Reducing the Error Accumulation in Car-Following Models Calibrated With Vehicle Trajectory Data

With the development of probe vehicle technologies and the emerging connected vehicle technologies, applications and models using trajectory data for calibration and validation significantly increase. However, the error accumulation issue accompanied by the calibration process has not been fully investigated and addressed. This paper explores the mechanism and countermeasures of the error accumulation problems of car-following models calibrated with microscopic vehicle trajectory data. In this paper, we first derive the error dynamic model based on an acceleration-based generic car-following model formulation. The stability conditions for the error dynamic model are found to be different from the model stability conditions. Therefore, adjusting feasible ranges of model parameters in the car-following model calibration to ensure model stability cannot guarantee the error stability. However, directly enforcing those error stability conditions can be ineffective, particularly when explicit formulations are difficult to obtain. To overcome this issue, we propose several countermeasures that incorporate error accumulation indicators into the error measures used in the calibration. Numerical experiments are conducted to compare the traditional and the proposed error measures through the calibration of five representative car-following models, i.e., General Motors, Bando, Gipps, FREeway SIMulation (FRESIM), and intelligent driver model (IDM) models, using field trajectory data. The results indicate that the weighted location mean absolute error (MAE) and the location MAE with crash rate penalty can achieve the best overall error accumulation performance for all five models. Meanwhile, traditional error measures, velocity MAE, and velocity Theil's U also achieve satisfactory error accumulation performance for FRESIM and IDM models, respectively.