低轨空间目标雷达探测信息处理技术
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摘要
低轨空间目标监测是进行空间态势感知、碰撞预警的重要基础，是利用空间资源、实现在轨空间安全的基本保证。构建低轨空间监测系统，实现低轨道目标的编目和跟踪任务具有重要意义。其中，探测信息处理是监测系统的核心，针对探测信息处理的技术研究不仅能够有效提升当前系统性能，适应未来监测需求，同时也可以从理论上指导构建更加合理的监测系统。
地基雷达作为低轨空间监测的主要设备，是获取低轨空间目标观测数据的主要来源。本文以低轨空间目标雷达监测系统，尤其是新的篱笆型监测雷达系统为研究背景，针对雷达监测系统构造过程中探测信息处理的关键技术和未来监测需求中具有普适性的前沿问题开展研究，主要的研究工作和取得的一些成果如下：
首先，分析了低轨空间目标环境，按照对空间目标属性认知的层次综述了低轨空间目标监测技术的发展现状和趋势，并阐述了低轨空间目标雷达探测信息处理的难点问题。此外，还对低轨空间目标的轨道运动特性和雷达探测模型的交叉学科的基础知识进行了梳理。
其次，研究了基于篱笆型雷达监测系统的弱小目标信号检测和参数估计问题。首先介绍了空间目标的雷达观测模型，分析了目标穿越波束屏障的稀疏特性，并通过轨道知识挖掘了篱笆型体制下目标的方位角和径向加速度的耦合关系，将原有的三维空间重构问题降维到二维空间，从而提升计算效率，改善重构精度。在此基础上，提出了用于弱小目标信号检测和参数估计的含轨道知识约束的稀疏重构方法。最后通过理论分析和大量仿真实验评估了正确稀疏重构概率、参数选择对估计精度影响，并对多目标的分辨能力进行了分析，结果表明了算法在低信噪比下优越的信号检测和参数估计性能和超分辨能力。
然后，研究了双屏篱笆体制的空间监测雷达的屏间数据关联问题。首先对双屏监测雷达体制进行了阐述，以信息集合的方式描述了观测数据。在此基础上，分析了信息集合所要满足的轨道知识约束条件，基于假设检验的方式，提出了利用不同假设关联集合表现在关联量，即径向速度上的差异程度对数据进行关联的方法。之后，基于建立的简化场景从理论上分析了算法在三维空间上的目标分辨能力。最后利用NORAD发布的轨道根数及仿真数据验证了算法的有效性，特别是对Iridium33和Cosmos2251碰撞产生的高密度碎片云进行数据关联时，表现出了很高的正确关联率。
之后，研究了含机动检测的多目标轨道相关技术。本文将机动检测和轨道相关作为两个不可分离的问题同时进行解决，更加符合实际情况。首先建立了一次切向速度方向变轨的目标运动模型和观测模型，然后提出了基于最大后验概率准则进行含机动检测的轨道相关原理和方法。为了计算最大后验概率，首先通过二阶锥规划算法求解了含约束的非线性最小二乘问题，实现了对机动参数的精确估计，其次通过JPDA算法计算最大后验概率，进行了机动事件的判别和轨道相关事件的确认。最后，通过理论推导和仿真实验对机动检测性能和关联性能进行了分析，验证了算法的有效性，同时对本文算法可推广应用的场景进行了阐释。
最后，研究了低轨空间群目标的跟踪技术。首先介绍了群目标的运动模型和观测模型，提出了含群中心的最优贝叶斯跟踪滤波器。在此基础上，通过贝叶斯原理，将贝叶斯滤波器分解为目标状态预测模型、群中心预测模型，观测概率模型、群中心和目标间相互作用的马尔科夫随机场(MRF)模型，并进行了详细的说明和求解。特别是通过建立群中心与目标间相互作用的MRF模型，使得我们既能够描述群目标整体运动趋势，又可以提升个体轨迹的跟踪精度。然后通过MCMC-Particle粒子滤波算法对以上贝叶斯跟踪滤波器进行实现，并分析了跟踪性能。最后又引入群的分离与合并机制，使得算法具备对多个群进行灵活跟踪的能力，提升了算法的实际应用价值，大量仿真结果表明了算法在低数据率、高杂波环境下的优越性能。
Low earth orbit (LEO) space surveillance systems are playing a crucial andfundamental role to support important functionalities of the space situational awarenessand orbital collision avoidance, which provide the guarantees for efficient utilization ofthe space resources and safety of the movements of the on-orbit spacecrafts. Theconstruction of an effective LEO space surveillance system that undertakes thecataloging and tracking tasks for LEO space objects is very important and challenging.Moreover, the information processing approach is a core component in any surveillancesystem. The investigation on information processing techniques will improve not onlyon the performances of the existing systems to satisfy the future needs of theestablishments of space surveillance systems, but also get a better understanding ontheoretical developments of more effective surveillance systems.
Serving as a major instrument of LEO space surveillance systems, theground-based radar systems are the dominating sources where the measurement data ofLEO space objects can be obtained. Therefore, the radar systems of a LEO spacesurveillance system, especially an emerging fence-type surveillance radar system, havebeen taken as the fundamental infrastructure in this thesis. Based on such aninfrastructure, we investigate the key techniques of information processing to constructa radar surveillance system and the general problems with frontiers to satisfy the futuredemands of space surveillance systems. The main results and contributions aresummarized as follows.
Firstly, the LEO space object environments are theoretically analyzed thatfollowed by the introductions of the development status and tendency of thesurveillance technologies of the LEO space objects based on the cognition progress forspace objects’ characteristics. The main challenging issues in the informationprocessing for exploring the LEO space objects by using a radar system are alsoelaborated. In addition, the basic interdisciplinary knowledge including the orbitalmovements and radar exploring technologies are also refined.
Secondly, the methodologies of signal detection and parameter estimation for thesmall space objects based on a fence-type space surveillance radar system areinvestigated. Moreover, the observation model of space objects based on the fence-typeradar system is also introduced. The sparse characteristics of space objects crossing thebeam fence are analyzed. Furthermore, the reconstruction problem in originalthree-dimensional space can be reduced into two-dimensional space by carefullyanalyzing the relations between the acceleration and the directions of arrival for thecorresponding LEO space debris based on a fence-type surveillance system, which canachieve a higher efficiency and improve the reconstruction accuracy. According to these, a sparse reconstruction method involving the orbital knowledge constraint is proposedfor the signal detection and parameter estimation of the small objects. Finally, thecorrect sparse reconstruction probability and the estimation accuracy affected by thevalue of selected parameters are evaluated by theoretical analysis and numeroussimulations. In addition, the resolution capability for multiple objects is also analyzed.The results demonstrate the robustness of the approach in scenarios with a lowSignal-to-Noise Ratio (SNR) and the super-resolution properties.
Subsequently, the data association problem for LEO space debris surveillancebased on a double fence radar system is also investigated. The surveillance mechanismsof a double fence radar system are elaborated that followed by the descriptions of theobservation data by using the information sets. Based on these constructions, weanalyze the set of orbital constraints on the LEO space debris in which the informationsets have to be satisfied. Moreover, combining with the hypothesis test methods, a noveldata association scheme is implemented by analyzing the discrepancy of the associationvariables, i.e. radial velocities, which are calculated according to the differenthypothetical associated sets. Furthermore, we also derive a theoretical analysis of theresolution performance in three-dimensional space for our proposed schemes. Thesuperiority and the effectiveness of our novel data association scheme are demonstratedby experimental results. The data used in our experiments is the LEO space debriscatalog produced by the North American Air Defense Command (NORAD) up to2009,especially for scenarios with high densities of LEO space debris, which were primarilyproduced by the collisions between Iridium33and Cosmos2251, which highly supportthe demonstration of the double fence space surveillance radar system.
In this thesis, we also explore the orbit correlation approach including themaneuver detection problems. We integrate these two problems mentioned above intoone interrelated problem, and consider them simultaneously under a scenario wherespace objects only perform a single in-track orbital maneuver during the time intervalsbetween observations. More precisely, we mathematically formulate such an integratedproblem as the Maximum A-Posteriori Probability (MAP) estimation. To solve theMAP estimation, the maneuvering parameters are firstly estimated by optimally solvingthe constrained non-linear least squares iterative process based on a Second-order ConeProgramming (SOCP) algorithm. Subsequently, the corresponding posterior probabilityof an orbital maneuver and a joint association event can be approximately calculated bythe Joint Probabilistic Data Association (JPDA) algorithm. The desired solution hasbeen derived based on the MAP criterions. The performances and advantages of theproposed approaches have been shown by both theoretical analysis and simulationresults. We have to address that the proposed algorithms can be adapted and extended tomany different situations.
