{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T18:13:34Z","timestamp":1775326414131,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,12,17]],"date-time":"2016-12-17T00:00:00Z","timestamp":1481932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Scalar Triangulation and Ranging (STAR) method, which is based upon the unique properties of magnetic gradient contraction, is a high real-time ferromagnetic target localization method. Only one measurement point is required in the STAR method and it is not sensitive to changes in sensing platform orientation. However, the localization accuracy of the method is limited by the asphericity errors and the inaccurate value of position leads to larger errors in the estimation of magnetic moment. To improve the localization accuracy, a modified STAR method is proposed. In the proposed method, the asphericity errors of the traditional STAR method are compensated with an iterative algorithm. The proposed method has a fast convergence rate which meets the requirement of high real-time localization. Simulations and field experiments have been done to evaluate the performance of the proposed method. The results indicate that target parameters estimated by the modified STAR method are more accurate than the traditional STAR method.<\/jats:p>","DOI":"10.3390\/s16122168","type":"journal-article","created":{"date-parts":[[2016,12,23]],"date-time":"2016-12-23T04:09:09Z","timestamp":1482466149000},"page":"2168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["A Modified Magnetic Gradient Contraction Based Method for Ferromagnetic Target Localization"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7164-7851","authenticated-orcid":false,"given":"Chen","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Electromagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}]},{"given":"Xiaojuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}]},{"given":"Xiaodong","family":"Qu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electromagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}]},{"given":"Xiao","family":"Pan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electromagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}]},{"given":"Guangyou","family":"Fang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electromagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"Luzhao","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electromagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1109\/TMAG.2010.2091964","article-title":"Recursive Bayesian method for magnetic dipole tracking with a tensor gradiometer","volume":"47","author":"Birsan","year":"2011","journal-title":"IEEE Trans. Magn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3451","DOI":"10.1088\/0957-0233\/18\/11\/027","article-title":"Localization and magnetic moment estimation of a ferromagnetic target by simulated annealing","volume":"18","author":"Sheinker","year":"2007","journal-title":"Meas. Sci. Technol."},{"key":"ref_3","first-page":"1","article-title":"Magnetic dipole localization based on magnetic gradient tensor data at a single point","volume":"8","author":"Yin","year":"2014","journal-title":"J. Appl. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/LGRS.2007.912088","article-title":"Bayesian mitigation of sensor position errors to improve unexploded ordnance detection","volume":"5","author":"Tantum","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1109\/TGRS.2008.921394","article-title":"Selecting a discrimination algorithm for unexploded ordnance remediation","volume":"46","author":"Beran","year":"2008","journal-title":"IEEE Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Young, J.A., Keenan, S.T., Clark, D.A., Leslie, K.E., Sullivan, P., Fairman, P., Williams, C., and Foley, C.P. (2010, January 22\u201326). A Superconducting Magnetic Tensor Gradiometer for Underwater UXO Detection. Proceedings of the ASEG Extended Abstracts 2010: 21st Geophysical Conference, Sydney, Australia.","DOI":"10.1081\/22020586.2010.12041889"},{"key":"ref_7","unstructured":"Kumar, S., Perry, A.R., Moeller, C.R., Skvoretz, D.C., Ebbert, M.J., Ostrom, R.K., Bennett, S.L., and Czipott, P.A. (2004, January 9\u201312). Real-time tracking magnetic gradiometer for underwater mine detection. Proceedings of the Techno-Ocean\u201904, Kobe, Japan."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.sna.2007.10.064","article-title":"Remote sensing of a magnetic target utilizing population based incremental learning","volume":"143","author":"Sheinker","year":"2008","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"20910","DOI":"10.3390\/s141120910","article-title":"A real-time localization system for an endoscopic capsule using magnetic sensors","volume":"14","author":"Pham","year":"2014","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"11001","DOI":"10.3390\/s140611001","article-title":"Magnetic Field Feature Extraction and Selection for Indoor Location Estimation","volume":"14","author":"Brena","year":"2014","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1109\/TMAG.1975.1058672","article-title":"Advanced superconducting gradiometer\/magnetometer arrays and a novel signal processing technique","volume":"11","author":"Wynn","year":"1975","journal-title":"IEEE Trans. Magn."},{"key":"ref_12","unstructured":"Wynn, W.M. (1997, January 3\u20138). Magnetic dipole localization with a gradiometer obtaining unique solutions. Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS\u201997), Singapore."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3291","DOI":"10.1109\/TMAG.2006.879151","article-title":"A closed-form formula for magnetic dipole localization by measurement of its magnetic field and spatial gradients","volume":"42","author":"Nara","year":"2006","journal-title":"IEEE Trans. Magn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4444","DOI":"10.1109\/TMAG.2012.2196418","article-title":"Properties of the linear Equations Derived from Euler\u2019s Equation and its Application to Magnetic Dipole Localization","volume":"48","author":"Nara","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1049\/iet-smt:20060129","article-title":"Detection and localization of magnetic objects","volume":"1","author":"Barrell","year":"2007","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_16","unstructured":"Vaizer, L., Lathrop, J., and Bono, J. (2004, January 9\u201312). Localization of magnetic dipole targets. Proceedings of the Techno-Ocean\u201904, Kobe, Japan."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.proeng.2010.11.001","article-title":"Detection and localization of improvised explosive devices based on 3-axis magnetic sensor array system","volume":"7","author":"Liu","year":"2010","journal-title":"Procedia Eng."},{"key":"ref_18","first-page":"1325","article-title":"Generalized Magnetic Gradient Contraction Based Method for Detection, Localization and Discrimination of Underwater Mines and Unexploded Ordnance","volume":"2","author":"Wiegert","year":"2010","journal-title":"Mine Warf. Ship Self-Def."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wiegert, R., Lee, K., and Oeschger, J. (2008, January 15\u201318). Improved magnetic STAR methods for real-time, point-by-point localization of unexploded ordnance and buried mines. Proceedings of the IEEE Oceanic Engineering Society, Quebec City, QC, Canada.","DOI":"10.1109\/OCEANS.2008.5152073"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4701","DOI":"10.1109\/TMAG.2012.2206603","article-title":"Asphericity Errors Correction of Magnetic Gradient Tensor Invariants Method for Magnetic Dipole Localization","volume":"48","author":"Sui","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"0751021","DOI":"10.1088\/0957-0233\/24\/7\/075102","article-title":"Calibration of a fluxgate magnetometer array and its application in magnetic object localization","volume":"24","author":"Pang","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","first-page":"1","article-title":"Integrated compensation of magnetometer array magnetic distortion field and improvement of magnetic object localization","volume":"99","author":"Pang","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.sna.2015.03.026","article-title":"One-step calibration of magnetic gradient tensor system with nonlinear least square method","volume":"229","author":"Yin","year":"2015","journal-title":"Sens. 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