{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T10:17:49Z","timestamp":1771669069337,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T00:00:00Z","timestamp":1558310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"hejiang Natural Science Foundation","award":["LY18F010010"],"award-info":[{"award-number":["LY18F010010"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571250, 61531018"],"award-info":[{"award-number":["61571250, 61531018"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The received signal strength (RSS) based target localization problem in underwater acoustic wireless sensor networks (UWSNs) is considered. Two cases with respect to target transmit power are considered. For the first case, under the assumption that the reference of the target transmit power is known, we derive a novel weighted least squares (WLS) estimator by using an approximation to the RSS expressions, and then transform the originally non-convex problem into a mixed semi-definite programming\/second-order cone programming (SD\/SOCP) problem for reaching an efficient solution. For the second case, there is no knowledge on the target transmit power, and we treat the reference power as an additional unknown parameter. In this case, we formulate a WLS estimator by using a further approximation, and present an iterative ML and mixed SD\/SOCP algorithm for solving the derived WLS problem. For both cases, we also derive the closed form expressions of the Cramer\u2013Rao Lower Bounds (CRLBs) on root mean square error (RMSE). Computer simulation results show the superior performance of the proposed methods over the existing ones in the underwater acoustic environment.<\/jats:p>","DOI":"10.3390\/s19102323","type":"journal-article","created":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T11:05:07Z","timestamp":1558350307000},"page":"2323","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["RSS-Based Target Localization in Underwater Acoustic Sensor Networks via Convex Relaxation"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5446-5426","authenticated-orcid":false,"given":"Shengming","family":"Chang","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, China"},{"name":"School of Electronic and Information Engineering, Ningbo University of Technology, Ningbo 315211, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9497-6762","authenticated-orcid":false,"given":"Youming","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2459-597X","authenticated-orcid":false,"given":"Yucheng","family":"He","sequence":"additional","affiliation":[{"name":"Xiamen Key Laboratory of Mobile Multimedia Communications, Huaqiao University, 668 Jimei Avenue, Xiamen 361021, China"}]},{"given":"Yongqing","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Acoustics, Chinese Academy of Science, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S1389-1286(01)00302-4","article-title":"Wireless sensor networks: A survey","volume":"38","author":"Akyildiz","year":"2002","journal-title":"Comput. 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