Finally, the group tracking methods of LEO space objects are studied as well. In this chapter, we firstly introduce the orbital movement model and the observation modelof group objects and propose the optimal Bayesian tracking filtering involving groupcenter. Subsequently, due to the Bayesian theorem, the Bayesian tracking procedure canbe broke down into some detailed modules including the state transition model of spaceobjects, the state transition model of the group centers, the interaction Markov RandomField (MRF) model between group centers and individual trajectories, and the posteriordensity model of observations. We mainly focus on how to use the interaction MRFmodel between group centers and individual trajectories. It has been shown that we canobtain not only a more robust estimation of object numbers and improve the accuracy ofthe estimated corresponding individual trajectory, but also depict the evolution of thegroups under scenarios with the low object detection probabilities. MCMC-Particlealgorithm has been utilized to calculate the Bayesian integral and fulfill group tracking.Furthermore, the mechanism for group configuration inference has been incorporatedinto our approach that makes the operations of merge and split for groups much moresmart and efficient during the tracking process. We also show that the proposedalgorithm has significant impacts for the practical applications. Finally, we evaluate theperformances of our algorithms by the simulations of tracking multiple closely spacedorbital objects. The results verified the effectiveness of our proposed schemes for thescenarios with a low detection probability in a high dense clutter.
地基雷达作为低轨空间监测的主要设备，是获取低轨空间目标观测数据的主要来源。本文以低轨空间目标雷达监测系统，尤其是新的篱笆型监测雷达系统为研究背景，针对雷达监测系统构造过程中探测信息处理的关键技术和未来监测需求中具有普适性的前沿问题开展研究，主要的研究工作和取得的一些成果如下：
首先，分析了低轨空间目标环境，按照对空间目标属性认知的层次综述了低轨空间目标监测技术的发展现状和趋势，并阐述了低轨空间目标雷达探测信息处理的难点问题。此外，还对低轨空间目标的轨道运动特性和雷达探测模型的交叉学科的基础知识进行了梳理。
其次，研究了基于篱笆型雷达监测系统的弱小目标信号检测和参数估计问题。首先介绍了空间目标的雷达观测模型，分析了目标穿越波束屏障的稀疏特性，并通过轨道知识挖掘了篱笆型体制下目标的方位角和径向加速度的耦合关系，将原有的三维空间重构问题降维到二维空间，从而提升计算效率，改善重构精度。在此基础上，提出了用于弱小目标信号检测和参数估计的含轨道知识约束的稀疏重构方法。最后通过理论分析和大量仿真实验评估了正确稀疏重构概率、参数选择对估计精度影响，并对多目标的分辨能力进行了分析，结果表明了算法在低信噪比下优越的信号检测和参数估计性能和超分辨能力。
然后，研究了双屏篱笆体制的空间监测雷达的屏间数据关联问题。首先对双屏监测雷达体制进行了阐述，以信息集合的方式描述了观测数据。在此基础上，分析了信息集合所要满足的轨道知识约束条件，基于假设检验的方式，提出了利用不同假设关联集合表现在关联量，即径向速度上的差异程度对数据进行关联的方法。之后，基于建立的简化场景从理论上分析了算法在三维空间上的目标分辨能力。最后利用NORAD发布的轨道根数及仿真数据验证了算法的有效性，特别是对Iridium33和Cosmos2251碰撞产生的高密度碎片云进行数据关联时，表现出了很高的正确关联率。
之后，研究了含机动检测的多目标轨道相关技术。本文将机动检测和轨道相关作为两个不可分离的问题同时进行解决，更加符合实际情况。首先建立了一次切向速度方向变轨的目标运动模型和观测模型，然后提出了基于最大后验概率准则进行含机动检测的轨道相关原理和方法。为了计算最大后验概率，首先通过二阶锥规划算法求解了含约束的非线性最小二乘问题，实现了对机动参数的精确估计，其次通过JPDA算法计算最大后验概率，进行了机动事件的判别和轨道相关事件的确认。最后，通过理论推导和仿真实验对机动检测性能和关联性能进行了分析，验证了算法的有效性，同时对本文算法可推广应用的场景进行了阐释。
最后，研究了低轨空间群目标的跟踪技术。首先介绍了群目标的运动模型和观测模型，提出了含群中心的最优贝叶斯跟踪滤波器。在此基础上，通过贝叶斯原理，将贝叶斯滤波器分解为目标状态预测模型、群中心预测模型，观测概率模型、群中心和目标间相互作用的马尔科夫随机场(MRF)模型，并进行了详细的说明和求解。特别是通过建立群中心与目标间相互作用的MRF模型，使得我们既能够描述群目标整体运动趋势，又可以提升个体轨迹的跟踪精度。然后通过MCMC-Particle粒子滤波算法对以上贝叶斯跟踪滤波器进行实现，并分析了跟踪性能。最后又引入群的分离与合并机制，使得算法具备对多个群进行灵活跟踪的能力，提升了算法的实际应用价值，大量仿真结果表明了算法在低数据率、高杂波环境下的优越性能。
Low earth orbit (LEO) space surveillance systems are playing a crucial andfundamental role to support important functionalities of the space situational awarenessand orbital collision avoidance, which provide the guarantees for efficient utilization ofthe space resources and safety of the movements of the on-orbit spacecrafts. Theconstruction of an effective LEO space surveillance system that undertakes thecataloging and tracking tasks for LEO space objects is very important and challenging.Moreover, the information processing approach is a core component in any surveillancesystem. The investigation on information processing techniques will improve not onlyon the performances of the existing systems to satisfy the future needs of theestablishments of space surveillance systems, but also get a better understanding ontheoretical developments of more effective surveillance systems.
Serving as a major instrument of LEO space surveillance systems, theground-based radar systems are the dominating sources where the measurement data ofLEO space objects can be obtained. Therefore, the radar systems of a LEO spacesurveillance system, especially an emerging fence-type surveillance radar system, havebeen taken as the fundamental infrastructure in this thesis. Based on such aninfrastructure, we investigate the key techniques of information processing to constructa radar surveillance system and the general problems with frontiers to satisfy the futuredemands of space surveillance systems. The main results and contributions aresummarized as follows.
Firstly, the LEO space object environments are theoretically analyzed thatfollowed by the introductions of the development status and tendency of thesurveillance technologies of the LEO space objects based on the cognition progress forspace objects’ characteristics. The main challenging issues in the informationprocessing for exploring the LEO space objects by using a radar system are alsoelaborated. In addition, the basic interdisciplinary knowledge including the orbitalmovements and radar exploring technologies are also refined.
Secondly, the methodologies of signal detection and parameter estimation for thesmall space objects based on a fence-type space surveillance radar system areinvestigated. Moreover, the observation model of space objects based on the fence-typeradar system is also introduced. The sparse characteristics of space objects crossing thebeam fence are analyzed. Furthermore, the reconstruction problem in originalthree-dimensional space can be reduced into two-dimensional space by carefullyanalyzing the relations between the acceleration and the directions of arrival for thecorresponding LEO space debris based on a fence-type surveillance system, which canachieve a higher efficiency and improve the reconstruction accuracy. According to these, a sparse reconstruction method involving the orbital knowledge constraint is proposedfor the signal detection and parameter estimation of the small objects. Finally, thecorrect sparse reconstruction probability and the estimation accuracy affected by thevalue of selected parameters are evaluated by theoretical analysis and numeroussimulations. In addition, the resolution capability for multiple objects is also analyzed.The results demonstrate the robustness of the approach in scenarios with a lowSignal-to-Noise Ratio (SNR) and the super-resolution properties.
Subsequently, the data association problem for LEO space debris surveillancebased on a double fence radar system is also investigated. The surveillance mechanismsof a double fence radar system are elaborated that followed by the descriptions of theobservation data by using the information sets. Based on these constructions, weanalyze the set of orbital constraints on the LEO space debris in which the informationsets have to be satisfied. Moreover, combining with the hypothesis test methods, a noveldata association scheme is implemented by analyzing the discrepancy of the associationvariables, i.e. radial velocities, which are calculated according to the differenthypothetical associated sets. Furthermore, we also derive a theoretical analysis of theresolution performance in three-dimensional space for our proposed schemes. Thesuperiority and the effectiveness of our novel data association scheme are demonstratedby experimental results. The data used in our experiments is the LEO space debriscatalog produced by the North American Air Defense Command (NORAD) up to2009,especially for scenarios with high densities of LEO space debris, which were primarilyproduced by the collisions between Iridium33and Cosmos2251, which highly supportthe demonstration of the double fence space surveillance radar system.
In this thesis, we also explore the orbit correlation approach including themaneuver detection problems. We integrate these two problems mentioned above intoone interrelated problem, and consider them simultaneously under a scenario wherespace objects only perform a single in-track orbital maneuver during the time intervalsbetween observations. More precisely, we mathematically formulate such an integratedproblem as the Maximum A-Posteriori Probability (MAP) estimation. To solve theMAP estimation, the maneuvering parameters are firstly estimated by optimally solvingthe constrained non-linear least squares iterative process based on a Second-order ConeProgramming (SOCP) algorithm. Subsequently, the corresponding posterior probabilityof an orbital maneuver and a joint association event can be approximately calculated bythe Joint Probabilistic Data Association (JPDA) algorithm. The desired solution hasbeen derived based on the MAP criterions. The performances and advantages of theproposed approaches have been shown by both theoretical analysis and simulationresults. We have to address that the proposed algorithms can be adapted and extended tomany different situations.
