In this paper a Bayesian method is proposed to estimate dynamic origin-destination (O-D) demand. The proposed method can synthesize multiple sources of data collected by various sensors, including link counts, turning movements at intersections, flows, and travel times on partial paths. Time-dependent demand for each O-D pair at each departure time is assumed to satisfy the normal distribution. The connections among multiple sources of field data and O-D demands for all departure times are established by their variance-covariance matrices. Given the prior distribution of dynamic O-D demands, the posterior distribution is developed by updating the traffic count information. Then, based on the posterior distribution, both point estimation and the corresponding confidence intervals of O-D demand variables are estimated. Further, a stepwise algorithm that can avoid matrix inversion, in which traffic counts are updated one by one, is proposed. Finally, a numerical example is conducted on Nguyen-Dupuis network to demonstrate the effectiveness of the proposed Bayesian method and solution algorithm. Results show that the total O-D variance is decreasing with each added traffic count, implying that updating traffic counts reduces O-D demand uncertainty. Using the proposed method, both total error and source-specific errors between estimated and observed traffic counts decrease by iteration. Specifically, using 52 multiple sources of traffic counts, the relative errors of almost 50% traffic counts are less than 5%, the relative errors of 85% traffic counts are less than 10%, the total error between the estimated and "true" O-D demands is relatively small, and the O-D demand estimation accuracy can be improved by using more traffic counts. It concludes that the proposed Bayesian method can effectively synthesize multiple sources of data and estimate dynamic O-D demands with fine accuracy.
Keywords: Bayesian statistic; dynamic O–D estimation; stepwise algorithm; synthesizing data.