On the calibration of stochastic car following models

Recent experimental and empirical observations have demonstrated that stochasticity plays a critical role in car following (CF) dynamics. To reproduce the observations, quite a few stochastic CF models have been proposed. However, while calibrating the deterministic CF models is well investigated, studies on how to calibrate the stochastic models are lacking. Motivated by this fact, this paper aims to address this fundamental research gap. Firstly, the CF experiment under the same driving environment is conducted and analyzed. Based on the experimental results, we test two previous calibration methods, i.e., the method to minimize the Multiple Runs Mean (MRMean) error and the method of maximum likelihood estimation (MLE). Deficiencies of the two methods have been identified. Next, we propose a new method to minimize the Multiple Runs Minimum (MRMin) error. Calibration based on the experimental data and the synthetic data demonstrates that the new method outperforms the two previous methods. Furthermore, the mechanisms of different methods are explored from the perspective of error analysis. The analysis indicates that the new method can be regarded as a nested optimization model. The method separates the aleatoric errors caused by stochasticity from the epistemic error caused by parameters, and it is able to deal with the two kinds of errors effectively. Finally, we find that under the calibration framework of stochastic CF models, the calibrated parameter set using spacing as MoP may not always outperform that using velocity as MoP. These findings are expected to enhance the understanding of the role of stochasticity in CF dynamics where the new calibration framework for stochastic CF models is established.