Finally, the group tracking methods of LEO space objects are studied as well. In this chapter, we firstly introduce the orbital movement model and the observation modelof group objects and propose the optimal Bayesian tracking filtering involving groupcenter. Subsequently, due to the Bayesian theorem, the Bayesian tracking procedure canbe broke down into some detailed modules including the state transition model of spaceobjects, the state transition model of the group centers, the interaction Markov RandomField (MRF) model between group centers and individual trajectories, and the posteriordensity model of observations. We mainly focus on how to use the interaction MRFmodel between group centers and individual trajectories. It has been shown that we canobtain not only a more robust estimation of object numbers and improve the accuracy ofthe estimated corresponding individual trajectory, but also depict the evolution of thegroups under scenarios with the low object detection probabilities. MCMC-Particlealgorithm has been utilized to calculate the Bayesian integral and fulfill group tracking.Furthermore, the mechanism for group configuration inference has been incorporatedinto our approach that makes the operations of merge and split for groups much moresmart and efficient during the tracking process. We also show that the proposedalgorithm has significant impacts for the practical applications. Finally, we evaluate theperformances of our algorithms by the simulations of tracking multiple closely spacedorbital objects. The results verified the effectiveness of our proposed schemes for thescenarios with a low detection probability in a high dense clutter.
引文
[1] Klinkrad H, Alby F, Crowther R, et al.. Space debris activities in Europe [C].Fifth European Conference on Space Debris, Darmstadt, Germany: ESA/ESOC,2009.
[2] Orbital debris quarterly news [R]. NASA Orbital Debris Program Office,2012,16(1).
[3] Klinkrad H, Johnson N L. Space debris environment remediation concepts [C].Fifth European Conference on Space Debris, Darmstadt, Germany: ESA/ESOC,2009.
[4] Deris backround [R]. First Announcement: Sixth European Conference on SpaceDebris,2013. http://www.congrexprojects.com/13a09.
[5] Pardini C, Anselmo L. Assessing the risk of orbital debris impact [J]. SpaceDebris,1999,1:59~80.
[6] Orbital debris quarterly news [R]. NASA Orbital Debris Program Office,2009,13(2).
[7] Orbital debris quarterly news [R]. NASA Orbital Debris Program Office,2010,14(3).
[8] Liou J C, Anz-Meador, P, D. An analysis of recent major breakups in the lowearth orbit region [C].61st International Astronautical Congress2010.
[9] X-37B orbital test vehicle [R]. Boeing Defense, Space&Security,2012.www.boeing.com
[10] X-37B lands this morning at Vandenberg AFB [N]. Santa Maria Times,2012-7-16.
[11] Thornill, Ted. Revealed: How America’s secret space plane has been in orbit forover a year-and no one knows what it's doing [N]. Daily Mail,2012-3-8.
[12] James L. On keeping the space environment safe for civil and commercial users[C]. Before the Subcommittee on Space and Aeronautics, House Committee onScience and Technology, April28,2009.
[13] Schumacher P W, Jr. US navel space surveillance upgrade program1999-2003[C]. Fifth European Conference on Space Debris, Darmstadt, Germany:ESA/ESOC,2009.
[14]杨朋翠,施浒立,李圣明.空间碎片地基雷达探测综述[J].天文研究与技术(国家天文台台刊),2007,4(4):320~326.
[15] IADC Space Debris Mitigation Guidelines [M]. IADC-02-01Revision1,2007.
[16] Liou J C, Matney M J, Anz-Meador P D, et al. The new NASA orbital debrisengineering model ORDEM2000[R]. NASA/TP-2002-210780. Houston: NASAJohnson Space Center,2002.
[17] Padget S A. Issues in space law and policy [D]. Monterey: Naval PostgraduateSchool,1996.
[18] Office of Science and Technology Policy. Interagency report on orbital debris [R].NASA,1995.
[19]朱毅麟.空间碎片环境近况[J].中国空间科学技术,1996,16(6):19~28.
[20] National Research Council. Orbital Debris: A Technical Assessment [M].Washington, DC: National Academy Press,1995.
[21] Liou J C. An assessment of the current LEO debris environment and the need foractive debris removal [C]. ISTC Space Debris Mitigation Workshop, Moscow,Russia,2010.
[22] Johnson N L. The world state of orbital debris measurements and modeling [J].Acta Astronautica,2004,54(4):267~272.
[23] Liou J C, Hall D T, Krisko P H. LEGEND–a three-dimensional LEO-to-GEOdebris evolutionary model [J]. Advances in Space Research,2004,34:981~986.
[24] Stabroth S, Wegener P, Klinkrad H. Software user manual MASTER-2005[Z],2006.
[25] Fukushige Shinya, Akahoshi Yasuhiro, Kitazawa Yukihito, et al.. Comparison ofdebris environment models: ORDEM2000, MASTER2001and MASTER2005[J]. IHI Engeering Review,2007,40(1):31~41.
[26] Liou J C, Johnson N L. Instability of the present LEO satellite populations [J].Advances in Space Research,2008,41:1046~1053.
[27]宋正鑫,胡卫东,郁文贤.空间碎片的雷达探测—技术与趋势[J].现代防御技术,2008,36(4):142~147.
[28]宋正鑫.空间碎片环境雷达监测关键技术研究[D].长沙:国防科学技术大学,2008.
[29] Settecerri T J, Stansbery E G. An introduction to processing orbital debris radardata [A]. AIAA-2000-0761.38th aerospace sciences meeting and exhibition [C],Reno: AIAA,2000.
[30] Foster J L, Benbrook J R, Stansbery E G. Detection of small radar cross-sectionorbital debris with the Haystack radar [J]. Advances in Space Research,2005,35(7):1210~1213.
[31] Stansbery E G, Foster J L, Jr. Monitoring the low Earth orbit debris environmentover an11-year solar cycle [J]. Advances in Space Research,2004,34(5):878~883.
[32] Settecerri T J, Stansbery E G, Matney M J. Haystack measurements of the orbitaldebris environment [J]. Advances in Space Research,1999,23(1):13~22.
[33] Goldstein R M, Goldstein S J, Jr and Kessler D J. Radar observation of spacedebris [J]. Planetary and Space Science,1998,46(8):1007~1013.
[34] Mehrholz D, Leushacke L, Banka D. Beam-park experiments at FGAN [J].Advances in Space Research,2004,34(5):863~871.
[35] Banka D, Leushacke L, Mehrholz D. Beam-park-experiment-1/2000with TIRA[J]. Space Debris,2000,2(2):83~96.
[36] Johnson N L. Orbital debris research in the U.S.[A]. In: Danesy D ed.Proceedings of the Fourth European Conference on Space Debris [C], Darmstadt:ESA,2005.5~10.
[37]祁先锋.空间碎片观测综述[J].中国航天,2005,28(7):24~26.
[38]李春来,欧阳自远,都亨.空间碎片与空间环境[J].第四纪研究,2002,22(6):540~551.
[39] McDonnell J A M, Ratcliff P R, Green S F et al. Microparticle populations atLEO altitudes: recent spacecraft measurements [J]. ICARUS,1997,127:55~64.
[40] Inter-Agency Space Debris Coordination Committee. IADC ObservationCampaigns [C].43rd Session of UNCOPUOS S&T SC,2006.
[41]袁振涛.空间目标普测型雷达信号检测与参数估计算法研究[D].长沙:国防科学技术大学,2009.
[42] Carl J R, Arndt G D, Bourgeois B A et al. Space-borne radar detection of orbitaldebris [C]. In: Global Telecommunications Conference, Technical ProgramConference Record. Houston: IEEE,1993.
[43] Grant H S, Curt B, Ramaswamy S, et al. The space-based visible program [C].AIAA2000-5334. AIAA Space2000Conference&Exposition, Long Beach, CA,September,2000.
[44] McCall G H. Space surveillance [R]. United States Air Force Space CommandPeterson AFB, CO,2001. www.fas.org/spp/military/program/track/mccall.pdf.
[45] Davis B J. LORAAS Based Ionospheric Measurements and Their Application toThe Navy Space Surveillance Fence [D]. USA: University of Colorado at Denver,2000.
[46] Schumacher P W, Jr, Gilbreath G C, Lydick E D, et al. Error analysis forlaser-based metric calibration of the Naval Space Surveillance System [C]. In:Part of the SPIE Conference on Laser Radar Technology and Applications Ш,Orlando: SPIE,1998.3380:202~215.
[47] Schumacher P W, Jr, Cooper D A. Angles-only data association in the navalspace surveillance system [C]. Proceedings of the1994sapce surveillanceworkshop. MIT Lincoln Laboratory,1994.
[48] Michal T, Eglizeaud J P, Bouchard J. GRAVES: the new French system for spacesurveillance [C]. Proceedings of the Fourth European Conference on SpaceDebris, Darmstadt: ESA,2005.
[49] Donath T, Schildknecht T, Brousse P. Proposal for a European space surveillancesystem [C]. Proceedings of the Fourth European Conference on Space Debris,Darmstadt: ESA,2005.
[50] Haines L, Phu P. Space fence PDR concept development phase [C].2011SpaceControl Conference, MIT Lincoln Laboratory,2011.
