{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T08:34:12Z","timestamp":1769934852239,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2019,10,7]],"date-time":"2019-10-07T00:00:00Z","timestamp":1570406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000140","name":"U.S. Department of Transportation","doi-asserted-by":"publisher","award":["69A3551747123"],"award-info":[{"award-number":["69A3551747123"]}],"id":[{"id":"10.13039\/100000140","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a novel model for estimating the number of vehicles along signalized approaches. The proposed estimation algorithm utilizes the adaptive Kalman filter (AKF) to produce reliable traffic vehicle count estimates, considering real-time estimates of the system noise characteristics. The AKF utilizes only real-time probe vehicle data. The AKF is demonstrated to outperform the traditional Kalman filter, reducing the prediction error by up to 29%. In addition, the paper introduces a novel approach that combines the AKF with a neural network (AKFNN) to enhance the vehicle count estimates, where the neural network is employed to estimate the probe vehicles\u2019 market penetration rate. Results indicate that the accuracy of vehicle count estimates is significantly improved using the AKFNN approach (by up to 26%) over the AKF. Moreover, the paper investigates the sensitivity of the proposed AKF model to the initial conditions, such as the initial estimate of vehicle counts, initial mean estimate of the state system, and the initial covariance of the state estimate. The results demonstrate that the AKF is sensitive to the initial conditions. More accurate estimates could be achieved if the initial conditions are appropriately selected. In conclusion, the proposed AKF is more accurate than the traditional Kalman filter. Finally, the AKFNN approach is more accurate than the AKF and the traditional Kalman filter since the AKFNN uses more accurate values of the probe vehicle market penetration rate.<\/jats:p>","DOI":"10.3390\/s19194325","type":"journal-article","created":{"date-parts":[[2019,10,7]],"date-time":"2019-10-07T03:34:01Z","timestamp":1570419241000},"page":"4325","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Developing a Neural\u2013Kalman Filtering Approach for Estimating Traffic Stream Density Using Probe Vehicle Data"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4251-1899","authenticated-orcid":false,"given":"Mohammad A.","family":"Aljamal","sequence":"first","affiliation":[{"name":"Charles E. Via, Jr. Department of Civil and Environmental Engineering, Center for Sustainable Mobility, Virginia Tech Transportation Institute, Virginia Tech, Blacksburg, VA 24061, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hossam M.","family":"Abdelghaffar","sequence":"additional","affiliation":[{"name":"Department of Computers Engineering and Systems, Engineering Faculty, Mansoura University, Mansoura, Dakahlia 35516, Egypt"},{"name":"Center for Sustainable Mobility, Virginia Tech Transportation Institute, Virginia Tech, Blacksburg, VA 24061, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5845-2929","authenticated-orcid":false,"given":"Hesham A.","family":"Rakha","sequence":"additional","affiliation":[{"name":"Charles E. Via, Jr. Department of Civil and Environmental Engineering, Center for Sustainable Mobility, Virginia Tech Transportation Institute, Virginia Tech, Blacksburg, VA 24061, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zmud, J., Goodin, G., Moran, M., Kalra, N., and Thorn, E. (2017). Advancing Automated and Connected Vehicles: Policy and Planning Strategies for State and Local Transportation Agencies, National Academies Press.","DOI":"10.17226\/24872"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Anand, R.A., Vanajakshi, L., and Subramanian, S.C. (2011, January 5\u20139). Traffic density estimation under heterogeneous traffic conditions using data fusion. 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