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.

I. Introduction

Car-Following models can be calibrated with both the macroscopic and microscopic data. Macroscopic data-based calibration methods focus on reproducing macroscopic traffic flow characteristics such as the field fundamental diagrams [3] and aggregated traffic state readings from detectors [4]–[6], in which car-following models are calibrated together with other microscopic models (e.g., lane-changing models). Car-following models can be also calibrated using microscopic vehicle trajectory data. When properly calibrated, the resulting model can replicate the step-by-step vehicle acceleration, velocity, and location observed in field car-following vehicle trajectories. Trajectory data-based calibration methods have attracted the attention of many researchers with the availability of microscopic trajectory data sets. Field vehicle trajectory data can be collected in two main approaches. The first and traditional approach is through a car-following driving test [1] with GPS loggers to record the vehicle dynamics. The other one is through passive data collection methods such as traffic video taken from high-rise buildings [10], [11] or helicopters [12], [13]. Furthermore, the latest development in probe vehicle technologies [14] and emerging connected vehicle technologies [15], [16] also provides new opportunities for obtaining trajectory data in real-time in the future. In this paper, our focus is on high-resolution vehicle trajectory data-based calibration. The data set used for analysis is the Next-Generation Simulation (NGSIM) US101 data, which has been widely used in studying microscopic traffic flow models [17]–[20]. Even with the increased interests of using microscopic vehicle trajectory data in microscopic traffic flow modeling and simulation, one critical problem is still not fully investigated, the error accumulation issue, which may significantly affect the validity and credibility of the results and findings.