Covariance correlations in collision avoidance probability calculations

Abstract

Collision-avoidance calculations between orbiting objects make use of covariance matrices to characterize the uncertainty of the orbital position in space and time. Both the potential collider and target each have such a covariance matrix that integrates uncertainties in the original state vector propagated forward in time as well as uncertainties in the atmospheric model for instance due to unpredictable variations in solar activity. For objects in low-Earth orbits, the longer the propagation, the more important the atmospheric uncertainty becomes. Currently, the collision probability is computed by assuming that the covariances characterizing the position uncertainties of the two objects are independent. Because of the coherent nature of atmospheric drag, this assumption is not necessarily true, especially for the down-range uncertainty. If the solar activity goes up, both objects will have increased drag. Likewise, if the solar activity goes down, both objects will have decreased drag. In this parametric study, we use two-line element set data to demonstrate this behavior and to make some simple estimates on its magnitude. We then estimate how much this may affect the accuracy of the calculated collision probability. We conclude with recommendations for future study.