空间目标轨道预报误差与碰撞概率问题研究

发布时间：2018-01-23 22:11

本文关键词： 碰撞预警轨道预报误差相对运动泊松级数碰撞概率显式表达式漏警率虚警率　出处：《国防科学技术大学》2013年博士论文　论文类型：学位论文

【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。
[Abstract]:With the increasing number of human space activities , the rapid growth of target quantity in orbit has exerted great influence on the sustainable development of space environment and space industry . Based on the theory of relative motion , the negative correlation between the initial error propagation characteristics and the position velocity error of the space target is studied . Considering that the orbit prediction error is small compared with the target vector diameter , the real state and the prediction state of the target are respectively corresponding to the two short distance space targets of " real " and " virtual " , and the orbit prediction error is regarded as the relative motion between them . Based on the algebraic method model , the negative correlation property of the circular orbit and the elliptical orbit is analyzed . The application of the characteristic in the selection of initial error covariance is discussed . The negative correlation characteristic is verified by historical orbit data . In this paper , a method for analyzing the periodic characteristics of orbit forecast errors based on historical orbit data and the fitting method of Poisson ' s series are presented . The value of the state prediction in the half cycle before and after the epoch of the track data is selected as the reference value , and the function of the polynomial term , trigonometric function term and mixing term is obtained by fitting the least square method . As the error fitting function , the Poisson ' s series can describe the long - term variation of the error with the prediction time and the periodic variation with the orbit position , and the Poisson coefficient matrix can be obtained before the collision early warning analysis is carried out . The explicit expression of collision probability in the case of circular orbit and general orbit is derived on the basis of near geometric analysis . The explicit expression of collision probability represented by the approximate distance RSW component representation and the approximate distance is deduced in the case of circular orbit . In the case of the general orbit , the explicit expression of the collision probability represented by the NTW component close to the geometric relation ( the height difference , the time difference , the velocity included angle and the velocity - size ratio ) of the approximate distance is derived . The eccentricity range suitable for explicit expression in the case of circular orbit is analyzed . For most LEO targets , the accuracy of explicit expression in the case of circular orbit is sufficient for the collision risk assessment and early warning decision . Based on the explicit expression of collision probability , the calculation method of collision probability sensitivity and maximum collision probability is analyzed , and a complete step of calculating the maximum collision probability is given . According to the explicit expression of the collision probability , the analytic expression of the maximum collision probability of the collision probability on the close distance RSW component , the orbit error standard deviation , the approach angle and the target size is analyzed . Based on the explicit expression of collision probability , the leakage alarm rate and false alarm rate of collision early warning are analyzed , and the comprehensive evaluation method of collision risk considering many factors is introduced and realized . The collision early warning is a discriminant analysis problem . According to the explicit expression of collision probability , the definition , calculation formula and basic law of collision warning are given . The comprehensive evaluation method of collision risk considering risk parameters and track quality parameters is introduced and realized . This paper introduces the system of space target collision early warning , and gives an example of system application by using two rows of orbit root number ( TLE ) data of cataloged target . The module composition and parallel computing environment of space target collision early warning software system are introduced . The application of the method of orbit prediction error analysis and collision probability analysis in software system is presented in this paper . The application example of collision warning software system is given by using TLE data of the target . Based on the demand of space target collision early - warning project in China , the problems of track forecast error and collision probability related to collision early warning are studied , the key problem of restricting engineering practice is solved , and collision early warning analysis method is developed , which can provide technical support for the establishment and improvement of space target collision early warning engineering system .

【学位授予单位】：国防科学技术大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：V528

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