Bilevel Generalized Least Squares Estimation of Dynamic Origin–Destination Matrix for Urban Network with Probe Vehicle Data

Abstract

Methods of estimating dynamic origin–destination (O-D) matrices for urban networks from probe vehicle data are explored. A speed–density function is derived and fitted for different types of roads with the use of the maximum likelihood method. Both a Bayesian method that carefully incorporates prior information and an ordinary method are used to estimate link flows from probe vehicle speed. A dynamic traffic assignment–based bilevel generalized least squares (GLS) estimator considering the distance between the estimated and target O-D matrices as well as the distance between the calculated and observed link flows is formulated to estimate dynamic O-D matrices from estimated link flows. In the iterative solution procedure, the upper level is solved with the extended Bell algorithm, and the microscopic dynamic traffic assignment system VISSIM is applied to produce the assignment matrix in the lower level. A medium-sized signalized network in Tokyo is modeled in a case study in which Bayesian and ordinary methods are compared both in link flow estimation and O-D matrix estimation. Further, the bilevel GLS estimator and bilevel ordinary least squares estimator are implemented and then compared in O-D estimation. The results validate the proposed bilevel GLS estimator.