Satellite conjunction analysis and the false confidence theorem

Satellite conjunction analysis is the assessment of collision risk during a close encounter between a satellite and another object in orbit. A counterintuitive phenomenon has emerged in the conjunction analysis literature: probability dilution, in which lower quality data paradoxically appear to reduce the risk of collision. We show that probability dilution is a special case of a broader structural deficiency in epistemic probability distributions. In probabilistic representations of statistical inference, there are always false propositions that have a high probability of being assigned a high degree of belief. This is the false confidence theorem. As a practical matter, its manifestation in satellite conjunction analysis is particularly detrimental. Under ordinary operating conditions, satellite navigators using epistemic probability of collision as their decision-motivating risk metric are rendered incapable of detecting an impending collision. An explicit remedy for false confidence can be found in the Martin--Liu theory of inferential models. In satellite conjunction analysis, we show that $K \sigma$ uncertainty ellipsoids satisfy the Martin--Liu validity criterion. Performing collision avoidance maneuvers based on ellipsoid overlap will ensure that operational collision risk is capped at the user-specified level.