An optimal estimation approach for the calibration of the car-following behavior of connected vehicles in a mixed traffic environment

In the test bed of connected vehicles, detailed trajectory data are collected for connected vehicles only. It brings challenges to study the car-following behavior of connected vehicles following nonconnected vehicles. This paper proposes an optimal estimation approach to calibrate connected vehicles' car-following behavior in a mixed traffic environment. Particularly, the state-space system dynamics is captured by the simplified car-following model with disturbances, where the trajectory of nonconnected vehicles are considered as unknown states, and the trajectory of connected vehicles are considered as measurements with errors. The objective of the reformulation is to obtain an optimal estimation of states and model parameters simultaneously. It is shown that the customized state-space model is identifiable with the mild assumption that the disturbance covariance of the state update process is diagonal. Then, a modified expectation-maximization (EM) algorithm based on the Kalman smoother is developed to solve the optimal estimation problem. The performance of the EM algorithm is validated through simulation data. The second part of this paper applies the empirical data of connected vehicles from the Michigan test bed and analyzes the mobility impact of connected vehicles with different penetration rates and demand scenarios.