{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T16:23:30Z","timestamp":1783700610454,"version":"3.55.0"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T00:00:00Z","timestamp":1522368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["No.51679057"],"award-info":[{"award-number":["No.51679057"]}]},{"name":"National Nature Science Foundation of China","award":["No.51409055"],"award-info":[{"award-number":["No.51409055"]}]},{"name":"National Nature Science Foundation of China","award":["No.51309067"],"award-info":[{"award-number":["No.51309067"]}]},{"name":"Science Foundation for Distinguished Young Scholars of Heilongjiang Province of China","award":["No.J2016JQ0052"],"award-info":[{"award-number":["No.J2016JQ0052"]}]},{"name":"Nature Science Foundation of Heilongjiang Province of China","award":["No.E2015050"],"award-info":[{"award-number":["No.E2015050"]}]},{"name":"Nature Science Foundation of Heilongjiang Province of China","award":["No.E2016020"],"award-info":[{"award-number":["No.E2016020"]}]},{"name":"Nature Science Foundation of Heilongjiang Province of China","award":["No.E2017014"],"award-info":[{"award-number":["No.E2017014"]}]},{"name":"Fundamental Research Funds for the Central Universities-Doctoral Candidate\u2019s Science and Technology Innovation Project"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To solve the navigation accuracy problems of multi-Unmanned Underwater Vehicles (multi-UUVs) in the polar region, a polar cooperative navigation algorithm for multi-UUVs considering communication delays is proposed in this paper. UUVs are important pieces of equipment in ocean engineering for marine development. For UUVs to complete missions, precise navigation is necessary. It is difficult for UUVs to establish true headings because of the rapid convergence of Earth meridians and the severe polar environment. Based on the polar grid navigation algorithm, UUV navigation in the polar region can be accomplished with the Strapdown Inertial Navigation System (SINS) in the grid frame. To save costs, a leader-follower type of system is introduced in this paper. The leader UUV helps the follower UUVs to achieve high navigation accuracy. Follower UUVs correct their own states based on the information sent by the leader UUV and the relative position measured by ultra-short baseline (USBL) acoustic positioning. The underwater acoustic communication delay is quantized by the model. In this paper, considering underwater acoustic communication delay, the conventional adaptive Kalman filter (AKF) is modified to adapt to polar cooperative navigation. The results demonstrate that the polar cooperative navigation algorithm for multi-UUVs that considers communication delays can effectively navigate the sailing of multi-UUVs in the polar region.<\/jats:p>","DOI":"10.3390\/s18041044","type":"journal-article","created":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T12:43:48Z","timestamp":1522413828000},"page":"1044","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Polar Cooperative Navigation Algorithm for Multi-Unmanned Underwater Vehicles Considering Communication Delays"],"prefix":"10.3390","volume":"18","author":[{"given":"Zheping","family":"Yan","sequence":"first","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lu","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tongda","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zewen","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.robot.2014.10.006","article-title":"Autonomous inspection of underwater structures","volume":"67","author":"Jacobi","year":"2015","journal-title":"Robot. 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