Rapid algorithm for covariance ellipsoid model based collision warning of space objects

The recent decades have witnessed a tremendous growth in the number of satellites and debris in space, leading to an increasingly high risk of collision between space objects. Collision warning aims at assessing the collision risk between space objects and attempts to identify possible collisions in order for satellites to perform evasive maneuvers in advance. Current collision warning methods are based on the computation of collision probability and comparison with some tolerance threshold. Such a threshold is usually set according to experience. In contrast, this paper proposes to use covariance ellipsoid with a user defined Mahalanobis distance to represent the most possible region in which the relative position vector distributes. Zero vector represents the collision event, and once it enters this ellipsoid, a collision warning occurs. A collision warning function along with a definite threshold is then formulated based on this criterion. Moreover, in order to rapidly predict the possible collision intervals, a self-adaptive Hermite interpolation technique is applied to approximate the collision warning function by piecewise cubic polynomials for efficient roots finding. Finally, the proposed collision warning criterion has been evaluated in several collision scenarios. Comparison experiments are also conducted with the brute force method and analytical propagators. The simulation shows that the calculation of collision warning interval based on the proposed criterion is effective, and the self-adaptive Hermite interpolation method performs high efficiency and accuracy.