[51] Doyle A. Space Fence radar to track space objects and debris [N],2012-03-13.http://sen.com/news/13032012.html.
[52] Lt Col Glen Shepherd. Space Surveillance Network [R]. HQ AFSPC/A3CD/Shared SSA Briefing,2006.
[53] Badhwar G D, Anz-Meador P D. Determination of area and mass distribution oforbital debris fragments [J]. Earth, Moon, and Planets,1989,45(4):29~51.
[54] Dickey M R, Culp R D. Determining characteristic mass for low-Earth-orbitingdebris objects [J]. Journal of Spacecraft and Rockets,1989,26(6):460~464.
[55] Thomas J S, G. Eugene S. An introduction to processing orbital debris radar data[C].38th Aerospace Sciences Meeting and Exhibit, AIAA2000-0761,2000.
[56] Lamboura R., Rajan N, Morgan T. Assessment of orbital debris size estimationfrom radar cross-section measurements [J]. Advances in Space Research,2004,34:1013~1020.
[57] Camp W W, Mayhan J T, O’Donnell R M. Wideband radar for ballistic missiledefense and range-Doppler imaging of satellites [J]. Lincoln Laboratory Journal,2000,12(2):267~280.
[58] Stansbery E G. Growth in the number of SSN tracked orbital objects [A]. PaperIAC-04-IAA.5.12.1.03.55th International Astronautical Congress [C],Vancouver: IAF,2004.
[59] Mehrholz D, Leushacke L, Banka D. Beam-park experiments at FGAN [J].Advances in Space Research,2004,34(5):863~871.
[60] Mehrholz D, Leushacke L, Flury W, et al.. Detecting, tracking and imaging spacedebris [M]. ESA bulletin,2002,109:128~134.
[61] Stokely C L, Foster J L, Jr, Stansbery E G et al. Haystack and HAX radarmeasurements of the orbital debris environment2003[R]. JSC-62815. Houston:NASA Johnson Space Center,2006.
[62] Matney M, Goldstein R, Kessler D et al. Recent results from Goldstone orbitaldebris radar [J]. Advances in Space Research,1999,23(1):5~12.
[63] Cooke W J. Garbage dump in the sky space debris and its impact [R]. NASAMarshall Space Flight Center,2006.
[64]史仁杰.美国空间监视网[J].空间碎片研究,2006,3:27~32.
[65]魏晨曦.俄罗斯的空间目标监视、识别、探测与跟踪系统[J].中国航天,2006,29(8):39~41.
[66] Khakhinov V V, Lebedev V P, Medvedev A V. Capabilities of the Irkutskincoherent scattering radar for space debris studies [C]. In: Proceedings of theFifth European Conference on Space Debris. Darmstadt: ESA,2009.
[67] European Space Agency. SSA PP and the protection of European spaceinfrastructures [C]. EISC Workshop, Cracow,2012,5.
[68] European Space Agency. SSA Preparatory Programme: ESA,2009–2012[C].Meeting at ASI,2012,7.
[69] Zedd M, Najmy L E. Modernizing the Naval Space Surveillance System.www.fas.org/spp/military/program/track/ModernizingNAVSPASUR.pdf.
[70]胡卫东,方艾里,徐劲.监测空间碎片的电子篱笆[J].空间碎片研究,2006,6(3):42~47.
[71]胡卫东,方艾里,徐劲.双搜索屏雷达空间碎片监测研究[J].空间碎片研究,2007,7(3):21~27.
[72] Jian Huang, Weidong Hu, Qin Xin, et al.. A novel data association scheme forLEO space debris surveillance based on a double fence radar system [J].Advances in Space Research.2012,50(11):1451~1461.
[73]杨朋翠,施浒立.空间碎片地基雷达探测工作频率探讨[J].现代雷达,2008,30(7):36~38.
[74]陈柱学,陆鹏程.电子篱笆系统工程设计参数分析[C].第五届全国空间碎片会议.中国烟台:国家国防科工局,2009.
[75]肖文书,刘炳奇. NAVSPASUR系统的空余覆盖和定位精度分析[C].第五届全国空间碎片会议.中国烟台:国家国防科工局,2009.
[76]赵绍颖,杨文军.用于空间目标监视的相控阵雷达需求分析[J].现代雷达,2006,28(1):16~19.
[77]刘静,张耀,都亨.空间碎片监测网的评价和优化[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[78]赵有等.亚太地基空间物体光学观测(APOSOS)系统项目的介绍和进展[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[79]王洋,李玉书.空间碎片地基雷达探测模式探讨[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[80]柳仲贵,郝世锋.一种天基空间目标编目测轨方案设想[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[81] Markkanen J, Lehtinen M, Huuskonen A, et al.. Measurements of small-sizedebris with backscatter of radio waves [R]. Final report, ESOC contract no.13945/99/D/CS,2002.
[82] Markkanen J, Lehtinen M, Landgraf M. Real-time space debris monitoring withEISCAT [J]. Advances in Space Research,2005,35(7):1197~1209.
[83] Maccone C. Advantages of Karhunen–Loève transformover fast Fouriertransformfor planetary radar and space debris detection [J]. Acta Astronautica,2007,60:775~779.
[84] Isoda K, Sakamoto T, Sato T. An efective orbit estimation algorithm for a spacedebris radar using the Quasi-Periodicity of the evaluation function [C]. In:Lacoste, H., Ouwehand, L.(Eds.), Proceedings of the European Conference onAntennas and Propagation: EuCAP2006, Vol. ESA SP-626. ESA, Nice,2006.
[85] Yuan Zhentao, Hu Weidong, Yu Wenxian The use of FrFT in radar systems forspace debris surveillance [C]. Proceedings of Fifth European Conference onSpace Debris, ESA/ESOC, Germany,2009.
[86] Jian Huang, Weidong Hu, Mounir Ghogho, et al.. A novel signal processingapproach for LEO space debris based on a fence-type space surveillance radarsystem [J]. Advances in Space Research.2012,50(11):1462~1472.
[87] Tommei G, Milani A., Rossi A. Orbit determination of space debris: admissibleregions. Celestial Mechanics and Dynamical Astronomy [J],2007,97(4):289~304.
[88] Farnocchia D, Tommei G, Milani A, et al.. Innovative methods of correlation andorbit determination for space debris [J]. Celestial Mechanics and DynamicalAstronomy,2010,107:169~185.
[89] Maruskin J M, Scheeres D J, Alfriend K T. Correlation of optical observations ofobjects in earth orbit [J]. Journal of Guidance, Control, and Dynamics,2009,32(1):194~209.
[90] Storch T R. Maneuver estimation model for relative orbit determination [D]. AirForce Institute of Technology Wright-Patterson AFB OH School of EngineeringAnd Management Air Force Institute of Technology, Ohio, Master thesis,2005.
[91] Patera R P. Space event detection method [J]. Journal of Spacecraft and Rockets,2008,45(3):554-559.
[92] Holzinger M J, Scheeres D J. Object correlation and maneuver detection usingoptimal control performance metrics [C]. Proceedings of the Advanced MauiOptical and Space Surveillance Technologies Conference, Hawaii,2010.
[93] Jian Huang, Weidong Hu, Qin Xin, Xiaoyong Du. An object correlation andmaneuver detection approach for space surveillance [J]. Research in Astronomyand Astrophysics,2012,12(10):1402~1416.
[94] Reid D B. An algorithm for tracking multiple targets [J]. IEEE Transactions onAutomatic Control,1979,24(6):84~90.
[95] Fortmann T E, Bar-Shalom Y, and Scheffe M. Sonar tracking of multiple targetsusing joint probabilistic data association [J]. IEEE Journal of OceanicEngineering,1983,8(3):173~184.
[96] Mahler R. Multitarget bayes filtering via first-order multi-target moments [J].IEEE Transactions on Aerospace and Electronic Systems,2003,39(4):1152~1178.
[97] Mahler R. PHD filters of higher order in target number [J]. IEEE Transactions onAerospace and Electronic Systems,2007,43(4):1523~1543.
[98]黄剑,胡卫东.基于贝叶斯框架的空间群目标跟踪技术[J].雷达学报,2013,2(1):86~96.
[99]郗晓宁,王威,高玉东.近地航天器轨道基础[M].长沙:国防科技大学出版社,2003.
[100]刘林.人造地球卫星轨道力学[M].北京:高等教育出版社,1992.
[101]张洪波.航天器轨道动力学与控制讲义[M].长沙:国防科学技术大学,2011.
[102]茅永兴.航天器轨道确定的单位矢量法[M].北京:国防工业出版社,2008.
[103] Goodyear W H. Complete general closed-form solution for coordinates andpartial derivatives of the two-body problem [J]. The Astronomical Journal,1965,70(3).
[104] Battin R H. An introduction to the mathematics and methods of astrodynamics[M]. American Institute of Aeronautics and Astronautics, Education Series,1987.
[105] Der G J. An elegant state transition matrix [J]. Journal of the AstronauticalSciences,1997,45(4):371~390.
[106] Curtis H D. Orbital Mechanics for Engineering Students [M]. ElsevierButterworth-Heinemann,2005.
