Calibrating car-following models via Bayesian dynamic regression

Car-following behavior modeling is critical for understanding traffic flow dynamics and developing high-fidelity microscopic simulation models. Most existing impulse-response car-following models prioritize computational efficiency and interpretability by using a parsimonious nonlinear function based on immediate preceding state observations. However, this approach disregards historical information, limiting its ability to explain real-world driving data. Consequently, serially correlated residuals are commonly observed when calibrating these models with actual trajectory data, hindering their ability to capture complex and stochastic phenomena. To address this limitation, we propose a dynamic regression framework incorporating time series models, such as autoregressive processes, to capture error dynamics. This statistically rigorous calibration outperforms the simple assumption of independent errors and enables more accurate simulation and prediction by leveraging higher-order historical information. We validate the effectiveness of our framework using HighD and OpenACC data, demonstrating improved probabilistic simulations. In summary, our framework preserves the parsimonious nature of traditional car-following models while offering enhanced probabilistic simulations. The code of this work is available at https://github.com/Chengyuan-Zhang/IDM_Bayesian_Calibration.