{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T16:54:16Z","timestamp":1779296056660,"version":"3.51.4"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T00:00:00Z","timestamp":1588723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61573251,61973232"],"award-info":[{"award-number":["No. 61573251,61973232"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>One of the major tasks in process industry is solid concentration (SC) estimation in solid\u2013liquid two-phase flow in any pipeline. The \u03b3-ray sensor provides the most used and direct measurement to SC, but it may be inaccurate due to very local measurements and inaccurate density baseline. Alternatively, under various conditions there are a tremendous amount of indirect measurements from other sensors that can be used to adjust the accuracy of SC estimation. Consequently, there is complementarity between them, and integrating direct and indirect measurements is helpful to improve the accuracy of SC estimation. In this paper, after recovering the interrelation of these measurements, we proposed a new SC estimation method according to Kalman filter fusion. Focusing on dredging engineering fields, SCs of representative flow pattern were tested. The results show that our proposed methods outperform the fused two types of measurements in real solid\u2013liquid two-phase flow conditions. Additionally, the proposed method has potential to be applied to other fields as well as dredging engineering.<\/jats:p>","DOI":"10.3390\/s20092657","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T03:10:38Z","timestamp":1588821038000},"page":"2657","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Solid Concentration Estimation by Kalman Filter"],"prefix":"10.3390","volume":"20","author":[{"given":"Yongguang","family":"Tan","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shihong","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,6]]},"reference":[{"key":"ref_1","unstructured":"Zych, M., Hanus, R., Petryka, L., Strzepowicz, A., and Zych, P. 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