{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:58:49Z","timestamp":1781949529184,"version":"3.54.5"},"reference-count":19,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T00:00:00Z","timestamp":1660262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundations of China","award":["51107145"],"award-info":[{"award-number":["51107145"]}]},{"name":"the National Natural Science Foundations of China","award":["51377165"],"award-info":[{"award-number":["51377165"]}]},{"name":"the National Natural Science Foundations of China","award":["51107145"],"award-info":[{"award-number":["51107145"]}]},{"name":"the National Natural Science Foundations of China","award":["51377165"],"award-info":[{"award-number":["51377165"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Localization of the underwater magnetic sensor arrays plays a pivotal role in the magnetic silencing facility. A localization approach is proposed for underwater sensors based on the optimization of magnetic field gradients in the inverse problem of localization. In the localization system, a solenoid coil carrying direct current serves as the magnetic source. By measuring the magnetic field generated by the magnetic source in different positions, an objective function is established. The position vector of the sensor is determined by a novel multi-swarm particle swarm optimization with dynamic learning strategy. Without the optimization of the magnetic source\u2019s positions, the sensors\u2019 positions, especially in the z-axis direction, struggle to meet the requested localization. A strategy is proposed to optimize the positions of the magnetic source based on magnetic field gradients in the three directions of x, y and z axes. Compared with the former method, the model experiments show that the proposed method could achieve a 10 cm location error for the position type 2 sensor and meet the request of localization.<\/jats:p>","DOI":"10.3390\/s22166017","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T23:44:03Z","timestamp":1660607043000},"page":"6017","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Localization Approach for Underwater Sensors in the Magnetic Silencing Facility Based on Magnetic Field Gradients"],"prefix":"10.3390","volume":"22","author":[{"given":"Guohua","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yufen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kena","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3321-1408","authenticated-orcid":false,"given":"Hanming","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Holmes, J.J. (2008). Reduction of a Ship\u2019s Magnetic Field Signatures, Morgan & Claypool.","DOI":"10.1007\/978-3-031-01708-7"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Holmes, J.J. (2007). Modeling a Ship\u2019s Ferromagnetic Signatures, Morgan & Claypool.","DOI":"10.1007\/978-3-031-01698-1"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Schulze, C., Chan, D., Funasaki, E., and Wong, K. (2010). Case Study of a Navy Magnetic Silencing Facility. Ports 2010: Building on the Past, Respecting the Future, ASCE.","DOI":"10.1061\/41098(368)136"},{"key":"ref_4","first-page":"176","article-title":"An overview of ship magnetic signature and silencing technologies","volume":"12","author":"Isa","year":"2019","journal-title":"Def. S T Tech. Bull."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chandrasekhar, V., Seah, W.K., Choo, Y.S., and Ee, H.V. (2006, January 25). Localization in underwater magnetic sensor networks: Survey and challenges. Proceedings of the 1st ACM International Workshop on Underwater Networks, Los Angeles, CA, USA.","DOI":"10.1145\/1161039.1161047"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1109\/COMST.2017.2684087","article-title":"Magnetic Field-Based Positioning Systems","volume":"19","author":"Pasku","year":"2017","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2021.3085107","article-title":"Multiclass Permanent Magnets Superstructure for Indoor Localization Using Artificial Intelligence","volume":"58","author":"Ivry","year":"2022","journal-title":"IEEE Trans. Magn."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hott, M., Harlakin, A., and Hoeher, P.A. (2020, January 21\u201323). Hybrid Communication and Localization Underwater Network Nodes based on Magnetic Induction and Visible Light for AUV Support. Proceedings of the 2020 International Conference on Information and Communication Technology Convergence (ICTC), Jeju Island, Korea (South).","DOI":"10.1109\/ICTC49870.2020.9289328"},{"key":"ref_9","first-page":"1","article-title":"Theoretical Investigation on the Linear Location Algorithm of the Magnetic Gradient Tensor Ranging by Use of Cuboid Triaxial Magnetic Array","volume":"57","author":"Yu","year":"2021","journal-title":"IEEE Trans. Magn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.phycom.2018.07.011","article-title":"3-D localization of wireless sensor nodes using near-field magnetic-induction communications","volume":"30","author":"Huang","year":"2018","journal-title":"Phys. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2010\/709318","article-title":"Silent localization of underwater sensors using magnetics","volume":"2010","author":"Callmer","year":"2010","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_12","first-page":"41","article-title":"Underwater Vector-magnetic Located by Using Magnetic Dipole Sources in the Offing","volume":"33","author":"Yang","year":"2011","journal-title":"J. Detect. Control"},{"key":"ref_13","first-page":"826","article-title":"Simulation Experiment Research for Magnetic Localization Method for Magnetic Sensor at Seabed","volume":"45","author":"Zhang","year":"2011","journal-title":"J. Shanghai Jiaotong Univ."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cerro, G., Ferrigno, L., Laracca, M., Milano, F., Bellitti, P., Serpelloni, M., and Casas Piedrafita, O. (2020, January 25\u201328). On a finite domain magnetic localization by means of TMR triaxial sensors. Proceedings of the 2020 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Dubrovnik, Croatia.","DOI":"10.1109\/I2MTC43012.2020.9129628"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/JSEN.2013.2287915","article-title":"; Zhou, G. Multi-Objectivization-Based Localization of Underwater sensors Using Magnetics","volume":"14","author":"Yu","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_16","unstructured":"Horrer, M. (2010). Basics of magnetics. Electromagnetic Field Theory for Engineers and Physicists, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"124101","DOI":"10.7498\/aps.71.20212223","article-title":"Applicability and optimization analysis of magnetic dipole array model","volume":"71","author":"Liu","year":"2022","journal-title":"Acta Phys. Sin."},{"key":"ref_18","first-page":"31","article-title":"Research on spatial magnetic field distributing of submarine based on magnetic dipole equivalent","volume":"35","author":"Zhang","year":"2013","journal-title":"Ship Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.asoc.2017.08.051","article-title":"A novel multi-swarm particle swarm optimization with dynamic learning strategy","volume":"61","author":"Ye","year":"2017","journal-title":"Appl. Soft. Comput."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6017\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:07:41Z","timestamp":1760141261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6017"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,12]]},"references-count":19,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22166017"],"URL":"https:\/\/doi.org\/10.3390\/s22166017","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,12]]}}}