动因素的绝对动力学模型进行对比,验证了所建立的相对动力学模型的正确性;同时,还通过数值仿真给出了所建立的非线性相对动力学模型相比于参考模型的误差。
为更真实地模拟天基光学测量数据,详细分析了影响天基光学观测的几何条件和光学条件:地球遮挡条件、地光条件地球阴影条件、日光条件、月光条件以及非直射条件,给出了满足各个条件的具体方程并进行了可观测弧段对比仿真,结果显示对于不同轨道高度的空间目标,各个天基光学可观测条件的影响程度不同。
由于本文所采用的是单纯的光学测量角度信息,在初定轨方法上选择了适用于一种测量信息且形式较为简洁的Laplace方法,并在改进的Laplace方法基础上,考虑了摄动的影响,推导给出了考虑摄动影响下的天基光学测量初定轨条件方程;对于初值的选取,考虑J2项摄动的影响,并在牛顿迭代基础上进行Aitken迭代加速,提高初值求取的精度和收敛速度。同时,针对天基观测弧段破碎的特点,通过仿真对短弧段初轨确定的进行了误差分析。
为了实现空间目标编目,在初定轨的基础上基于最小二乘(LS)原理对多个弧段的测量信息进行批处理,利用牛顿迭代法实现空间目标的轨道改进。针对新发现的空间目标和已编目的空间目标两种情况,利用非线性相对动力学模型实现定轨和轨道预报,仿真结果显示,非线性相对动力学模型可以用于引导天基光学敏感器完成空间监视任务,本文提出的利用非线性相对动力学模型实现空间目标轨道确定的方法是可行的。
最后,通过仿真分析了天基光学平台轨道高度、空间目标轨道高度、观测弧长和采样周期对轨道确定精度的影响。
Space-based surveillance owns advantages of ground-based surveillance in monitoring coverage and real-time performance. And due to optical equipment’s light weight, small size and low power consumption, optical measurement is used in space-base surveillance with great application prospects. This thesis focus on the orbit determination of space objects base on space-based surveillance, and proposes using the nonlinear relative dynamic model in orbit improvement and prediction.
First of all, nonlinear relative dynamic model is established based on Lagrange equation, taking the Earth J2 perturbation into consideration. This dynamic model is used in orbit improvement and prediction. Comparison with the absolute dynamic model considering the same factor proves that the nonlinear relative dynamic model can be used to describe the relative emotion between the space object and space-based optical platform. Besides, error between nonlinear relative dynamic model and the reference model is calculated.
Then the observing conditions are analyzed to simulated space-based optical measurement data correctly. The Earth’s shelter and shade, the Earth’s light condition, the Moon’s light condition, the Sun’s light condition and indirection condition are taking into consideration. Corresponding specific equations are give and simulations are taken to analyzed the affections of each observing condition on observations arc.
As the observational data used here is simply optical angle information, Laplace method, which is simple and suit for observational data of one type, is used in initial orbit determination. Based on the improved Laplace method, perturbations are taken into consideration to better the initial orbit determination method’s accuracy. And the initial value for iteration is obtained by Newton iteration accelerated by Aitken method, considering the Earth J2 perturbation. Besides, simulations are taken to analyze the ill-condition performance in initial orbit determination using short arc data.
Principle of least square and Newton iteration are used to handle several observations arc data to improve the accuracy of initial orbit determination. The nonlinear relative dynamic model is used in orbit determination and prediction in the simulations of new space objects and objects cataloged, simulation results shows that the idea using nonlinear relative dynamic model in orbit determination and prediction based on space-based optical measurement data is practicable.
At last, based on all the theories above, simulations are taken to analyze the orbit height of space-based optical platform and space object, observation arc length and sample period’s impact on the orbit determination accuracy.
