【作者】 白显宗；

【导师】 唐国金； 陈磊；

【作者基本信息】 国防科学技术大学 ， 航空宇航科学与技术， 2013， 博士

【摘要】 随着人类航天活动的日益频繁，在轨空间目标数量快速增长，已对空间环境和航天事业的可持续发展产生了重大影响，必须加强对空间目标碰撞预警问题的研究。本文以空间目标碰撞预警过程为研究对象，针对碰撞预警中涉及的轨道预报误差和碰撞概率问题进行研究。主要成果如下：基于相对运动理论研究了空间目标初始误差传播特性和位置速度误差的负相关特性。考虑到轨道预报误差与目标矢径相比是小量，将目标的真实状态和预报状态分别对应于一“实”一“虚”两个近距离空间目标，将轨道预报误差看作它们之间的相对运动。基于代数法模型的C-W方程和T-H方程分别进行了圆轨道和椭圆轨道的初始误差传播分析。基于几何法模型在近圆轨道假设下对位置速度误差的负相关特性进行了分析，讨论了该特性在初始误差协方差选取中的应用。利用历史轨道数据对负相关特性进行了验证。提出了基于历史轨道数据的轨道预报误差周期特性分析方法和泊松级数拟合方法。选取轨道数据历元时刻前后半个周期内的状态预报值为参考值，在全轨道周期内求差以反映周期特性。利用最小二乘方法拟合得到了泊松系数矩阵，分别讨论了多项式项、三角函数项、混合项的作用。作为误差拟合函数，泊松级数可以描述误差随预报时间的长期变化和随在轨位置的周期变化，而且泊松系数矩阵可以在进行碰撞预警分析之前就得到。在接近几何分析的基础上推导了圆轨道和一般轨道情形下碰撞概率的显式表达式。在圆轨道情形下推导了接近距离的RSW分量表示和接近几何关系（过轨道面交线高度差和时间差、轨道夹角等）表示的碰撞概率显式表达式。在一般轨道情形下推导了接近几何关系（过速度公垂线高度差、时间差、速度夹角、速度大小比）表示的和接近距离的NTW分量表示的碰撞概率显式表达式。分析了圆轨道情形下显式表达式适用的偏心率范围，对于大多数LEO目标，圆轨道情形下显式表达式的精度对于碰撞风险评估和预警决策而言是足够的。基于碰撞概率的显式表达式分析了碰撞概率灵敏度和最大碰撞概率的计算方法，给出了计算最大碰撞概率的完整步骤。根据碰撞概率的显式表达式，分析了碰撞概率对接近距离的RSW分量、轨道误差标准差、接近角度和目标大小的两类灵敏度。在误差椭球形状固定和不定两种情况下推导得到了以接近几何关系或接近距离的分量表示的最大碰撞概率的解析表达式。讨论了当接近距离的一个分量为零时的特殊情况，给出了计算最大碰撞概率的完整步骤。基于碰撞概率的显式表达式对碰撞预警的漏警率和虚警率进行了分析，介绍并实现了考虑多因素的碰撞风险综合评估方法。碰撞预警实质上是一个判别分析问题。根据碰撞概率的显式表达式定义了碰撞预警的安全区域和危险区域，给出了漏警率和虚警率的定义、计算公式和基本规律。介绍并实现了综合考虑风险参数和轨道品质参数的碰撞风险综合评估方法。介绍了空间目标碰撞预警软件系统，利用编目目标的两行轨道根数（TLE）数据给出了系统应用实例。介绍了空间目标碰撞预警软件系统的模块组成和并行计算环境，本文提出的轨道预报误差分析方法和碰撞概率分析方法在软件系统中得到了应用。利用编目目标的TLE数据给出碰撞预警软件系统的应用实例。论文以我国空间目标碰撞预警工程需求为牵引，研究了碰撞预警涉及的轨道预报误差和碰撞概率问题，解决了制约工程实践的关键问题，发展了碰撞预警分析方法，可为空间目标碰撞预警工程系统的建立和完善提供技术支持。更多还原

