基于月球平动点轨道的星座自主定轨研究
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摘要
随着空间科学技术的发展,平动点及其附近的周期和拟周期轨道得到了越来越多的应用和重视。在探月热潮的大背景下,本文利用Halo轨道与绕月轨道的力模型差异及其独特的空间构型,研究了在没有地面支持的情况下,由绕月低轨卫星LMO和Halo轨道飞行器组成两星星座,利用星间观测SST实现星座自主定轨的可行性,为月球探测和重力场反演等任务中的精密轨道确定(特别是月球背面)提供了新的途径。论文的主要结论有:
1、引入稳定系数和线性稳定阶数两个指标来判断周期轨道的稳定性,分析了地月系L1点和L2点附近Halo轨道族的运动稳定性,为星座中Halo轨道的选取提供了参考依据。
2、从力模型和轨道形态等方面深入探讨了Halo轨道与传统二体轨道的本质差异,揭示并利用数值仿真验证了LMO-LL2Halo星座及LMO-LL1Halo星座的系统可观性。
3、基于运动稳定性和结构稳定性的双重影响,考察了Halo轨道的选取对定轨精度的影响。首先,星座自主定轨精度与Halo轨道族的运动稳定性密切相关,其次,即使是稳定阶数为0(运动稳定性最好)的某些Halo轨道,距离月球越近,系统的结构稳定性越差,定轨结果也相应变差。
4、仿真分析了LMO-LL2Halo星座的自主定轨精度。若仅采用测距观测量并忽略测距系统偏差,采用10天的定轨弧段,星座中LMO卫星的定轨精度优于Halo卫星的定轨精度。LMO卫星在R/T/N方向的定轨精度均在米级,Halo卫星则优于20m,T方向精度最差。轨道外推15天,LMO定轨精度仍在米级,Halo卫星的定轨精度则在百米级。
5、采用附加先验信息的方法能够改善测距系统偏差自校准能力差的特性。测距系统偏差在30米以内时,LMO卫星的定轨精度在米级,Halo卫星的定轨精度优于30米。轨道外推15天,LMO卫星的定轨精度变化不大,均保持在米级,Halo卫星的定轨精度受测距系统偏差的影响较大。测距系统偏差越小,定轨结果越好。当测距系统偏差为10米时,Halo卫星的定轨精度在百米之内。
6、测距观测量与测速观测量进行联合定轨时,采用一定精度的测速观测量能够提高定轨精度。定轨结果受测速观测量精度的影响;测速观测量的精度为1mm/s时,测距系统偏差对定轨结果影响不大。
With the development of space science and technology, libration points and its nearby orbits and quasi-periodic orbits have been more and more applications. Halo orbit has its unique configuration in the space, and there are differences in the force model between Halo orbit and lunar orbit. In the background of Lunar detection, This paper study the system feasibility of the Lunar-Halo orbit satellite constellation in the situation in the absence of ground support, which may provides a new way for the precise orbit determination in lunar exploration, especially the observation on the back of the moon.
Main conclusions of the paper are:
1. Stability Index and Linear Stability Order are introduced to judge orbits’stability. The stability of Halo orbit near the L1and L2 point in the Earth-Moon system is analyzed, providing a selected basis of Halo orbit in the Lunar-Halo orbit satellite constellation.
2. Analyze the characteristic of force model and configuration in Halo and two-body orbits, and then prove the system observability of the LMO-LL2Halo and LMO-LL1Halo orbit satellites constellations by numerical simulation.
3. The selection of Halo orbit has influences in the result of orbit determination. The stability of Halo orbit affects the result. When the Halo orbit is close to the moon, even if the Linear Stability Order is 0, orbit determination results will be affected due to poor structural stability of orbits.
4. Regardless of the ranging system bias and velocity observables, the orbit determination accuracy of LMO in the direction of R/T/N are in meter-scale in the statistical observation arc, and the orbit determination accuracy of Halo satellite are better than 20 meters, in which the direction accuracy for both T are worse than the other two directions. The orbit determination accuracy of LMO satellite is better than Halo satellite’s. Track extrapolation 15 days, LMO orbit determination accuracy is in meter-scale, and Halo satellite orbit determination accuracy is in 100 m level.
