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.