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The completion problem can be formulated as recovering missing replica entries from partial observations, for which Bayesian matrix completion methods provide a probabilistic framework. However, the relatively high effective rank of replica libraries constructed from cross correlation functions requires more observations for reliable completion. To address this issue, a physics guided extension of Bayesian matrix completion with graphs (BMCG) is proposed. An envelope transform (ET) is applied to mitigate rapid propagation induced phase oscillations, thereby reducing the effective rank of the replica library. The circular structures revealed by ET are exploited to construct an initialization for BMCG. By incorporating ET-based rank reduction and circular-pattern initialization into BMCG, the proposed method enables reliable replica recovery. Simulations and experimental results demonstrate the effectiveness of the proposed method in localization, with observations of the sources of opportunity available only along a limited number of trajectories.<\/jats:p>","DOI":"10.1121\/10.0046802","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T12:02:29Z","timestamp":1790856149000},"page":"2756-2768","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Physics-guided Bayesian matrix completion of replica libraries for underwater source localization"],"prefix":"10.1121","volume":"160","author":[{"given":"Sitian","family":"Wang","sequence":"first","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou 310027,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9440-3219","authenticated-orcid":false,"given":"Ting","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou 310027,","place":["China"]},{"name":"Zhejiang Provincial Key Laboratory of Multi-Modal Communication Networks and Intelligent Information Processing 2 , College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8205-9334","authenticated-orcid":false,"given":"Jianlong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou 310027,","place":["China"]},{"name":"Zhejiang Provincial Key Laboratory of Multi-Modal Communication Networks and Intelligent Information Processing 2 , College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9138-8773","authenticated-orcid":false,"given":"Wen","family":"Xu","sequence":"additional","affiliation":[{"name":"Ocean Academy, Zhejiang University 3 , Zhoushan 316021,","place":["China"]},{"name":"National Key Lab of Deep-Sea Science and Intelligent Technology, The Institute of Deepsea Science and Engineering, Chinese Academy of Sciences 4 , Sanya 572000,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0471-062X","authenticated-orcid":false,"given":"Peter","family":"Gerstoft","sequence":"additional","affiliation":[{"name":"Scripps Institution of Oceanography, University of California San Diego 5 , La Jolla, California 92093,","place":["USA"]},{"name":"DTU Electro, Technical University of Denmark 6 , Kongens Lyngby 2800,","place":["Denmark"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"issue":"4","key":"2026100108022461700_c1","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1109\/48.262292","article-title":"An overview of matched field methods in ocean acoustics","volume":"18","year":"1993","journal-title":"IEEE J. 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