[107]王威,于志坚,郗晓宁.航天器轨道确定—模型与算法[M].北京:国防工业出版社,2007.
[108] Sidi M J. Spacecraft dynamics and control: A practical engineering approach [M].Cambridge University Press,1997.
[109] Montebugnoli S, Pupillo G, Salerno E, et al.. A potential integratedmultiwavelength radar system at the medicina radiotelescopes [C]. In:Proceedings of the Fifth European Conference on Space Debris. Darmstadt: ESA,2009.
[110] Kay S M著;罗鹏飞等译.统计信号处理基础—估计与检测理论[M].北京:电子工业出版社,2006.
[111]黄培康等著.雷达目标特性[M].北京:电子工业出版社,2005.
[112]丁鹭飞,耿富录.雷达原理[M].西安:电子科技大学出版社,2006.
[113]赵宏钟,付强.雷达信号的加速度分辨性能分析[J].中国科学E辑:技术科学,2003,33(7):638~646.
[114]袁振涛,胡卫东,郁文贤.“电子篱笆”型空间监视雷达测向数据关联算法[J].宇航学报,2009,30(5).
[115] Ba-Ngu Vo. Random Set/Point Process in Multi-Target Tracking [EB/OL].
[2008-09-08]. http://www.ee.unimelb.edu.au/staff/bv.
[116] Bar-Shalom Y, Daum F, Huang J. The probabilistic data association filter:estimation in the presence of measurement origin un-certainty [J]. IEEE ControlSystems Magazine,2009,29(6):82~100.
[117] Goodman I R, Mahler R, Nguen T. Mathematics of Data Fusion [M]. San Diego:Academic Publishers,1997.
[118] Mahler R. Statistical Multisource-Multitarget Information Fusion [M]. Norwood,MA: Artech House,2007.
[119] Vo B N, Ma W K. The Gaussian Mixture Probability Hypothesis Density Filter[J]. IEEE Transactions on Signal Processing,2006,54(11):4091~4104.
[120] Vo B T, Vo B N, Cantoni A. Analytic Implementations of the CardinalizedProbability Hypothesis Density Filter [J]. IEEE Transactions on SignalProcessing,2007,55(7):3553~3576.
[121] Vo B N, Singh S S, Doucet A. Sequential Monte Carlo Methods for MultitargetFiltering with Random Finite Sets [J]. IEEE Transactions on Aerospace andElectronic Systems,2005,41(4):1224~1245.
[122] William N, Li J, Godsill S, et al.. Multitarget initiation, tracking and terminationusing Bayesian Monte Carlo methods [J]. The Computer Journal,2007,50(6):674~693.
[123] Salmond D J, Gordon N.J. Group and extended object tracking[C], Signal andData Processing of Small Targets, SPIE Volume3809,1999.
[124] Ulmke M, Koch W. Road-Map Assisted Ground Moving Target Tracking [J].IEEE Transactions on Aerospace and Electronic Systems,2006,42(4):1264~1274.
[125] Khan Z, Balch T, Dellaert F. MCMC-Based Particle Filtering for tracking avariable number of interacting targets [J]. IEEE Transactions on Pattern Analysisand Machine Intelligence,2005,27(11):1805~1819.
[126] Pang S K, Li J, Godsill S J. Detection and tracking of coordinated groups [J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(1):472~502.
[127] Ristic B, et al. Beyond the Kalman Filter: Particle Filters for TrackingApplications [M]. Artech House,2004.
[128] Knowles S H, Smith R H, Waltman W B. Experimental observations of navalspace surveillance satellite signals with an out-of-plane receiving station [R].Naval Research Laboratory,1982.
[129] Sdunnus H, Beltrami P, Klinkrad H. Comparison of debris flux models [J].Advances in Space Research,2004,34:1000~1005.
[130] Cetin M. Feature-enhanced synthetic aperture radar imaging [D], Ph.D. thesis,Boston University, College of Engineering,2001.
[131] Cabrera S D, Parks T W. Extrapolation and spectral estimation with iterativeweighted norm modification [J]. IEEE Transactions on Signal Processing,1991,39(4):842~851.
[132] Cetin M, Malioutov D M, Willsky A S. A variational technique for sourcelocalization based on a sparse signal reconstruction perspective [C]. In:2002IEEE International Conference on ASSP, Orlando, FL,2002.
[133] Muthukrishnan S. Data Streams: Algorithms and Applications [M]. NowPublishers, Boston,2005.
[134] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAM Review,2001,43:129~159.
[135] Donoho D L, Huo X. Uncertainty principles and ideal atomic decompositions [J].IEEE Transactions on Information Theory,2001,47:2845~2862.
[136] Elad M, Bruckstein A. A generalized uncertainty principle and sparserepresentations in pairs of bases [J]. IEEE Transactions on Information Theory,2002,48:2558~2567.
[137] Candès E, Tao T. Decoding by linear programming [J]. IEEE Transactions onInformation Theory.2005,51(12):4203~4215.
[138] Candès E, Romberg J, Tao T. Stable signal recovery from incomplete andinaccurate measurements [J]. Communications on Pure and Applied Mathematics,2006,59(8):1207~1223.
[139] Candès E, Romberg J, Tao T. Robust uncertainty principles: exact signalreconstruction from highly incomplete frequency information [J]. IEEETransactions on Information Theory,2006,52(2):489~509.
[140] Donoho D L, Elad M, Temlyakov V N. Stable recovery of sparse overcompleterepresentations in the presence of noise [J]. IEEE Transactions on InformationTheory,2006,52(1):6~18.
[141] Lobo M, Vandenberghe L, Boyd S, et al. Applications of the second-order coneprogramming [J]. Linear Algebra and its Appication,1998,284:193~228.
[142] Sturm J F. Using SeDuMi1.02, a MATLAB toolbox for optimization oversymmetric cones [J]. Optimization Methods and Software,1999,11-12(1~4):625~653.
[143] Malioutov D M. A Sparse Signal Reconstruction Perspective for SourceLocalization with Sensor Arrays [D]. Massachusetts Institute of Technology,2003.
[144] Vaidyanathan P P. Generalizations of the sampling theorem: seven decades afterNyquist [J]. IEEE Transactions on Circuits Systems I,2001,48(9):1094~1109.
[145] Wohlberg B. Noise sensitivity of sparse signal sepresentations: reconstructionerror bounds for the inverse problem [J]. IEEE Transactions on Signal Processing,2003,51(12):3053~3060.
[146] Austin C D, Moses R L, Ash J N, et al.. On the relation between sparsereconstruction and parameter estimation with model orderselection [J]. IEEEJournal of Selected Topics Signal Proces,2010,4(3):560~569.
[147] Efron B. Defining the curvature of a statistical problem (with applications tosecond order efficiency)[J]. The Annals of Statistics,1975,3(6):1189~1242.
[148] Amari S. Differential geometry of curved exponential families-curvatures andinformation loss [J]. The Annals of Statistics,1982,10(2):357~385.
[149] Grenander U, Miller M I, Srivastava A. Hilbert-Schmidt lower bounds forestimators on matrix Lie groups for ATR [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence,1998,20(8):790~802.
[150] Xavier J, Barroso V. The Riemannian geometry of certain parameter estimationproblems with singular Fisher information matrices [C].2004IEEE InternationalConference on Acoustics, Speech and Signal Processing (ICASSP '04), Montreal,Quebec,2004:1021~1024.
[151] Smith S T. Covariance, subspace, and intrinsic Cramér-Rao bounds [J]. IEEETransac-tions on Signal Processing,2005,53(5):1610~1630.
[152] Xavier J, Barroso V. Intrinsic variance lower bound (IVLB)-An extension of theCramér-Rao bound to Riemannian manifolds [C].2005IEEE InternationalConference on Acoustics, Speech and Signal Processing (ICASSP '05),Philadelphia, Pennsylvania,2005:1033~1036.
[153]王永良,陈辉,彭应宁等.空间谱估计理论与算法[M].北京:清华大学出版社,2004.
[154]曹志斌,徐劲,马剑波等.电子篱笆稀疏资料定轨方法研究[J].天文学报,2008,49(4):444~454.
[155] Celestial Track. http://celestrack.com.
[156] Space-Track.Org, United States Strategic Command. http://www.space-track.org.
[157] Kelecy T, Jah M. Detection and orbit determination of a satellite executing lowthrust maneuvers [J]. Acta Astronautica,2010,66:798~809.
[158] Bar-Shalom Y, Li X R. Estimation and Tracking: Principles, Techniques, andSoftware [M]. Norwood, MA: Artech House,1995.
[159] Petropoulos A E. Refinements to the Q-law for low-thrust orbit transfers [C].5thAAS/AIAA Space Flight Mechanics Conference, Copper Mountain, Colorado,2005.
[160] Figueiredo M, Nowak R D, Wright S J. Gradient Projection for SparseReconstruction: Application to Compressed Sensing and Other Inverse Problems
[C]. IEEE Journal of Selected Topics In Signal Processing,2007,1(4):586~597.
