{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:04:14Z","timestamp":1774051454325,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T00:00:00Z","timestamp":1626825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Humanities and Social Science Foundation of the Ministry of education in China","award":["18YJCZH274"],"award-info":[{"award-number":["18YJCZH274"]}]},{"name":"the Science and technology Project of Jiangsu Province, China","award":["BK20190926"],"award-info":[{"award-number":["BK20190926"]}]},{"name":"the Science and Technology Project of Zhejiang Province grant numbers","award":["2021C01011"],"award-info":[{"award-number":["2021C01011"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["22120210251"],"award-info":[{"award-number":["22120210251"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["22120210252"],"award-info":[{"award-number":["22120210252"]}]},{"name":"the Social Science Fund of Jiangsu Province","award":["20GLC015"],"award-info":[{"award-number":["20GLC015"]}]},{"name":"the Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["19KJB580003"],"award-info":[{"award-number":["19KJB580003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper a Bayesian method is proposed to estimate dynamic origin\u2013destination (O\u2013D) 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\u2013D pair at each departure time is assumed to satisfy the normal distribution. The connections among multiple sources of field data and O\u2013D demands for all departure times are established by their variance-covariance matrices. Given the prior distribution of dynamic O\u2013D 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\u2013D 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\u2013Dupuis network to demonstrate the effectiveness of the proposed Bayesian method and solution algorithm. Results show that the total O\u2013D variance is decreasing with each added traffic count, implying that updating traffic counts reduces O\u2013D 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 \u201ctrue\u201d O\u2013D demands is relatively small, and the O\u2013D 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\u2013D demands with fine accuracy.<\/jats:p>","DOI":"10.3390\/s21154971","type":"journal-article","created":{"date-parts":[[2021,7,22]],"date-time":"2021-07-22T22:37:14Z","timestamp":1626993434000},"page":"4971","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Bayesian Method for Dynamic Origin\u2013Destination Demand Estimation Synthesizing Multiple Sources of Data"],"prefix":"10.3390","volume":"21","author":[{"given":"Hang","family":"Yu","sequence":"first","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Se Yuan Road #9, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6138-5130","authenticated-orcid":false,"given":"Senlai","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Se Yuan Road #9, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Se Yuan Road #9, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9649-5121","authenticated-orcid":false,"given":"Yuntao","family":"Guo","sequence":"additional","affiliation":[{"name":"Key Laboratory of Road and Traffic Engineering, Ministry of Education, Department of Traffic Engineering Tongji University, 4800 Cao\u2019an Road, Shanghai 201804, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2222-4745","authenticated-orcid":false,"given":"Tianpei","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Se Yuan Road #9, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0191-2615(88)90024-0","article-title":"A unified framework for estimating or updating origin\/destination matrices from traffic counts","volume":"22","author":"Cascetta","year":"1988","journal-title":"Transp. 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