{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:16:57Z","timestamp":1760235417100,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:00:00Z","timestamp":1629417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["61703333, 62076201, U1934222"],"award-info":[{"award-number":["61703333, 62076201, U1934222"]}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["2019JQ-746 and 2019JQ-740"],"award-info":[{"award-number":["2019JQ-746 and 2019JQ-740"]}]},{"DOI":"10.13039\/501100010228","name":"Natural Science Foundation of Shaanxi Provincial Department of Education","doi-asserted-by":"publisher","award":["20JS088"],"award-info":[{"award-number":["20JS088"]}],"id":[{"id":"10.13039\/501100010228","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets\u2019 numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets\u2019 intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments.<\/jats:p>","DOI":"10.3390\/e23081082","type":"journal-article","created":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T08:44:45Z","timestamp":1629449085000},"page":"1082","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment"],"prefix":"10.3390","volume":"23","author":[{"given":"Xiaohua","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Shaanxi Key Laboratory for Network Computing and Security Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Shaanxi Key Laboratory for Network Computing and Security Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-334X","authenticated-orcid":false,"given":"Wasiq","family":"Ali","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3742-4029","authenticated-orcid":false,"given":"Haiyan","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Shaanxi Key Laboratory for Network Computing and Security Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/JOE.2010.2098810","article-title":"An overview of sequential Bayesian filtering in ocean acoustics","volume":"36","author":"Yardim","year":"2011","journal-title":"IEEE J. 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