[161] Matney M J, Anz-Meador P, Foster J L. Covariance correlations in collisionavoidance probability calculations [J]. Advances in Space Research,2004,34(5):1109~1114.
[162] Comaniciu D, Bamesh V, Meer P. Kernel-based object tracking [J]. IEEETransactions on Pattern Analysis and Machine Intelligence,2003,25(5):564~577.
[163] Gilks W R, Richardson S, Spiegelhalter D J. Markov Chain Monte Carlo inPractice [M]. Lynnfield, MA: Chapman and Hall/CRC,1996.
[164] MacQueen J. Some methods for classification and analysis of multivariateobservations [C]. Proceedings of the5th Symposium on Mathematical Statisticsand Probability, Berkeley, University of California Press,1967:281~297.
[2] Orbital debris quarterly news [R]. NASA Orbital Debris Program Office,2012,16(1).
[3] Klinkrad H, Johnson N L. Space debris environment remediation concepts [C].Fifth European Conference on Space Debris, Darmstadt, Germany: ESA/ESOC,2009.
[4] Deris backround [R]. First Announcement: Sixth European Conference on SpaceDebris,2013. http://www.congrexprojects.com/13a09.
[5] Pardini C, Anselmo L. Assessing the risk of orbital debris impact [J]. SpaceDebris,1999,1:59~80.
[6] Orbital debris quarterly news [R]. NASA Orbital Debris Program Office,2009,13(2).
[7] Orbital debris quarterly news [R]. NASA Orbital Debris Program Office,2010,14(3).
[8] Liou J C, Anz-Meador, P, D. An analysis of recent major breakups in the lowearth orbit region [C].61st International Astronautical Congress2010.
[9] X-37B orbital test vehicle [R]. Boeing Defense, Space&Security,2012.www.boeing.com
[10] X-37B lands this morning at Vandenberg AFB [N]. Santa Maria Times,2012-7-16.
[11] Thornill, Ted. Revealed: How America’s secret space plane has been in orbit forover a year-and no one knows what it's doing [N]. Daily Mail,2012-3-8.
[12] James L. On keeping the space environment safe for civil and commercial users[C]. Before the Subcommittee on Space and Aeronautics, House Committee onScience and Technology, April28,2009.
[13] Schumacher P W, Jr. US navel space surveillance upgrade program1999-2003[C]. Fifth European Conference on Space Debris, Darmstadt, Germany:ESA/ESOC,2009.
[14]杨朋翠,施浒立,李圣明.空间碎片地基雷达探测综述[J].天文研究与技术(国家天文台台刊),2007,4(4):320~326.
[15] IADC Space Debris Mitigation Guidelines [M]. IADC-02-01Revision1,2007.
[16] Liou J C, Matney M J, Anz-Meador P D, et al. The new NASA orbital debrisengineering model ORDEM2000[R]. NASA/TP-2002-210780. Houston: NASAJohnson Space Center,2002.
[17] Padget S A. Issues in space law and policy [D]. Monterey: Naval PostgraduateSchool,1996.
[18] Office of Science and Technology Policy. Interagency report on orbital debris [R].NASA,1995.
[19]朱毅麟.空间碎片环境近况[J].中国空间科学技术,1996,16(6):19~28.
[20] National Research Council. Orbital Debris: A Technical Assessment [M].Washington, DC: National Academy Press,1995.
[21] Liou J C. An assessment of the current LEO debris environment and the need foractive debris removal [C]. ISTC Space Debris Mitigation Workshop, Moscow,Russia,2010.
[22] Johnson N L. The world state of orbital debris measurements and modeling [J].Acta Astronautica,2004,54(4):267~272.
[23] Liou J C, Hall D T, Krisko P H. LEGEND–a three-dimensional LEO-to-GEOdebris evolutionary model [J]. Advances in Space Research,2004,34:981~986.
[24] Stabroth S, Wegener P, Klinkrad H. Software user manual MASTER-2005[Z],2006.
[25] Fukushige Shinya, Akahoshi Yasuhiro, Kitazawa Yukihito, et al.. Comparison ofdebris environment models: ORDEM2000, MASTER2001and MASTER2005[J]. IHI Engeering Review,2007,40(1):31~41.
[26] Liou J C, Johnson N L. Instability of the present LEO satellite populations [J].Advances in Space Research,2008,41:1046~1053.
[27]宋正鑫,胡卫东,郁文贤.空间碎片的雷达探测—技术与趋势[J].现代防御技术,2008,36(4):142~147.
[28]宋正鑫.空间碎片环境雷达监测关键技术研究[D].长沙:国防科学技术大学,2008.
[29] Settecerri T J, Stansbery E G. An introduction to processing orbital debris radardata [A]. AIAA-2000-0761.38th aerospace sciences meeting and exhibition [C],Reno: AIAA,2000.
[30] Foster J L, Benbrook J R, Stansbery E G. Detection of small radar cross-sectionorbital debris with the Haystack radar [J]. Advances in Space Research,2005,35(7):1210~1213.
[31] Stansbery E G, Foster J L, Jr. Monitoring the low Earth orbit debris environmentover an11-year solar cycle [J]. Advances in Space Research,2004,34(5):878~883.
[32] Settecerri T J, Stansbery E G, Matney M J. Haystack measurements of the orbitaldebris environment [J]. Advances in Space Research,1999,23(1):13~22.
[33] Goldstein R M, Goldstein S J, Jr and Kessler D J. Radar observation of spacedebris [J]. Planetary and Space Science,1998,46(8):1007~1013.
[34] Mehrholz D, Leushacke L, Banka D. Beam-park experiments at FGAN [J].Advances in Space Research,2004,34(5):863~871.
[35] Banka D, Leushacke L, Mehrholz D. Beam-park-experiment-1/2000with TIRA[J]. Space Debris,2000,2(2):83~96.
[36] Johnson N L. Orbital debris research in the U.S.[A]. In: Danesy D ed.Proceedings of the Fourth European Conference on Space Debris [C], Darmstadt:ESA,2005.5~10.
[37]祁先锋.空间碎片观测综述[J].中国航天,2005,28(7):24~26.
[38]李春来,欧阳自远,都亨.空间碎片与空间环境[J].第四纪研究,2002,22(6):540~551.
[39] McDonnell J A M, Ratcliff P R, Green S F et al. Microparticle populations atLEO altitudes: recent spacecraft measurements [J]. ICARUS,1997,127:55~64.
[40] Inter-Agency Space Debris Coordination Committee. IADC ObservationCampaigns [C].43rd Session of UNCOPUOS S&T SC,2006.
[41]袁振涛.空间目标普测型雷达信号检测与参数估计算法研究[D].长沙:国防科学技术大学,2009.
[42] Carl J R, Arndt G D, Bourgeois B A et al. Space-borne radar detection of orbitaldebris [C]. In: Global Telecommunications Conference, Technical ProgramConference Record. Houston: IEEE,1993.
[43] Grant H S, Curt B, Ramaswamy S, et al. The space-based visible program [C].AIAA2000-5334. AIAA Space2000Conference&Exposition, Long Beach, CA,September,2000.
[44] McCall G H. Space surveillance [R]. United States Air Force Space CommandPeterson AFB, CO,2001. www.fas.org/spp/military/program/track/mccall.pdf.
[45] Davis B J. LORAAS Based Ionospheric Measurements and Their Application toThe Navy Space Surveillance Fence [D]. USA: University of Colorado at Denver,2000.
[46] Schumacher P W, Jr, Gilbreath G C, Lydick E D, et al. Error analysis forlaser-based metric calibration of the Naval Space Surveillance System [C]. In:Part of the SPIE Conference on Laser Radar Technology and Applications Ш,Orlando: SPIE,1998.3380:202~215.
[47] Schumacher P W, Jr, Cooper D A. Angles-only data association in the navalspace surveillance system [C]. Proceedings of the1994sapce surveillanceworkshop. MIT Lincoln Laboratory,1994.
[48] Michal T, Eglizeaud J P, Bouchard J. GRAVES: the new French system for spacesurveillance [C]. Proceedings of the Fourth European Conference on SpaceDebris, Darmstadt: ESA,2005.
[49] Donath T, Schildknecht T, Brousse P. Proposal for a European space surveillancesystem [C]. Proceedings of the Fourth European Conference on Space Debris,Darmstadt: ESA,2005.
[50] Haines L, Phu P. Space fence PDR concept development phase [C].2011SpaceControl Conference, MIT Lincoln Laboratory,2011.
[51] Doyle A. Space Fence radar to track space objects and debris [N],2012-03-13.http://sen.com/news/13032012.html.
[52] Lt Col Glen Shepherd. Space Surveillance Network [R]. HQ AFSPC/A3CD/Shared SSA Briefing,2006.
[53] Badhwar G D, Anz-Meador P D. Determination of area and mass distribution oforbital debris fragments [J]. Earth, Moon, and Planets,1989,45(4):29~51.
[54] Dickey M R, Culp R D. Determining characteristic mass for low-Earth-orbitingdebris objects [J]. Journal of Spacecraft and Rockets,1989,26(6):460~464.
[55] Thomas J S, G. Eugene S. An introduction to processing orbital debris radar data[C].38th Aerospace Sciences Meeting and Exhibit, AIAA2000-0761,2000.
