Monitoring of Traffic Manoeuvres with Imprecise Information

Abstract

In monitoring, we algorithmically check if a single behavior satisfies a property. Here, we consider monitoring for Multi-Lane Spatial Logic (MLSL). The behavior is given as a finite transition sequence of MLSL and the property is that a spatial MLSL formula should hold at every point in time within the sequence. In our procedure we transform the transition sequence and the formula to the first-order theory of real-closed fields, which is decidable, such that the resulting formula is valid iff the MLSL formula holds throughout the transition sequence. We then assume that temporal data may have an error of up to $\varepsilon$, and that spatial data may have an error of up to $\delta$. We extend our procedure to check if the MLSL formula $\varepsilon$-$\delta$-robustly holds throughout the transition sequence.