# Satellite conjunction analysis and the false confidence theorem

## TL;DR

This paper identifies a fundamental flaw called false confidence in probabilistic satellite conjunction analysis, proposes a validity criterion to address it, and demonstrates that uncertainty ellipsoids provide reliable collision risk estimates.

## Contribution

It introduces the Martin–Liu validity criterion to detect false confidence and shows that uncertainty ellipsoids satisfy this criterion, improving collision risk assessment.

## Key findings

- Probability dilution is caused by false confidence.
- Uncertainty ellipsoids satisfy the validity criterion.
- Collision risk can be reliably capped using ellipsoid overlap.

## Abstract

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, namely, probability dilution, in which lower quality data paradoxically appear to reduce the risk of collision. We show that probability dilution is a symptom of a fundamental deficiency in probabilistic representations of statistical inference, in which there are propositions that will consistently be assigned a high degree of belief, regardless of whether or not they are true. We call this deficiency false confidence. In satellite conjunction analysis, it results in a severe and persistent underestimate of collision risk exposure. We introduce the Martin--Liu validity criterion as a benchmark by which to identify statistical methods that are free from false confidence. Such inferences will necessarily be non-probabilistic. In satellite conjunction analysis, we show that uncertainty ellipsoids satisfy the validity criterion. Performing collision avoidance maneuvers based on ellipsoid overlap will ensure that collision risk is capped at the user-specified level. Further, this investigation into satellite conjunction analysis provides a template for recognizing and resolving false confidence issues as they occur in other problems of statistical inference.