[56] Lamboura R., Rajan N, Morgan T. Assessment of orbital debris size estimationfrom radar cross-section measurements [J]. Advances in Space Research,2004,34:1013~1020.
[57] Camp W W, Mayhan J T, O’Donnell R M. Wideband radar for ballistic missiledefense and range-Doppler imaging of satellites [J]. Lincoln Laboratory Journal,2000,12(2):267~280.
[58] Stansbery E G. Growth in the number of SSN tracked orbital objects [A]. PaperIAC-04-IAA.5.12.1.03.55th International Astronautical Congress [C],Vancouver: IAF,2004.
[59] Mehrholz D, Leushacke L, Banka D. Beam-park experiments at FGAN [J].Advances in Space Research,2004,34(5):863~871.
[60] Mehrholz D, Leushacke L, Flury W, et al.. Detecting, tracking and imaging spacedebris [M]. ESA bulletin,2002,109:128~134.
[61] Stokely C L, Foster J L, Jr, Stansbery E G et al. Haystack and HAX radarmeasurements of the orbital debris environment2003[R]. JSC-62815. Houston:NASA Johnson Space Center,2006.
[62] Matney M, Goldstein R, Kessler D et al. Recent results from Goldstone orbitaldebris radar [J]. Advances in Space Research,1999,23(1):5~12.
[63] Cooke W J. Garbage dump in the sky space debris and its impact [R]. NASAMarshall Space Flight Center,2006.
[64]史仁杰.美国空间监视网[J].空间碎片研究,2006,3:27~32.
[65]魏晨曦.俄罗斯的空间目标监视、识别、探测与跟踪系统[J].中国航天,2006,29(8):39~41.
[66] Khakhinov V V, Lebedev V P, Medvedev A V. Capabilities of the Irkutskincoherent scattering radar for space debris studies [C]. In: Proceedings of theFifth European Conference on Space Debris. Darmstadt: ESA,2009.
[67] European Space Agency. SSA PP and the protection of European spaceinfrastructures [C]. EISC Workshop, Cracow,2012,5.
[68] European Space Agency. SSA Preparatory Programme: ESA,2009–2012[C].Meeting at ASI,2012,7.
[69] Zedd M, Najmy L E. Modernizing the Naval Space Surveillance System.www.fas.org/spp/military/program/track/ModernizingNAVSPASUR.pdf.
[70]胡卫东,方艾里,徐劲.监测空间碎片的电子篱笆[J].空间碎片研究,2006,6(3):42~47.
[71]胡卫东,方艾里,徐劲.双搜索屏雷达空间碎片监测研究[J].空间碎片研究,2007,7(3):21~27.
[72] Jian Huang, Weidong Hu, Qin Xin, et al.. A novel data association scheme forLEO space debris surveillance based on a double fence radar system [J].Advances in Space Research.2012,50(11):1451~1461.
[73]杨朋翠,施浒立.空间碎片地基雷达探测工作频率探讨[J].现代雷达,2008,30(7):36~38.
[74]陈柱学,陆鹏程.电子篱笆系统工程设计参数分析[C].第五届全国空间碎片会议.中国烟台:国家国防科工局,2009.
[75]肖文书,刘炳奇. NAVSPASUR系统的空余覆盖和定位精度分析[C].第五届全国空间碎片会议.中国烟台:国家国防科工局,2009.
[76]赵绍颖,杨文军.用于空间目标监视的相控阵雷达需求分析[J].现代雷达,2006,28(1):16~19.
[77]刘静,张耀,都亨.空间碎片监测网的评价和优化[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[78]赵有等.亚太地基空间物体光学观测(APOSOS)系统项目的介绍和进展[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[79]王洋,李玉书.空间碎片地基雷达探测模式探讨[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[80]柳仲贵,郝世锋.一种天基空间目标编目测轨方案设想[C].第六届全国空间碎片学术交流会.中国成都:国家国防科工局,2011.
[81] Markkanen J, Lehtinen M, Huuskonen A, et al.. Measurements of small-sizedebris with backscatter of radio waves [R]. Final report, ESOC contract no.13945/99/D/CS,2002.
[82] Markkanen J, Lehtinen M, Landgraf M. Real-time space debris monitoring withEISCAT [J]. Advances in Space Research,2005,35(7):1197~1209.
[83] Maccone C. Advantages of Karhunen–Loève transformover fast Fouriertransformfor planetary radar and space debris detection [J]. Acta Astronautica,2007,60:775~779.
[84] Isoda K, Sakamoto T, Sato T. An efective orbit estimation algorithm for a spacedebris radar using the Quasi-Periodicity of the evaluation function [C]. In:Lacoste, H., Ouwehand, L.(Eds.), Proceedings of the European Conference onAntennas and Propagation: EuCAP2006, Vol. ESA SP-626. ESA, Nice,2006.
[85] Yuan Zhentao, Hu Weidong, Yu Wenxian The use of FrFT in radar systems forspace debris surveillance [C]. Proceedings of Fifth European Conference onSpace Debris, ESA/ESOC, Germany,2009.
[86] Jian Huang, Weidong Hu, Mounir Ghogho, et al.. A novel signal processingapproach for LEO space debris based on a fence-type space surveillance radarsystem [J]. Advances in Space Research.2012,50(11):1462~1472.
[87] Tommei G, Milani A., Rossi A. Orbit determination of space debris: admissibleregions. Celestial Mechanics and Dynamical Astronomy [J],2007,97(4):289~304.
[88] Farnocchia D, Tommei G, Milani A, et al.. Innovative methods of correlation andorbit determination for space debris [J]. Celestial Mechanics and DynamicalAstronomy,2010,107:169~185.
[89] Maruskin J M, Scheeres D J, Alfriend K T. Correlation of optical observations ofobjects in earth orbit [J]. Journal of Guidance, Control, and Dynamics,2009,32(1):194~209.
[90] Storch T R. Maneuver estimation model for relative orbit determination [D]. AirForce Institute of Technology Wright-Patterson AFB OH School of EngineeringAnd Management Air Force Institute of Technology, Ohio, Master thesis,2005.
[91] Patera R P. Space event detection method [J]. Journal of Spacecraft and Rockets,2008,45(3):554-559.
[92] Holzinger M J, Scheeres D J. Object correlation and maneuver detection usingoptimal control performance metrics [C]. Proceedings of the Advanced MauiOptical and Space Surveillance Technologies Conference, Hawaii,2010.
[93] Jian Huang, Weidong Hu, Qin Xin, Xiaoyong Du. An object correlation andmaneuver detection approach for space surveillance [J]. Research in Astronomyand Astrophysics,2012,12(10):1402~1416.
[94] Reid D B. An algorithm for tracking multiple targets [J]. IEEE Transactions onAutomatic Control,1979,24(6):84~90.
[95] Fortmann T E, Bar-Shalom Y, and Scheffe M. Sonar tracking of multiple targetsusing joint probabilistic data association [J]. IEEE Journal of OceanicEngineering,1983,8(3):173~184.
[96] Mahler R. Multitarget bayes filtering via first-order multi-target moments [J].IEEE Transactions on Aerospace and Electronic Systems,2003,39(4):1152~1178.
[97] Mahler R. PHD filters of higher order in target number [J]. IEEE Transactions onAerospace and Electronic Systems,2007,43(4):1523~1543.
[98]黄剑,胡卫东.基于贝叶斯框架的空间群目标跟踪技术[J].雷达学报,2013,2(1):86~96.
[99]郗晓宁,王威,高玉东.近地航天器轨道基础[M].长沙:国防科技大学出版社,2003.
[100]刘林.人造地球卫星轨道力学[M].北京:高等教育出版社,1992.
[101]张洪波.航天器轨道动力学与控制讲义[M].长沙:国防科学技术大学,2011.
[102]茅永兴.航天器轨道确定的单位矢量法[M].北京:国防工业出版社,2008.
[103] Goodyear W H. Complete general closed-form solution for coordinates andpartial derivatives of the two-body problem [J]. The Astronomical Journal,1965,70(3).
[104] Battin R H. An introduction to the mathematics and methods of astrodynamics[M]. American Institute of Aeronautics and Astronautics, Education Series,1987.
[105] Der G J. An elegant state transition matrix [J]. Journal of the AstronauticalSciences,1997,45(4):371~390.
[106] Curtis H D. Orbital Mechanics for Engineering Students [M]. ElsevierButterworth-Heinemann,2005.
[107]王威,于志坚,郗晓宁.航天器轨道确定—模型与算法[M].北京:国防工业出版社,2007.
[108] Sidi M J. Spacecraft dynamics and control: A practical engineering approach [M].Cambridge University Press,1997.
[109] Montebugnoli S, Pupillo G, Salerno E, et al.. A potential integratedmultiwavelength radar system at the medicina radiotelescopes [C]. In:Proceedings of the Fifth European Conference on Space Debris. Darmstadt: ESA,2009.
[110] Kay S M著;罗鹏飞等译.统计信号处理基础—估计与检测理论[M].北京:电子工业出版社,2006.
