{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T00:18:17Z","timestamp":1781137097030,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T00:00:00Z","timestamp":1542758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"973 Program","doi-asserted-by":"publisher","award":["2015CB351703"],"award-info":[{"award-number":["2015CB351703"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91648208"],"award-info":[{"award-number":["91648208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation-Shenzhen Joint Research Program","award":["U1613219"],"award-info":[{"award-number":["U1613219"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, robust first and second-order divided difference filtering algorithms based on correntropy are proposed, which not only retain the advantages of divided difference filters, but also exhibit robustness in the presence of non-Gaussian noises, especially when the measurements are contaminated by heavy-tailed noises. The proposed filters are then applied to the problem of ship positioning. In order to improve the accuracy and reliability of ship positioning, the positioning method combines the Dead Reckoning (DR) algorithm and the Global Positioning System (GPS). Experimental results of an illustrative example show the superior performance of the new algorithms when applied to ship positioning.<\/jats:p>","DOI":"10.3390\/s18114080","type":"journal-article","created":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T09:18:25Z","timestamp":1542878305000},"page":"4080","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Correntropy Based Divided Difference Filtering for the Positioning of Ships"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4659-8955","authenticated-orcid":false,"given":"Xi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1710-3818","authenticated-orcid":false,"given":"Badong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5028-5839","authenticated-orcid":false,"given":"Shiyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaoyi","family":"Du","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,21]]},"reference":[{"key":"ref_1","unstructured":"Wu, Q., Gao, Z., and Wan, D. 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