Computing Collision Probability Using Linear Covariance and Unscented Transforms

摘要

For a cluster of satellites flying in close proximity, the probability of collision (Pc) is of great interest. For a given cluster configuration (geometry), navigation noise, controller, and maneuver execution error, the most reliable way to compute Pc is through Monte Carlo simulations. However, Monte Carlo requires running a large number of cases to accurately determine Pc. This is time-consuming and usually not practical for the low level of Pc that may be desired. An alternative to Monte Carlo that requires much less computational resources involves the use of linear covariance to propagate the position and velocity dispersions of the cluster satellites. This method however is limited by its linear assumptions and is unstable for nonlinear problems that can arise in cluster flight. The use of unscented transforms for covariance propagation is shown to be more stable in this case. A method to incorporate the effects of navigation noise, closed-loop control, and maneuver execution error is developed. A sample cluster scenario is evaluated using the covariance method with a hybrid method of computing Pc that combines the Mahalanobis distance metric and the maximum instantaneous probability. The results are shown to match the Monte Carlo results with a high confidence interval.