5. Using the method of additional prior information can improve the ranging system bias from the characteristics of poor self calibration. When ranging system bias is within 30 meters, the orbit determination accuracy of LMO satellite is in meter-scale in statistical observation arc, and the orbit determination accuracy of Halo satellite is better than 30 meters. Track extrapolation 15 days, the orbit determination accuracy of LMO satellite changes little, remaining in the meter-scale, and the orbit determination of Halo Satellite has great influences by the ranging system bias. The orbit results are better when ranging system bias is smaller. When the ranging system bias is within 10 meters, the determination accuracy of Halo satellite orbit is within 100 meters.
6. Combined orbit with distance measurement and velocity measurements for orbit determination can improve precision of orbit determination, when the velocity measurements have certain accuracy. Higher the accuracy of the velocity measurements are, better the orbit determination results are; when the velocity measurements with an accuracy of 1 mm/s, the distance measuring system error has little effect on the orbit results.
1、引入稳定系数和线性稳定阶数两个指标来判断周期轨道的稳定性,分析了地月系L1点和L2点附近Halo轨道族的运动稳定性,为星座中Halo轨道的选取提供了参考依据。
2、从力模型和轨道形态等方面深入探讨了Halo轨道与传统二体轨道的本质差异,揭示并利用数值仿真验证了LMO-LL2Halo星座及LMO-LL1Halo星座的系统可观性。
3、基于运动稳定性和结构稳定性的双重影响,考察了Halo轨道的选取对定轨精度的影响。首先,星座自主定轨精度与Halo轨道族的运动稳定性密切相关,其次,即使是稳定阶数为0(运动稳定性最好)的某些Halo轨道,距离月球越近,系统的结构稳定性越差,定轨结果也相应变差。
4、仿真分析了LMO-LL2Halo星座的自主定轨精度。若仅采用测距观测量并忽略测距系统偏差,采用10天的定轨弧段,星座中LMO卫星的定轨精度优于Halo卫星的定轨精度。LMO卫星在R/T/N方向的定轨精度均在米级,Halo卫星则优于20m,T方向精度最差。轨道外推15天,LMO定轨精度仍在米级,Halo卫星的定轨精度则在百米级。
5、采用附加先验信息的方法能够改善测距系统偏差自校准能力差的特性。测距系统偏差在30米以内时,LMO卫星的定轨精度在米级,Halo卫星的定轨精度优于30米。轨道外推15天,LMO卫星的定轨精度变化不大,均保持在米级,Halo卫星的定轨精度受测距系统偏差的影响较大。测距系统偏差越小,定轨结果越好。当测距系统偏差为10米时,Halo卫星的定轨精度在百米之内。
6、测距观测量与测速观测量进行联合定轨时,采用一定精度的测速观测量能够提高定轨精度。定轨结果受测速观测量精度的影响;测速观测量的精度为1mm/s时,测距系统偏差对定轨结果影响不大。
With the development of space science and technology, libration points and its nearby orbits and quasi-periodic orbits have been more and more applications. Halo orbit has its unique configuration in the space, and there are differences in the force model between Halo orbit and lunar orbit. In the background of Lunar detection, This paper study the system feasibility of the Lunar-Halo orbit satellite constellation in the situation in the absence of ground support, which may provides a new way for the precise orbit determination in lunar exploration, especially the observation on the back of the moon.
Main conclusions of the paper are:
1. Stability Index and Linear Stability Order are introduced to judge orbits’stability. The stability of Halo orbit near the L1and L2 point in the Earth-Moon system is analyzed, providing a selected basis of Halo orbit in the Lunar-Halo orbit satellite constellation.
2. Analyze the characteristic of force model and configuration in Halo and two-body orbits, and then prove the system observability of the LMO-LL2Halo and LMO-LL1Halo orbit satellites constellations by numerical simulation.
