A probabilistic approach for the calibration of incomplete microscopic traffic models

Digital Twins (DTs) are steadily gaining popularity for the study of large systems in real time. In order to build an efficient and reliable DT, it is crucial to perform calibration prior to its use, that is, to use real data to estimate unknown parameters in the DT, that are of great importance for the actual physical process. This work studies the calibration of the Intelligent Driver Model (IDM) to infer driver behaviour, a crucial task when building a DT of the traffic network. We introduce a statistical model to calibration which takes into account the model uncertainty, while also taking into account possible correlations between individual vehicles that have similar characteristics. In contrast with other works in the literature, we assume that vehicles belong to a pre-specified group and develop a Bayesian approach to derive the posterior distributions of the parameters that characterise each group's behaviour. We apply the proposed approach to the IDM and derive probability density functions of the unknown model parameters and the model uncertainty. The proposed probabilistic approach is validated using realistic SUMO micro-simulations of a highway stretch. We present estimation results that show that the proposed approach can accurately derive the posterior distributions of the calibration parameters. In addition, we compare the proposed approach with a literature methodology and show that our approach higher quality posterior distributions of the parameters of interest than the literature approach.