基于拉普拉斯变换的空间目标碰撞概率计算方法

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。

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

The collision probability of space object is an important information for judging whether a colli-sion occurs in the space debris collision warning,and is important for the maneuvering avoidance of the space-craft.Based on the Laplace transformation and the definition of the power series,the collision probability cal-culation 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.