On the calibration of stochastic car following models

Abstract

Recent empirical and theoretical findings highlight the critical role of stochasticity in car-following (CF) dynamics. Although several stochastic CF models have been proposed, their calibration remains relatively underexplored compared to deterministic models. This article addresses this gap by utilizing four stochastic CF models to conduct a comprehensive evaluation of two existing calibration methods—minimizing multiple runs mean error (MRMean) and maximum likelihood estimation (MLE) as well as a newly proposed method, minimizing multiple runs minimum (MRMin) error, based on synthetic trajectories. Results show that MRMean and MLE exhibit significant biases in estimating the ground truth values of stochastic model parameters, while MRMin achieves nearly zero estimation errors. Specifically, MRMean eliminates stochasticity, transforming models into deterministic ones, whereas MRMin successfully separates aleatoric errors caused by randomness and epistemic errors caused by parameters, as demonstrated through a theoretical error analysis. Furthermore, CF experiments conducted in an identical driving environment reveal that differences in spacing are more pronounced than differences in speed. Calibration against experimental trajectories verifies the conclusions drawn from synthetic trajectories and theoretical analysis. Additionally, the covariance matrix of parameters is estimated using bootstrap sampling, highlighting MRMin’s ability to capture the inherent stochasticity of CF behavior. These findings deepen our understanding of CF stochasticity and provide a robust framework for calibrating stochastic models.