3. The selection of Halo orbit has influences in the result of orbit determination. The stability of Halo orbit affects the result. When the Halo orbit is close to the moon, even if the Linear Stability Order is 0, orbit determination results will be affected due to poor structural stability of orbits.
4. Regardless of the ranging system bias and velocity observables, the orbit determination accuracy of LMO in the direction of R/T/N are in meter-scale in the statistical observation arc, and the orbit determination accuracy of Halo satellite are better than 20 meters, in which the direction accuracy for both T are worse than the other two directions. The orbit determination accuracy of LMO satellite is better than Halo satellite’s. Track extrapolation 15 days, LMO orbit determination accuracy is in meter-scale, and Halo satellite orbit determination accuracy is in 100 m level.
5. Using the method of additional prior information can improve the ranging system bias from the characteristics of poor self calibration. When ranging system bias is within 30 meters, the orbit determination accuracy of LMO satellite is in meter-scale in statistical observation arc, and the orbit determination accuracy of Halo satellite is better than 30 meters. Track extrapolation 15 days, the orbit determination accuracy of LMO satellite changes little, remaining in the meter-scale, and the orbit determination of Halo Satellite has great influences by the ranging system bias. The orbit results are better when ranging system bias is smaller. When the ranging system bias is within 10 meters, the determination accuracy of Halo satellite orbit is within 100 meters.
6. Combined orbit with distance measurement and velocity measurements for orbit determination can improve precision of orbit determination, when the velocity measurements have certain accuracy. Higher the accuracy of the velocity measurements are, better the orbit determination results are; when the velocity measurements with an accuracy of 1 mm/s, the distance measuring system error has little effect on the orbit results.
引文
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[6]黄颖.“嫦娥一号”探月卫星顺利升空我国无线电管理部门提供重要保障[J]. 2007(11): 1.
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[8]郑为民杨艳. VLBI软件相关处理机研究进展及其在深空探测中的应用[J].世界科技研究与发展. 2005, 27(5): 7-15.
[9] R.W. Farquhar, D.W. Dunham, Guo Yan-ping and V.J. Madams. Utilization of libration points for human exploration in the sun-earth-moon system and beyond[J]. Acta Astronautica, 2004(55):687-700.
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[13]陈金平,尤政,焦文海.基于星间距离和方向观测的导航卫星自主定轨研究[J].宇航学报. 2005, 26(1):43-46.
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[22]马高峰.地-月参考系及其转换研究[D].解放军信息工程大学测绘学院, 2005.
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[24]刘林,胡松杰,王海红.人造地球卫星精密定轨[M].南京:南京大学天文系, 2004: 54, 73-75.
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[28]周济林,天体力学基础[M].南京:南京大学天文系,2003.
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[30] G.Gomez, J.Masdemont and C.Simo. QuasiHalo Orbits Associated With Libration Points[J], Journal of Astronautical Sciences, 42(2), 1998:135-176.
[31]张守余.地月系共线平动点附近的周期和拟周期轨道理论[D].郑州,解放军信息工程大学测绘学院, 2009.
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[33]赵砚,易东云,潘晓刚,李贞杰.基于天基光学观测的空间目标可见性分析[J].飞行器测控学报, 2007, 26(3): 5-12.
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[2] D.W. Dunham and R.W. Farquhar, Libration Point Missions[R], Johns Hopkins University, Applied Physics Laboratory, 1978– 2002.
[3]北晨.我国将发射“夸父”卫星“逐日”[J].军民两用技术与产品. 2006(9): 9.
[4]庞之浩.英德探月计划及航天国际合作简析[J].中国航天. 2007(12): 33-37.
[5]康娟.日发射首颗探月卫星[J].新世纪领导者. 2007(9): 61.
[6]黄颖.“嫦娥一号”探月卫星顺利升空我国无线电管理部门提供重要保障[J]. 2007(11): 1.
