Probability based collision monitoring method within formation flying

A probability density function based collision monitoring method within formation flying is developed and simulated. The approach for collision monitoring presented in this paper is to propagate the uncertainty covariance using linear relative dynamic model and integrate collision probability density function over the defined collision region (the combined shape of satellites) to calculate the collision probability between two individual satellites in formation. The calculated collision probability in this paper, considering the shape of combined satellites, and the probability is calculated at instantaneous time, so it is suitable to predict when and how fast a collision might be happened. Simulations results show that the along-track projected two-dimensional (X-Z plane) collision probability is the most reliable as the along-track uncertainty is much higher than the radial and cross-track components. In addition, results show that the collision probability is sensitive to the geometry of formation and the uncertainty covariance. Moreover, the methodology developed in this paper has been used to test the passive operational safety of different formation geometry.