首先,为了直接描述空间目标相对于天基光学平台的运动,基于拉格朗日方程,建立考虑地球J2摄动影响的非线性相对动力学模型,用于空间目标的轨道微分改进和轨道预报。与考虑同样摄动因素的绝对动力学模型进行对比,验证了所建立的相对动力学模型的正确性;同时,还通过数值仿真给出了所建立的非线性相对动力学模型相比于参考模型的误差。
为更真实地模拟天基光学测量数据,详细分析了影响天基光学观测的几何条件和光学条件:地球遮挡条件、地光条件地球阴影条件、日光条件、月光条件以及非直射条件,给出了满足各个条件的具体方程并进行了可观测弧段对比仿真,结果显示对于不同轨道高度的空间目标,各个天基光学可观测条件的影响程度不同。
由于本文所采用的是单纯的光学测量角度信息,在初定轨方法上选择了适用于一种测量信息且形式较为简洁的Laplace方法,并在改进的Laplace方法基础上,考虑了摄动的影响,推导给出了考虑摄动影响下的天基光学测量初定轨条件方程;对于初值的选取,考虑J2项摄动的影响,并在牛顿迭代基础上进行Aitken迭代加速,提高初值求取的精度和收敛速度。同时,针对天基观测弧段破碎的特点,通过仿真对短弧段初轨确定的进行了误差分析。
为了实现空间目标编目,在初定轨的基础上基于最小二乘(LS)原理对多个弧段的测量信息进行批处理,利用牛顿迭代法实现空间目标的轨道改进。针对新发现的空间目标和已编目的空间目标两种情况,利用非线性相对动力学模型实现定轨和轨道预报,仿真结果显示,非线性相对动力学模型可以用于引导天基光学敏感器完成空间监视任务,本文提出的利用非线性相对动力学模型实现空间目标轨道确定的方法是可行的。
最后,通过仿真分析了天基光学平台轨道高度、空间目标轨道高度、观测弧长和采样周期对轨道确定精度的影响。
Space-based surveillance owns advantages of ground-based surveillance in monitoring coverage and real-time performance. And due to optical equipment’s light weight, small size and low power consumption, optical measurement is used in space-base surveillance with great application prospects. This thesis focus on the orbit determination of space objects base on space-based surveillance, and proposes using the nonlinear relative dynamic model in orbit improvement and prediction.
First of all, nonlinear relative dynamic model is established based on Lagrange equation, taking the Earth J2 perturbation into consideration. This dynamic model is used in orbit improvement and prediction. Comparison with the absolute dynamic model considering the same factor proves that the nonlinear relative dynamic model can be used to describe the relative emotion between the space object and space-based optical platform. Besides, error between nonlinear relative dynamic model and the reference model is calculated.
Then the observing conditions are analyzed to simulated space-based optical measurement data correctly. The Earth’s shelter and shade, the Earth’s light condition, the Moon’s light condition, the Sun’s light condition and indirection condition are taking into consideration. Corresponding specific equations are give and simulations are taken to analyzed the affections of each observing condition on observations arc.
As the observational data used here is simply optical angle information, Laplace method, which is simple and suit for observational data of one type, is used in initial orbit determination. Based on the improved Laplace method, perturbations are taken into consideration to better the initial orbit determination method’s accuracy. And the initial value for iteration is obtained by Newton iteration accelerated by Aitken method, considering the Earth J2 perturbation. Besides, simulations are taken to analyze the ill-condition performance in initial orbit determination using short arc data.
Principle of least square and Newton iteration are used to handle several observations arc data to improve the accuracy of initial orbit determination. The nonlinear relative dynamic model is used in orbit determination and prediction in the simulations of new space objects and objects cataloged, simulation results shows that the idea using nonlinear relative dynamic model in orbit determination and prediction based on space-based optical measurement data is practicable.
At last, based on all the theories above, simulations are taken to analyze the orbit height of space-based optical platform and space object, observation arc length and sample period’s impact on the orbit determination accuracy.
