{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:41:19Z","timestamp":1760110879589,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T00:00:00Z","timestamp":1718236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41906162"],"award-info":[{"award-number":["41906162"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>For a multi-hydrophone synthetic aperture sonar (SAS), the instability of the platform and underwater turbulence easily lead to two-dimensional (2-D) space-variant (SV) motion errors. Such errors can cause serious imaging problems and are very difficult to compensate for. In this study, we propose a 2-D SV motion compensation algorithm for a multi-hydrophone SAS based on sub-beam compensation. The proposed algorithm is implemented using the following four-step process: (1) The motion error of each sub-beam is obtained by substituting the sonar\u2019s motion parameters measured in the exact motion error model established in this study. (2) The sub-beam\u2019s targets of all targets are compensated for motion error by implementing two-phase multiplications on the raw data of the multiple-hydrophone SAS in the order of hydrophone by hydrophone. (3) The data of the sub-beam\u2019s target compensated motion error are extracted from the raw data by utilizing the mapping relationship between the azimuth angle and the Doppler frequency. (4) The imaging result of each sub-beam is obtained by performing a monostatic imaging algorithm on each sub-beam\u2019s data and coherently added to obtain high-resolution imaging results. Finally, the validity of the proposed algorithm was tested using simulation and real data.<\/jats:p>","DOI":"10.3390\/rs16122144","type":"journal-article","created":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T10:41:03Z","timestamp":1718275263000},"page":"2144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two-Dimensional Space-Variant Motion Compensation Algorithm for Multi-Hydrophone Synthetic Aperture Sonar Based on Sub-Beam Compensation"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3560-6478","authenticated-orcid":false,"given":"Haoran","family":"Wu","sequence":"first","affiliation":[{"name":"Naval Institute of Underwater Acoustic Technology, Naval University of Engineering, Wuhan 430033, China"}]},{"given":"Fanyu","family":"Zhou","sequence":"additional","affiliation":[{"name":"Naval Institute of Underwater Acoustic Technology, Naval University of Engineering, Wuhan 430033, China"}]},{"given":"Zhimin","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Military Marine Environment Construction Office, Beijing 100161, China"}]},{"given":"Jingsong","family":"Tang","sequence":"additional","affiliation":[{"name":"Naval Institute of Underwater Acoustic Technology, Naval University of Engineering, Wuhan 430033, China"}]},{"given":"Heping","family":"Zhong","sequence":"additional","affiliation":[{"name":"Naval Institute of Underwater Acoustic Technology, Naval University of Engineering, Wuhan 430033, China"}]},{"given":"Jiafeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Naval Institute of Underwater Acoustic Technology, Naval University of Engineering, Wuhan 430033, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1109\/JOE.2009.2020853","article-title":"Synthetic Aperture Sonar: A Review of Current Status","volume":"34","author":"Hayes","year":"2009","journal-title":"IEEE J. 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Syst."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/12\/2144\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:58:08Z","timestamp":1760108288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/12\/2144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,13]]},"references-count":20,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["rs16122144"],"URL":"https:\/\/doi.org\/10.3390\/rs16122144","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,6,13]]}}}