【Abstract】 The amount of on-orbit space objects has been growing continuously because ofthe increasing and frequent aerospace activities, which has been strongly affecting thespace environment and the sustainable development of aerospace industry. Thishighlights the practical necessity of conjunction assessment and collision avoidance.Taking the process of conjunction assessment as research object, this dissertation mainlystudies the orbital prediction error and collision probability problems involved inconjunction assessment. The main achievements are summarized as follows:The propagation characteristics of initial orbital error and negativecorrelation characteristics of position and velocity error are studied based on therelative motion theory. Considering that the orbital prediction error is much smallerthan the radius of object, the true state and predicted state of space object can be seen astwo objects: a real one and a virtual one, and the prediction error can be seen as therelative motion between them. The propagation characteristics of initial error of circularand eccentric orbit are respectively analyzed based on C-W Equations and T-HEquations, which belong to the algebraic model. The negative correlation characteristicsof position and velocity error in the case of near-circular orbit are studied based on thegeometrical model of relative motion. The application of negative correlationcharacteristics in the determination of initial error covariance is discussed. Thecorrelation characteristics are validated by historical orbital data.A methodology for periodicity characterization and Poisson series fitting fororbital prediction error based on historical orbital data is presented. The predictedstates in an orbital period centered at its epoch are taken as reference states. Thecomparison is conducted in a whole period so that the residuals can reflect theperiodicity. The Poisson coefficient matrices of each error components are fitted usingleast squares method. Effects of polynomial, trigonometric, and mixed terms of Poissonseries are discussed. As error-fitting function, the Poisson series can describe variationof error with respect to propagation duration and on-orbit position of objects. ThePoisson coefficient matrices can be obtained before close approach analysis.The explicit expressions of collision probability (Pc) in the cases of circularorbit and general orbit are derived based on analysis of conjunction geometry. Inthe case of circular orbit, Pcis expressed as explicit functions of the RSW componentsof relative position or the conjunction geometries (crossing altitude difference and timedifference of the line of intersection of two orbital planes, the angle between orbitalplanes, etc.). In the case of general orbit, Pcis expressed as explicit functions of theconjunction geometries (crossing altitude difference and time difference of the commonperpendicular line to two velocities, the angle between two velocities, etc.) or the NTW components of relative position. The explicit expression relates Pcwith components ofrelative position. The eccentricity’s bound of explicit expression in the case of circularis determined. The precision of explicit expression is sufficient for conjunction riskassessment and decision-making for most LEO objects.The sensitivity of Pcand maximum collision probability (Pcmax) is analyzedbased on the explicit expression of Pc, the integrated procedure for estimating Pcmaxis provided. The sensitivities of Pcto RSW components of relative position, orbitalerror standard deviations, conjunction angle and object’s size are analyzed based on theexplicit expression of Pc. Analytical expressions of Pcmaxin terms of conjunctiongeometries or components of relative position are deduced in both cases of fixed andarbitrary error ellipsoid shape. Special cases when one of the coordinates in conjunctionplane tends to zero are discussed. The integrated procedure for estimating Pcmaxandcorresponding error standard deviations is provided.The probabilities of missing alarm and false alarm are studied based on theexplicit expressions of Pc, the comprehensive assessment of collision riskconsidering multi-factors is researched. The conjunction assessment is substantially adiscriminant analysis problem. The safety-region and danger-region of conjunctionassessment are defined by using explicit expression of Pc. The definition, formulae, andbasic property of probabilities of missing alarm and false alarm are provided. Thecomprehensive assessment of collision risk considering both risk assessment and qualityassessment parameters is introduced and implemented.The conjunction assessment software system is introduced and demonstratedby Two Line Element (TLE) data of space catalogued objects. The constituentmodules and parallel computing environment of conjunction assessment softwaresystem are introduced, in which the methods of orbital error analysis and collisionprobability analysis achieved in this dissertation have been applied. The softwaresystem is demonstrated by TLE data of space catalogued objects.Motivated by practical requirement of conjunction assessment, this dissertationfocuses on the involved orbit error and collision probability problem. This dissertationhas developed the conjunction assessment methodology. The achievements will providetechnical support for the establishment and improvement of conjunction assessmentengineering system.更多还原