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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 607195, 8 pages
Research Article

A Bayesian Combined Model for Time-Dependent Turning Movement Proportions Estimation at Intersections

School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received 1 April 2014; Revised 23 June 2014; Accepted 1 July 2014; Published 17 July 2014

Academic Editor: X. Zhang

Copyright © 2014 Pengpeng Jiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Time-dependent turning movement flows are very important input data for intelligent transportation systems but are impossible to be detected directly through current traffic surveillance systems. Existing estimation models have proved to be not accurate and reliable enough during all intervals. An improved way to address this problem is to develop a combined model framework that can integrate multiple submodels running simultaneously. This paper first presents a back propagation neural network model to estimate dynamic turning movements, as well as the self-adaptive learning rate approach and the gradient descent with momentum method for solving. Second, this paper develops an efficient Kalman filtering model and designs a revised sequential Kalman filtering algorithm. Based on the Bayesian method using both historical data and currently estimated results for error calibration, this paper further integrates above two submodels into a Bayesian combined model framework and proposes a corresponding algorithm. A field survey is implemented at an intersection in Beijing city to collect both time series of link counts and actual time-dependent turning movement flows, including historical and present data. The reported estimation results show that the Bayesian combined model is much more accurate and stable than other models.