北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (4): 810-819.doi: 10.13700/j.bh.1001-5965.2017.0263

• 论文 • 上一篇    下一篇

基于拉普拉斯变换的空间目标碰撞概率计算方法

霍俞蓉1, 李智2, 韩蕾2   

  1. 1. 装备学院航天装备系, 北京 101416;
    2. 装备学院航天指挥系, 北京 101416
  • 收稿日期:2017-04-26 出版日期:2018-04-20 发布日期:2018-04-27
  • 通讯作者: 李智 E-mail:lizhizys000@163.com
  • 作者简介:霍俞蓉,女,博士研究生。主要研究方向:空间碎片碰撞预警;李智,男,博士,教授,博士生导师。主要研究方向:空间态势感知、空间环境;韩蕾,女,博士,讲师。主要研究方向:航天器飞行动力学。
  • 基金资助:
    国家“863”计划(2015SQ704102)

Computation method of collision probability of space object based on Laplace transformation

HUO Yurong1, LI Zhi2, HAN Lei2   

  1. 1. Department of Space Equipment, Equipment Academy, Beijing 101416, China;
    2. Department of Space Command, Equipment Academy, Beijing 101416, China
  • Received:2017-04-26 Online:2018-04-20 Published:2018-04-27
  • Supported by:
    National High-tech Research and Development Program of China (2015 SQ704102)

摘要: 碰撞概率是空间碎片碰撞预警中评判碰撞发生可能性大小的重要依据,对航天器机动规避具有重要意义。基于拉普拉斯变换的碰撞概率计算方法利用拉普拉斯变换以及幂级数的定义,推导了在短时间接近情况下碰撞概率的幂级数表达式,分析了碰撞概率的截断误差并确定了在不同精度要求下的幂级数项数。针对2009年美俄卫星的碰撞事件,将基于拉普拉斯变换的碰撞概率计算结果与Chan方法、Monte Carlo方法的计算结果进行比较,验证了基于拉普拉斯变换方法在计算精度上的优势。

关键词: 空间碎片, 碰撞预警, 碰撞概率, 拉普拉斯变换, 幂级数

Abstract: The collision probability of space object is an important information for judging whether a collision occurs in the space debris collision warning, and is important for the maneuvering avoidance of the spacecraft. Based on the Laplace transformation and the definition of the power series, the collision probability calculation method and the collision probability expression expressed by the power series in the short-term encounter were discussed. The truncation error in the form of power series was determined and the number of terms of power series was analyzed under different precision requirements. The results of collision probability calculation based on Laplace transformation are compared with those of Chan method and Monte Carlo method for 2009 US-Russian satellite collision event. The validity of Laplace transformation method and the advantage of computing accuracy are verified.

Key words: space debris, collision warning, collision probability, Laplace transformation, power series

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