{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:42:18Z","timestamp":1760233338086,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and ICT","award":["021M3F6A1085889"],"award-info":[{"award-number":["021M3F6A1085889"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Frequency\u2013wavenumber (f\u2013k) analysis can estimate the direction of arrival (DOA) of broadband signals received on a vertical array. When the vertical array configuration is sparse, it results in an aliasing error due to spatial sampling; thus, several striation patterns can emerge in the f\u2013k domain. This paper extends the f\u2013k analysis to a sparse receiver-array, wherein a multitude of sidelobes prevent resolving the DOA estimates due to spatial aliasing. The frequency difference-wavenumber (\u0394f\u2013k) analysis is developed by adopting the concept of frequency difference, and demonstrated its performance of DOA estimation to a sparse receiver array. Experimental results verify the robustness of the proposed \u0394f\u2013k analysis in the estimation of the DOA of cracking sounds generated by the snapping shrimps, which were recorded by a sparse vertical array configuration during the shallow water experiment.<\/jats:p>","DOI":"10.3390\/s23010337","type":"journal-article","created":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T02:54:42Z","timestamp":1672282482000},"page":"337","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Direction-of-Arrival Estimation Based on Frequency Difference\u2013Wavenumber Analysis for Sparse Vertical Array Configuration"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1839-1666","authenticated-orcid":false,"given":"Donghyeon","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Convergence Study on the Ocean Science and Technology, Korea Maritime and Ocean University, Busan 49112, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gihoon","family":"Byun","sequence":"additional","affiliation":[{"name":"Department of Convergence Study on the Ocean Science and Technology, Korea Maritime and Ocean University, Busan 49112, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8514-3187","authenticated-orcid":false,"given":"Jeasoo","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Ocean Engineering, Korea Maritime and Ocean University, Busan 49112, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1121\/1.2139074","article-title":"The array invariant","volume":"119","author":"Lee","year":"2006","journal-title":"J. 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[3rd ed.]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/337\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:54:37Z","timestamp":1760147677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/337"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,28]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23010337"],"URL":"https:\/\/doi.org\/10.3390\/s23010337","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,12,28]]}}}