Highlights • A general framework is developed for combining any general traffic flow model with statistical learning for traffic parameters estimation considering arterial corridor with several signalized intersections using vehicle trajectories with low penetration rate. • By combining a dynamic traffic flow model with BN, the framework establishes the learning process for traffic parameters estimation, such as traffic arrivals, traffic states as well as traffic flow model parameters. • The proposed framework is evaluated with different traffic flow models using the NGSIM dataset with three signalized intersections. • To illustrate this framework, the combination of BN with CTM and VISSIM is mainly considered, as these traffic simulation models can replicate complex traffic flow dynamics, especially in accommodating dynamic arrival patterns and spillback effects among multiple signalized intersections. • For the CTM-BN model, the mean absolute percentage error (MAPE) of the estimation is generally below 5% when the penetration rate is above 12%. Regarding the VISSIM-BN model, the MAPE of the estimation is generally below 5% when the penetration rate is above 6%.

Abstract This work focuses on traffic parameters estimation based on trajectory data in an arterial corridor with multiple signalized intersections. We develop a general framework that can combine various traffic flow models with Bayesian Network (BN) for estimating the overall traffic parameters using partially observed vehicle trajectory data (with unknown penetration rate). The BN is formulated to establish the probabilistic relationship between the traffic arrival process, traffic states, traffic flow model parameters and observed vehicle trajectories. More specifically, given traffic arrival information (e.g., traffic arrival volume) and fundamental diagram parameters (e.g., capacity, jam density, and free flow speed), vehicle trajectories are derived or simulated based on traffic flow modelling (e.g., shockwave analysis, Cell Transmission Model (CTM), or microscopic traffic simulation model VISSIM). Here, the extracted entry time of an observed vehicle at a pre-defined location upstream of the signal and its travel time are used to establish the probabilistic relationship. On the other hand, they are also the input parameters of the model for the estimation. Then, by combining a dynamic traffic flow model with Bayesian inference, we develop a framework to establish the learning process for traffic parameters estimation, such as traffic volume and traffic flow model parameters. The proposed framework is evaluated with different traffic flow models using the NGSIM dataset of an arterial corridor with three signalized intersections. For the CTM-BN model, the mean absolute percentage error (MAPE) of the estimation is generally below 5% when the penetration rate is above 12%. Regarding the VISSIM-BN model, the MAPE of the estimation is generally below 5% when the penetration rate is above 6%. These results demonstrate the applicability of the framework even under a relatively low penetration rate, and that the fidelity of the dynamic traffic model used does influence the estimation performance.