引文
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[2]李颖,张占月,方季花.空间目标监视系统发展现状及展望[J].国际太空,2004,6:28-32
[3]乔凯,王志乐,丛明煜.空间目标天基与地基监视系统对比分析[J].光学技术,2006,32(5):744-749
[4]王杰娟,于小红.国外天基空间目标监视研究现状与特点分析[J].装备指挥技术学院学报,2006,17(4):33-37
[5]周海银,潘小刚,李董辉.基于天基空间目标监视系统的定轨技术研究[J].系统仿真学报,008,20(13):3538-3547
[6]李强.单星对卫星目标的被动定轨与跟踪关键技术研究[D].长沙:国防科技大学研究生院,2007
[7]杨嘉屏,范秦鸿,张云彤等.航天器轨道动力学与控制(上)[M].北京:宇航出版社,1995
[8]余建慧,苏增立,谭谦.空间目标天基光学测量模式分析.量子电子学报,2006, 23(6):772-776
[9] Seiji Katagiri , Yousuke Yamamoto . Technology of Precise Orbit Determination.FUJITSU Sci. Tech.J,2008,44(4):401-409
[10] Jayant Sharma,Grant H. Stokes,Curt von Braun, George Zollinger,Andrew J. Wiseman.Toward Operational Spaced-Based Space Surveillance.Lincoln Laboratory Journal,2002,13(2):309-333
[11] Kawase K,Ogawa Y,Watanable Y, et al.Non-destructive tera-hertz imaging of illicit drugs using spectral fingerprints[J].Optics Express,2003,11(20):2549-2554
[12] Robert Shishko.NASA Systems Engineering Handbook [R].NASA 2004,98-112
[13] Stokes,Von Braun,Sridharan,Harrison,and Sharma.The Space-Based Visible Program.Lincoln Laboratory Journal.1998,11(2):205-23
[14]于志坚.航天测控系统工程[M].国防工业出版社,2008:290-292
[15] E. Michael Gaposchkin, Curt von Braun, and Jayant Sharma.Space-Based Space Surveillance with the Space-Based Visible.Journal of Guidance,control,and Dynamics, 2000,23(1):148-152
[16]何立萍.国外空间侦查监视系统的发展[J].航天电子对抗,2007,23(6):7-11
[17] Jayant Sharma.Space-Based Visible Space Surveillance Performance.Journal of Guidance,control,and Dynamics,2000,23(1):153-158
[18]张晓玲,张宝峰.基于光轴垂直双目例题视觉系统的物体运行姿态研究[J].光电子?激光,010,21(11):1693-1697
[19]张栋.天基信息系统的资源建模与能力计算方法研究[D].长沙:国防科技大学研究生院,2007
[20]钱宗峰,张更新.建立我军天基信息系统的几点思考[J].国防技术基础,2005,(1):19-21
[21]谭莹.天基空间目标探测技术[J].空间电子技术,2006(3):5-9
[22] Sridharan R, PensaA F.Space surveillance network capabilities.Proceedings of SPIE - The International Society for Optical Engineering.1998, 34:88~100
[23]李焱,康开华.美国空间监视系统最新发展及趋势分析[J].航天器工程,2008,17(2):76-81
[24] United StatesAir Force Scientific Advisory Board Report.Space surveillance asteroids and comets and space.Volume I:Space Surveillance.SAB-TR-96-04,June 1997
[25] StokesG H , von Braun C , Sridharan R , etc . The space-based visible program.Lincoln Laboratory Journal,1998,11(2):205-238
[26] Harrison D C and Chow J C?The space based visible sensor.Johns Hopkins Apl Technical Digest,1996,17(2):226-236
[27] StokesG H,VigghHerbertEm,KentP J.Space-based visible (SBV) surveillance data verification and telemetry processing.InternationalTelemetering Conference (Proceedings),1996,32:477-484
[28] BurnhamW F,morton F E,Sridharan R,etc.Mission planning for space-based surveillancewith the Space-Based Visible sensor.Journal ofGuidance, Control and Dynamics,2000,23(1):165-169
[29] Von Braun C,Jayant S,michaelG E.Space-Based Visiblemetric accuracy.Journal ofGuidance,Control and Dynamics,2000,23(1):175~181
[30]李骏.空间目标天基光学监视跟踪关键技术研究[D].长沙:国防科技大学研究生院,2009
[31]朱彦伟.航天器近距离相对运动轨迹规划与控制研究[D].长沙:国防科技大学研究生院,2009
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