Mathematics – Probability
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011acasn..52...73x&link_type=abstract
Acta Astronomica Sinica, vol. 52, no. 1, p.73-85
Mathematics
Probability
Space Vehicles, Methods: Analytical
Scientific paper
The calculation of collision probability is the foundation of collision detection and avoidance maneuver for space objects. Now an assumption of linear relative motion is usually applied in the calculation of collision probability and then the complex 3-dimensional problem can be reduced to a 2-dimensional integral of probability density function over the area of circle. However, if the relative velocity value is very small, the term of linear relative motion is not valid. So it is necessary to consider the calculation of collision probability for nonlinear relative motion. The method used to calculate collision probability for nonlinear relative motion is studied, and test cases are designed to prove the validity of this method. It is applicable to collision probability problems involving relative velocity and error covariance varying with time. The results indicate that it is necessary to calculate collision probability with this nonlinear method under certain circumstances. For example, for elliptical relative motions in Satellite Formation Flying, when the relative velocity is below 100 m/s, the relative error between the linear method and the nonlinear method exceeds 5%; for the problem of conjunction analysis of two satellites with circular orbit, when the relative velocity is below 10 m/s, the relative error is also larger than 1%. Some significant conclusions are obtained for collision detection system of our country.
Xiong Yong-Qing
Xu Xiu-Lian
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