Robust parameter estimation of car-following models considering practical non-identifiability

Realistic simulations of microscopic traffic are required by a wide range of applications, from the design of local infrastructure solutions, to the testing of vehicle-tailored traffic management strategies, particularly in the context of an upcoming mixed traffic involving connected and autonomous vehicles. Recent studies point out that an accurate knowledge of the heterogeneity of vehicles behaviour is key to reproducing realistic microscopic simulations. Car-following models are able to capture such heterogeneity via behavioural parameters. Researchers have looked at getting realistic parameters of car-following models using trajectory datasets. It requires data filtering, parameter identification for each leader-follower couple, evaluation of statistical dependencies between the estimated parameters and parameters sampling. However, we have found that the parameter identification part, arguably the most important, is often overlooked, as the parameters that can be estimated, i.e. that are identifiable, highly depend on the leading vehicle trajectory. While global sensitivity analyses help disregard insensitive parameters, there is a need to complement them with a systematic statistical approach to get insights about the robustness of parameters estimates, i.e. the shape of the objective function nearby the estimates. In this paper, we first isolate parameters that can be identified, then perform parameter estimation, and finally verify that the confidence region of the estimates lies within the physical bounds of the parameters. This involves variance-based global sensitivity analyses to reduce the parameter space, log likelihood estimation for point estimation and use of the likelihood-ratio technique for interval estimation. Outputs are distributions of the estimated parameters and of their confidence values, for any investigated car-following models and datasets.