[7]平劲松河野裕介河野宣之花田英夫松本晃治Rise Group.日本SELENE月球探测计划和卫星间多普勒跟踪的数学模型[J].天文学进展. 2001, 19(3): 354-364.
[8]郑为民杨艳. VLBI软件相关处理机研究进展及其在深空探测中的应用[J].世界科技研究与发展. 2005, 27(5): 7-15.
[9] R.W. Farquhar, D.W. Dunham, Guo Yan-ping and V.J. Madams. Utilization of libration points for human exploration in the sun-earth-moon system and beyond[J]. Acta Astronautica, 2004(55):687-700.
[10] M.P. Ananda, et a1. Global positioning system (GPS) autonomous navigation[A]. IEEE Position Location and Navigation Symposium [C]. 1990.:435-455.
[11] H.B. Bemstein, et a1. GPS user positioning accuracy with Black IIR autonomous navigation (Autonav)[A]. Proceedings of the ION GPS-93[C]. Salt Lake City, UT, 1993:235-250.
[12]刘林,刘迎春.关于星-星相对测量自主定轨中的亏秩问题[J] .飞行器测控学报.2000,19(3):13-16.
[13]陈金平,尤政,焦文海.基于星间距离和方向观测的导航卫星自主定轨研究[J].宇航学报. 2005, 26(1):43-46.
[14] M. Beckman,“Orbit Determination Issues for Libration Point Orbits,”Libration Point Orbits and Applications, Parador d’Aiguablava, Girona, Spain, Jun. 10-14, 2002.
[15] K. Hill and G. Born,“Autonomous Interplanetary Orbit Determination Using Satellite-to-Satellite Tracking,”Journal of Guidance, Control, and Dynamics, Volume 30(3), 2007.
[16] K. Hill, M. W. Lo, and G. H. Born,“Linked, Autonomous, Interplanetary Satellite Orbit Navigation (LiAISON),”AAS 05-399, AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, CA, Aug. 7-11, 2005.
[17]雷辉.单颗导航卫星定轨研究[D].中国科学院研究生院, 2007.
[18]夏一飞.球面天文学[M].南京:南京大学出版社, 2000.
[19]李济生.人造卫星精密轨道确定[M].北京:解放军出版社, 1995.
[20]刘林,胡松杰,王歆.航天动力学引论[M].南京:南京大学出版社, 2005.
[21]刘林,王歆.月球探测器轨道力学[M].北京:国防工业出版社, 2006.
[22]马高峰.地-月参考系及其转换研究[D].解放军信息工程大学测绘学院, 2005.
[23] K.A. Hill. Autonomous Navigation in Libration Point Orbits[D]. University of Colorado, Boulder, 2007.
[24]刘林,胡松杰,王海红.人造地球卫星精密定轨[M].南京:南京大学天文系, 2004: 54, 73-75.
[25] R.S. Bucy, K.D. Renne. Digital synthesis of nonlinear filter[J], Automatica, 1971,7(3):287-289.
[26]刘林,王海红,胡松杰.卫星定轨综述[J].飞行器测控学报. 2005. Vol. 24 No. 2:28-34
[27]刘林,侯锡云,王海红.关于共线平动点的特征及其在深空探测中的应用[J],天文学进展, 2006, Vol. 24 No. 2.
[28]周济林,天体力学基础[M].南京:南京大学天文系,2003.
[29] D.L. Richardson. Analytic construction of Periodic Orbits about the collinear points[J]. Celestial Mechanics. Volume 22, 1980:241-253.
[30] G.Gomez, J.Masdemont and C.Simo. QuasiHalo Orbits Associated With Libration Points[J], Journal of Astronautical Sciences, 42(2), 1998:135-176.
[31]张守余.地月系共线平动点附近的周期和拟周期轨道理论[D].郑州,解放军信息工程大学测绘学院, 2009.
[32] E.T. Campbell. Bifurcations from Families of Periodic Soultions in the CRTBP with Application to Trajectory Design [D], Purdue University, 1999.
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