{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:46:33Z","timestamp":1760237193816,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,13]],"date-time":"2020-03-13T00:00:00Z","timestamp":1584057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Basic Research Program of China (973 Program)","award":["2018YFB1601300, 2016YFB0100903"],"award-info":[{"award-number":["2018YFB1601300, 2016YFB0100903"]}]},{"name":"Australia Research Council","award":["DE190100931"],"award-info":[{"award-number":["DE190100931"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper introduces a new methodology for reconstructing vehicle densities of freeway segments by utilizing the limited data collected by traffic-counting sensors and developing a macroscopic traffic stream model formulated as a switched reduced-order state observer design problem with unknown or partially known inputs. Specifically, the traffic network is modeled as a hybrid dynamic system in a state space that incorporates unknown inputs. For freeway segments with traffic-counting sensors installed, vehicle densities are directly computed using field traffic count data. A reduced-order state observer is designed to analyze traffic state transitions for freeway segments without field traffic count data to indirectly estimate the vehicle densities for each freeway segment. A simulation-based experiment is performed applying the methodology and using data of a segment of Beijing Jingtong freeway in Beijing, China. The model execution results are compared with the field data associated with the same freeway segment, and highly consistent results are achieved. The proposed methodology is expected to be adopted by traffic engineers to evaluate freeway operations and develop effective management strategies.<\/jats:p>","DOI":"10.3390\/s20061609","type":"journal-article","created":{"date-parts":[[2020,3,18]],"date-time":"2020-03-18T08:20:44Z","timestamp":1584519644000},"page":"1609","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Hybrid Dynamic Traffic Model for Freeway Flow Analysis Using a Switched Reduced-Order Unknown-Input State Observer"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6434-8714","authenticated-orcid":false,"given":"Yuqi","family":"Guo","sequence":"first","affiliation":[{"name":"Research Institute of Highway, Ministry of Transport of China, Beijing 100088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Li","sequence":"additional","affiliation":[{"name":"Research Institute of Highway, Ministry of Transport of China, Beijing 100088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5502-901X","authenticated-orcid":false,"given":"Matthew Daniel","family":"Christie","sequence":"additional","affiliation":[{"name":"School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW 2522, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6500-7460","authenticated-orcid":false,"given":"Zongzhi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel Angel","family":"Sotelo","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, University of Alcal\u00e1, 28801 Alcal\u00e1 de Henares (Madrid), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yulin","family":"Ma","sequence":"additional","affiliation":[{"name":"Suzhou Automotive Research Institute, Tsinghua University, Suzhou 215134, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongmei","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Institute of Highway, Ministry of Transport of China, Beijing 100088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhixiong","family":"Li","sequence":"additional","affiliation":[{"name":"Suzhou Automotive Research Institute, Tsinghua University, Suzhou 215134, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TAC.1966.1098323","article-title":"Observers for multivariable systems","volume":"11","author":"Luenberger","year":"2003","journal-title":"IEEE Trans. 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