Probabilistic recovery criteria for robust state-based conflict detection and resolution under navigation uncertainty

Abstract

Safety-critical autonomous systems make irreversible real-time decisions from noisy state estimates, and the reliability of those decisions depends on how sensor uncertainty is propagated through the decision rule. In state-based conflict detection and resolution (CD&R) for Uncrewed Aerial Systems (UASs), one such decision is recovery, the moment at which an aircraft may safely disengage a resolution manoeuvre and resume navigation. Because this decision is evaluated at close range near the end of resolution, it is particularly vulnerable to navigation uncertainty. This paper develops a probabilistic safety assessment method, as a refinement of the two-criteria free-to-revert (FTR) recovery rule, using tractable uncertainty propagation. Navigation uncertainty is propagated through the closest-point-of-approach (CPA) geometry, and recovery is permitted only when both criteria are satisfied above a prescribed confidence threshold γ. Monte Carlo simulations show that the probabilistic method (γ=0.999) achieves a mean intrusion prevention rate (IPR) of 0.999 under low uncertainty and 0.989 under high uncertainty, compared with 0.956 and 0.789 for the deterministic FTR. At small crossing angles under high uncertainty, the deterministic FTR degrades to an IPR of 0.430, while the probabilistic method remains above 0.922. The method’s advantage persists across six non-Gaussian navigation-noise models, where its intrusion prevention rate remains essentially unchanged (0.999) while the deterministic baselines degrade. The confidence threshold acts as a target reliability level for the recovery decision and provides a tunable safety–efficiency trade-off, allowing the balance between protection against premature recovery and separation efficiency to be controlled through a single parameter.