{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:43:09Z","timestamp":1740141789387,"version":"3.37.3"},"reference-count":13,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2013,2,1]],"date-time":"2013-02-01T00:00:00Z","timestamp":1359676800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61172123","60901059","12JK0526"],"award-info":[{"award-number":["61172123","60901059","12JK0526"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61172123","60901059","12JK0526"],"award-info":[{"award-number":["61172123","60901059","12JK0526"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Educational Department Foundation of Shaanxi Province","award":["61172123","60901059","12JK0526"],"award-info":[{"award-number":["61172123","60901059","12JK0526"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Distributed Sensor Networks"],"published-print":{"date-parts":[[2013,2,1]]},"abstract":"<jats:p> A novel circle fitting algorithm is proposed in this paper. The key points of this paper are given as follows: (i) it formulates the circle fitting problem into the special source localization one in wireless sensor networks (WSN); (ii) the multidimensional scaling (MDS) analysis is applied to the data points, and thus the propagator-like method is proposed to represent the circle center parameters as the functions of the circle radius; (iii) the virtual source localization model can be rerepresented as special nonlinear equations of a unique variable (the circle radius) rather than the original three ones (the circle center and radius), and thus the classical fixed-point iteration algorithm is applied to determine the radius and the circle center parameters. The effectiveness of the proposed circle fitting approach is demonstrated using the simulation and experimental results. <\/jats:p>","DOI":"10.1155\/2013\/203719","type":"journal-article","created":{"date-parts":[[2013,2,26]],"date-time":"2013-02-26T21:03:01Z","timestamp":1361912581000},"page":"203719","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Circle Fitting Using a Virtual Source Localization Algorithm in Wireless Sensor Networks"],"prefix":"10.1177","volume":"9","author":[{"given":"Junli","family":"Liang","sequence":"first","affiliation":[{"name":"Xi'an University of Technology, Xi'an 710048, China"},{"name":"University of Florida, Gainesville, FL 32611, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miaohua","family":"Zhang","sequence":"additional","affiliation":[{"name":"Xi'an University of Technology, Xi'an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianju","family":"Zeng","sequence":"additional","affiliation":[{"name":"College of Management, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1931-8989","authenticated-orcid":false,"given":"Kexin","family":"Zhao","sequence":"additional","affiliation":[{"name":"University of Florida, Gainesville, FL 32611, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Li","sequence":"additional","affiliation":[{"name":"University of Florida, Gainesville, FL 32611, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2013,2,26]]},"reference":[{"key":"B1-2013-203719","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(87)90116-2"},{"key":"B2-2013-203719","doi-asserted-by":"publisher","DOI":"10.1016\/0167-5087(83)90575-6"},{"first-page":"63","volume-title":"Proceedings of APRS Workshop on Digital Image Computing","author":"Coath G.","key":"B3-2013-203719"},{"key":"B4-2013-203719","doi-asserted-by":"publisher","DOI":"10.1145\/361237.361242"},{"key":"B5-2013-203719","doi-asserted-by":"publisher","DOI":"10.1049\/cp:19950683"},{"key":"B6-2013-203719","doi-asserted-by":"publisher","DOI":"10.1007\/BF02276879"},{"key":"B7-2013-203719","doi-asserted-by":"publisher","DOI":"10.1007\/BF00939613"},{"key":"B8-2013-203719","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(91)90049-Q"},{"key":"B9-2013-203719","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2003.896092"},{"key":"B10-2013-203719","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2007.909342"},{"volume-title":"Multidimensional Scaling","year":"2001","author":"Cox T. 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