Estimating event probabilities via signal temporal logic and first occurrence distributions.

The article focuses on a novel method for estimating the probability of events represented by Signal Temporal Logic (STL) formulas, using the probability distributions of their first occurrence times in continuous time domains. This approach leverages atomic predicates with known first-occurrence-description (FOD) and time-point-description (TPD) functions to efficiently compute probabilities of complex temporal events without requiring high-precision signal predictions or extensive computational resources. The method assumes independence among sub-events and provides algorithms to estimate event probabilities and their distributions based on the FOD and TPD functions of simpler subformulas. Empirical evaluations on simulated unmanned aerial vehicle (UAV) motion and autonomous driving scenarios demonstrate the method’s effectiveness and smoother probability estimations compared to deep learning baselines, while also discussing limitations related to the independence assumption and potential extensions integrating more expressive temporal logics and deep learning techniques.