Calibrating Car-Following Models via Bayesian Dynamic Regression

Chengyuan Zhang, Wenshuo Wang, Lijun Sun
Transportation Research Part C: Emerging Technologies (2024). Volume 168. Pages/article 104719.

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Why account for serially correlated car-following residuals?

Dynamic regression combines a parsimonious car-following model with autoregressive error dynamics, retaining historical information for calibration and probabilistic simulation.

Abstract

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 .

Full abstract from the linked arXiv version, checked 2026-09-13. The bibliographic record above identifies the journal publication; the abstract is the preprint text.

Research summary

An instantaneous car-following rule does not necessarily explain the temporal dependence remaining in observed trajectories. This paper couples the car-following mean with autoregressive residual dynamics inside a Bayesian calibration framework.

The result is a stochastic model in which recent residual history informs subsequent responses. The deterministic car-following component remains interpretable, while the error process represents temporal structure that independent noise would discard.

How does this relate to memory-augmented IDM?

Both approaches model residual dependence. MA-IDM uses a Gaussian process; dynamic regression uses an autoregressive time-series specification. The distinction concerns the model for temporal dependence, and should be assessed through fitted dynamics and predictive simulation.

How can I explore the method?

Read the notes on autoregressive processes and connections among stochastic processes, then consult the reference implementation.

ISTTT25 slides · Presentation · From driver variability to traffic simulation