空间目标碰撞预警中的碰撞概率问题研究
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摘要
论文主要研究空间目标碰撞预警与规避机动中与碰撞概率相关的问题,包括空间目标碰撞概率的计算方法、显式表达式、影响因素和置信度,以及轨道预报误差传播特性,为空间目标碰撞预警和规避机动打下基础。
介绍了空间碎片环境概况,分析了空间目标碰撞预警和规避机动的关键技术,提出了基于碰撞概率的空间目标碰撞预警和规避机动的基本框架。
研究了空间目标碰撞概率的计算方法。定义了相遇坐标系和积分计算坐标系,通过坐标转换和误差投影,将碰撞概率的计算问题转化为2维概率密度函数(PDF)在圆域内的积分问题。通过压缩空间的方法,将不等方差PDF在圆域内的积分化为等方差PDF在椭圆域内的积分,提出了两种概率积分计算方法:极坐标变换化为一重积分方法和圆近似无穷级数方法。根据近似结果分析了最大碰撞概率和相应的误差方差的表达式。简单讨论了低相对速度情况下碰撞概率的计算问题。
在圆轨道情况下推导了空间目标碰撞概率的显式表达式,将碰撞概率表示为交会几何条件(过交线高度差、过交线时间差、轨道夹角等)和RSW坐标系误差方差的显式函数。根据显式表达式对碰撞概率的诸影响因素进行了分析,得到了一些有意义的结论。对空间目标碰撞概率的置信度及其估计方法进行了讨论。引入碰撞概率置信区间和置信度的概念来描述计算得到碰撞概率的可信程度。碰撞概率是交会条件和位置误差的确定函数,碰撞概率的置信度取决于误差方差的置信度。基于误差方差的置信度和置信区间,利用显式表达式对碰撞概率的置信度和置信区间进行了分析,得到了一定简化条件下碰撞概率置信度的评估方法。
分析了碰撞概率计算中所需误差协方差矩阵的传播特性。对位置预报误差传播进行了分析,得到了TLE预报误差的特性,提出了一种假设解释了该特性。基于Hill方程和CADET方法进行了TLE初值方差传播分析,分别利用不考虑摄动偏差和考虑大气摄动偏差的Hill方程对TLE初值误差进行了分离。
最后,对一次空间碰撞规避机动实例和美国公布的一周碰撞概率最大交会事件进行了碰撞概率分析,对碰撞概率方法进行了综合应用。结果表明,本文中提出的碰撞概率方法是正确的,可以在工程实际中有效应用。
The collision probability problems in space objects collision detection and avoidance were mainly researched in this thesis, including calculational methods, the explicit expression, influencing factors and the confidence level of the collision probability, and propagation characteristics of the error covariance of the orbital prediction, which laid the foundation of the collision detection and avoidance of space objects.
The brief situation of the orbital environment was introduced, and then, key techniques of the collision detection and avoidance of space objects were discussed, and the basic frame of the collision detection and avoidance based on the collision probability was advanced.
Calculational methods of the collision probability were deeply studied. The encounter coordinates and the integral-calculation coordinates were defined, with the help of coordinate transformation and the projection of the position error covariance, the 3-dimensional collision probability problem was degraded into the integral of a 2-dimensional probability density function (PDF) over the region of a circle. Through the space compression, the integral of anisotropic PDF over the region of the circle was transformed to the integral of isotropic PDF over the region of an ellipse. And two calculational methods of the probability integral were advanced. The expressions of the maximal collision probability and the corresponding position error covariance were deeply analyzed based on the approximate results. The calculation of the collision probability in the case of the lower relative velocity was also discussed.
The explicit expression of the collision probability was deduced under the assumption that the orbit was a circle, the collision probability was expressed as an explicit function of the encounter geometry (crossing altitude difference and time difference of the line of the intersection of the two orbital planes, orbital planes included angle) and position error variance in RSW coordinates. With the help of the explicit expression, the influencing factors of the collision probability were analyzed, some significant conclusions were obtained.
The confidence level of the collision probability and its estimation technique were discussed. For describing the creditability of the calculated collision probability, concepts of the confidence interval of the collision probability and confidence level were introduced. Considering that the collision probability was a function of the encounter geometry and the position error variance, the confidence level of the collision probability was determined by the confidence level of the position error variance. Based on the confidence level and the confidence interval of the position error variance, the confidence level and the confidence interval of the collision probability were analyzed with the explicit expression of collision probability.
Characteristics of the propagation of the error covariance matrix which was essential in the probability calculation were analyzed; an assumption was advanced to explain the characteristics. Based on Hill equation and the CADET technique, the propagation of the initial error covariance of TLE was discussed. By using the Hill equation which took no account of the perturbation deviation and the Hill equation which took account of atmospheric drag deviation respectively, the initial error covariance of TLE was separated.
