Bounding the Success Probability of Naval Mine-Clearance Missions Conducted by AUVs

The success of mine-clearance missions conducted by Autonomous Underwater Vehicles (AUVs) mainly depends on two inter-related factors: the AUV behavior and the validation of a mission assumption. AUVs are typically modeled as stochastic dynamical systems and controlled using probabilistic techniques, such as Kalman filtering, to handle environmental uncertainties and inherent behavioral randomness. Assumption validation, on the other hand, often relies on set-based conditions, such as detecting an object on the seabed using an onboard exteroceptor, resulting in a three-valued logic outcome: success, failure, or uncertain. Thus, estimating mission success involves computing the probability of an event whose realization can be uncertain and influenced by a stochastic system (i.e. the AUV). In this paper, we extend traditional binary outcome models to a three-valued logic framework and introduce an empirical estimator based on the Monte Carlo method to bound the success probability within an interval. As with the standard binary outcome Monte Carlo estimator, the accuracy of this estimated interval improves with the number of trials, following the law of large numbers.