[111]黄培康等著.雷达目标特性[M].北京:电子工业出版社,2005.
[112]丁鹭飞,耿富录.雷达原理[M].西安:电子科技大学出版社,2006.
[113]赵宏钟,付强.雷达信号的加速度分辨性能分析[J].中国科学E辑:技术科学,2003,33(7):638~646.
[114]袁振涛,胡卫东,郁文贤.“电子篱笆”型空间监视雷达测向数据关联算法[J].宇航学报,2009,30(5).
[115] Ba-Ngu Vo. Random Set/Point Process in Multi-Target Tracking [EB/OL].
[2008-09-08]. http://www.ee.unimelb.edu.au/staff/bv.
[116] Bar-Shalom Y, Daum F, Huang J. The probabilistic data association filter:estimation in the presence of measurement origin un-certainty [J]. IEEE ControlSystems Magazine,2009,29(6):82~100.
[117] Goodman I R, Mahler R, Nguen T. Mathematics of Data Fusion [M]. San Diego:Academic Publishers,1997.
[118] Mahler R. Statistical Multisource-Multitarget Information Fusion [M]. Norwood,MA: Artech House,2007.
[119] Vo B N, Ma W K. The Gaussian Mixture Probability Hypothesis Density Filter[J]. IEEE Transactions on Signal Processing,2006,54(11):4091~4104.
[120] Vo B T, Vo B N, Cantoni A. Analytic Implementations of the CardinalizedProbability Hypothesis Density Filter [J]. IEEE Transactions on SignalProcessing,2007,55(7):3553~3576.
[121] Vo B N, Singh S S, Doucet A. Sequential Monte Carlo Methods for MultitargetFiltering with Random Finite Sets [J]. IEEE Transactions on Aerospace andElectronic Systems,2005,41(4):1224~1245.
[122] William N, Li J, Godsill S, et al.. Multitarget initiation, tracking and terminationusing Bayesian Monte Carlo methods [J]. The Computer Journal,2007,50(6):674~693.
[123] Salmond D J, Gordon N.J. Group and extended object tracking[C], Signal andData Processing of Small Targets, SPIE Volume3809,1999.
[124] Ulmke M, Koch W. Road-Map Assisted Ground Moving Target Tracking [J].IEEE Transactions on Aerospace and Electronic Systems,2006,42(4):1264~1274.
[125] Khan Z, Balch T, Dellaert F. MCMC-Based Particle Filtering for tracking avariable number of interacting targets [J]. IEEE Transactions on Pattern Analysisand Machine Intelligence,2005,27(11):1805~1819.
[126] Pang S K, Li J, Godsill S J. Detection and tracking of coordinated groups [J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(1):472~502.
[127] Ristic B, et al. Beyond the Kalman Filter: Particle Filters for TrackingApplications [M]. Artech House,2004.
[128] Knowles S H, Smith R H, Waltman W B. Experimental observations of navalspace surveillance satellite signals with an out-of-plane receiving station [R].Naval Research Laboratory,1982.
[129] Sdunnus H, Beltrami P, Klinkrad H. Comparison of debris flux models [J].Advances in Space Research,2004,34:1000~1005.
[130] Cetin M. Feature-enhanced synthetic aperture radar imaging [D], Ph.D. thesis,Boston University, College of Engineering,2001.
[131] Cabrera S D, Parks T W. Extrapolation and spectral estimation with iterativeweighted norm modification [J]. IEEE Transactions on Signal Processing,1991,39(4):842~851.
[132] Cetin M, Malioutov D M, Willsky A S. A variational technique for sourcelocalization based on a sparse signal reconstruction perspective [C]. In:2002IEEE International Conference on ASSP, Orlando, FL,2002.
[133] Muthukrishnan S. Data Streams: Algorithms and Applications [M]. NowPublishers, Boston,2005.
[134] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAM Review,2001,43:129~159.
[135] Donoho D L, Huo X. Uncertainty principles and ideal atomic decompositions [J].IEEE Transactions on Information Theory,2001,47:2845~2862.
[136] Elad M, Bruckstein A. A generalized uncertainty principle and sparserepresentations in pairs of bases [J]. IEEE Transactions on Information Theory,2002,48:2558~2567.
[137] Candès E, Tao T. Decoding by linear programming [J]. IEEE Transactions onInformation Theory.2005,51(12):4203~4215.
[138] Candès E, Romberg J, Tao T. Stable signal recovery from incomplete andinaccurate measurements [J]. Communications on Pure and Applied Mathematics,2006,59(8):1207~1223.
[139] Candès E, Romberg J, Tao T. Robust uncertainty principles: exact signalreconstruction from highly incomplete frequency information [J]. IEEETransactions on Information Theory,2006,52(2):489~509.
[140] Donoho D L, Elad M, Temlyakov V N. Stable recovery of sparse overcompleterepresentations in the presence of noise [J]. IEEE Transactions on InformationTheory,2006,52(1):6~18.
[141] Lobo M, Vandenberghe L, Boyd S, et al. Applications of the second-order coneprogramming [J]. Linear Algebra and its Appication,1998,284:193~228.
[142] Sturm J F. Using SeDuMi1.02, a MATLAB toolbox for optimization oversymmetric cones [J]. Optimization Methods and Software,1999,11-12(1~4):625~653.
[143] Malioutov D M. A Sparse Signal Reconstruction Perspective for SourceLocalization with Sensor Arrays [D]. Massachusetts Institute of Technology,2003.
[144] Vaidyanathan P P. Generalizations of the sampling theorem: seven decades afterNyquist [J]. IEEE Transactions on Circuits Systems I,2001,48(9):1094~1109.
[145] Wohlberg B. Noise sensitivity of sparse signal sepresentations: reconstructionerror bounds for the inverse problem [J]. IEEE Transactions on Signal Processing,2003,51(12):3053~3060.
[146] Austin C D, Moses R L, Ash J N, et al.. On the relation between sparsereconstruction and parameter estimation with model orderselection [J]. IEEEJournal of Selected Topics Signal Proces,2010,4(3):560~569.
[147] Efron B. Defining the curvature of a statistical problem (with applications tosecond order efficiency)[J]. The Annals of Statistics,1975,3(6):1189~1242.
[148] Amari S. Differential geometry of curved exponential families-curvatures andinformation loss [J]. The Annals of Statistics,1982,10(2):357~385.
[149] Grenander U, Miller M I, Srivastava A. Hilbert-Schmidt lower bounds forestimators on matrix Lie groups for ATR [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence,1998,20(8):790~802.
[150] Xavier J, Barroso V. The Riemannian geometry of certain parameter estimationproblems with singular Fisher information matrices [C].2004IEEE InternationalConference on Acoustics, Speech and Signal Processing (ICASSP '04), Montreal,Quebec,2004:1021~1024.
[151] Smith S T. Covariance, subspace, and intrinsic Cramér-Rao bounds [J]. IEEETransac-tions on Signal Processing,2005,53(5):1610~1630.
[152] Xavier J, Barroso V. Intrinsic variance lower bound (IVLB)-An extension of theCramér-Rao bound to Riemannian manifolds [C].2005IEEE InternationalConference on Acoustics, Speech and Signal Processing (ICASSP '05),Philadelphia, Pennsylvania,2005:1033~1036.
[153]王永良,陈辉,彭应宁等.空间谱估计理论与算法[M].北京:清华大学出版社,2004.
[154]曹志斌,徐劲,马剑波等.电子篱笆稀疏资料定轨方法研究[J].天文学报,2008,49(4):444~454.
[155] Celestial Track. http://celestrack.com.
[156] Space-Track.Org, United States Strategic Command. http://www.space-track.org.
[157] Kelecy T, Jah M. Detection and orbit determination of a satellite executing lowthrust maneuvers [J]. Acta Astronautica,2010,66:798~809.
[158] Bar-Shalom Y, Li X R. Estimation and Tracking: Principles, Techniques, andSoftware [M]. Norwood, MA: Artech House,1995.
[159] Petropoulos A E. Refinements to the Q-law for low-thrust orbit transfers [C].5thAAS/AIAA Space Flight Mechanics Conference, Copper Mountain, Colorado,2005.
[160] Figueiredo M, Nowak R D, Wright S J. Gradient Projection for SparseReconstruction: Application to Compressed Sensing and Other Inverse Problems
[C]. IEEE Journal of Selected Topics In Signal Processing,2007,1(4):586~597.
[161] Matney M J, Anz-Meador P, Foster J L. Covariance correlations in collisionavoidance probability calculations [J]. Advances in Space Research,2004,34(5):1109~1114.
[162] Comaniciu D, Bamesh V, Meer P. Kernel-based object tracking [J]. IEEETransactions on Pattern Analysis and Machine Intelligence,2003,25(5):564~577.
[163] Gilks W R, Richardson S, Spiegelhalter D J. Markov Chain Monte Carlo inPractice [M]. Lynnfield, MA: Chapman and Hall/CRC,1996.
[164] MacQueen J. Some methods for classification and analysis of multivariateobservations [C]. Proceedings of the5th Symposium on Mathematical Statisticsand Probability, Berkeley, University of California Press,1967:281~297.