In the end, a space collision avoidance maneuver example and a weekly probability-maximum encounter event published by SCORATES were analyzed by the means of the collision probability presented previously. The results indicated that the collision probability method advanced in this thesis was accurate and efficient, and could be used in engineering practice.
介绍了空间碎片环境概况,分析了空间目标碰撞预警和规避机动的关键技术,提出了基于碰撞概率的空间目标碰撞预警和规避机动的基本框架。
研究了空间目标碰撞概率的计算方法。定义了相遇坐标系和积分计算坐标系,通过坐标转换和误差投影,将碰撞概率的计算问题转化为2维概率密度函数(PDF)在圆域内的积分问题。通过压缩空间的方法,将不等方差PDF在圆域内的积分化为等方差PDF在椭圆域内的积分,提出了两种概率积分计算方法:极坐标变换化为一重积分方法和圆近似无穷级数方法。根据近似结果分析了最大碰撞概率和相应的误差方差的表达式。简单讨论了低相对速度情况下碰撞概率的计算问题。
在圆轨道情况下推导了空间目标碰撞概率的显式表达式,将碰撞概率表示为交会几何条件(过交线高度差、过交线时间差、轨道夹角等)和RSW坐标系误差方差的显式函数。根据显式表达式对碰撞概率的诸影响因素进行了分析,得到了一些有意义的结论。对空间目标碰撞概率的置信度及其估计方法进行了讨论。引入碰撞概率置信区间和置信度的概念来描述计算得到碰撞概率的可信程度。碰撞概率是交会条件和位置误差的确定函数,碰撞概率的置信度取决于误差方差的置信度。基于误差方差的置信度和置信区间,利用显式表达式对碰撞概率的置信度和置信区间进行了分析,得到了一定简化条件下碰撞概率置信度的评估方法。
分析了碰撞概率计算中所需误差协方差矩阵的传播特性。对位置预报误差传播进行了分析,得到了TLE预报误差的特性,提出了一种假设解释了该特性。基于Hill方程和CADET方法进行了TLE初值方差传播分析,分别利用不考虑摄动偏差和考虑大气摄动偏差的Hill方程对TLE初值误差进行了分离。
最后,对一次空间碰撞规避机动实例和美国公布的一周碰撞概率最大交会事件进行了碰撞概率分析,对碰撞概率方法进行了综合应用。结果表明,本文中提出的碰撞概率方法是正确的,可以在工程实际中有效应用。
The collision probability problems in space objects collision detection and avoidance were mainly researched in this thesis, including calculational methods, the explicit expression, influencing factors and the confidence level of the collision probability, and propagation characteristics of the error covariance of the orbital prediction, which laid the foundation of the collision detection and avoidance of space objects.
The brief situation of the orbital environment was introduced, and then, key techniques of the collision detection and avoidance of space objects were discussed, and the basic frame of the collision detection and avoidance based on the collision probability was advanced.
Calculational methods of the collision probability were deeply studied. The encounter coordinates and the integral-calculation coordinates were defined, with the help of coordinate transformation and the projection of the position error covariance, the 3-dimensional collision probability problem was degraded into the integral of a 2-dimensional probability density function (PDF) over the region of a circle. Through the space compression, the integral of anisotropic PDF over the region of the circle was transformed to the integral of isotropic PDF over the region of an ellipse. And two calculational methods of the probability integral were advanced. The expressions of the maximal collision probability and the corresponding position error covariance were deeply analyzed based on the approximate results. The calculation of the collision probability in the case of the lower relative velocity was also discussed.
The explicit expression of the collision probability was deduced under the assumption that the orbit was a circle, the collision probability was expressed as an explicit function of the encounter geometry (crossing altitude difference and time difference of the line of the intersection of the two orbital planes, orbital planes included angle) and position error variance in RSW coordinates. With the help of the explicit expression, the influencing factors of the collision probability were analyzed, some significant conclusions were obtained.
The confidence level of the collision probability and its estimation technique were discussed. For describing the creditability of the calculated collision probability, concepts of the confidence interval of the collision probability and confidence level were introduced. Considering that the collision probability was a function of the encounter geometry and the position error variance, the confidence level of the collision probability was determined by the confidence level of the position error variance. Based on the confidence level and the confidence interval of the position error variance, the confidence level and the confidence interval of the collision probability were analyzed with the explicit expression of collision probability.
Characteristics of the propagation of the error covariance matrix which was essential in the probability calculation were analyzed; an assumption was advanced to explain the characteristics. Based on Hill equation and the CADET technique, the propagation of the initial error covariance of TLE was discussed. By using the Hill equation which took no account of the perturbation deviation and the Hill equation which took account of atmospheric drag deviation respectively, the initial error covariance of TLE was separated.
In the end, a space collision avoidance maneuver example and a weekly probability-maximum encounter event published by SCORATES were analyzed by the means of the collision probability presented previously. The results indicated that the collision probability method advanced in this thesis was accurate and efficient, and could be used in engineering practice.
引文
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