{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T16:46:19Z","timestamp":1774889179660,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,29]],"date-time":"2018-09-29T00:00:00Z","timestamp":1538179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61503073 and 61703090"],"award-info":[{"award-number":["61503073 and 61703090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Research Fund of Science and Technology Department, Jilin Province","award":["20170101125JC"],"award-info":[{"award-number":["20170101125JC"]}]},{"name":"Science and Technology Research Fund of Education Department, Jilin Province","award":["JJKH20170103KJ"],"award-info":[{"award-number":["JJKH20170103KJ"]}]},{"name":"Research Fund for Distinguished Young Scholars of Jilin City","award":["20166005"],"award-info":[{"award-number":["20166005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The geomagnetic field is as fundamental a constituent of passive navigation as Earth\u2019s gravity. In cases where no other external attitude reference is available, for the direct heading angle estimation by a typical magnetic compass, a two-step optimized correction algorithm is proposed to correct the model coefficients caused by hard and soft iron nearby. Specifically, in Step 1, a Levenberg-Marquardt (L-M) fitting estimator with an ellipsoid constraint is applied to solve the hard magnetic coefficients. In Step 2, a Lagrange multiplier estimator is used to deal with the soft magnetic iron circumstance. The essential attribute of \u201cthe two-step\u201d lies in its eliminating the coupling effects of hard and soft magnetic fields, and their mutual interferences on the pure geomagnetic field. Under the conditions of non-deterministic magnetic interference sources with noise, the numerical simulation by referring to International Geomagnetic Reference Field (IGRF), and the laboratory tests based upon the turntable experiments with Honeywell HMR3000 compass (Honeywell, Morristown, NJ, USA) conducted, the experimental results indicate that, in the presence of the variation of multi-magnetic interferences, the RMSE (Root Mean Square Error) value of the estimated total magnetic flux density by the proposed two-step estimator falls to 0.125 \u03bcT from its initial 2.503 \u03bcT, and the mean values of the heading angle error estimates are less than 1\u00b0. The proposed solution therefore, exhibits ideal convergent properties, fairly meeting the accuracy requirements of non-tactical level navigation applications.<\/jats:p>","DOI":"10.3390\/s18103284","type":"journal-article","created":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T08:23:50Z","timestamp":1538468630000},"page":"3284","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Optimized Two-Step Magnetic Correction Strategy by Means of a Lagrange Multiplier Estimator with an Ellipsoid Constraint"],"prefix":"10.3390","volume":"18","author":[{"given":"Linlin","family":"Xia","sequence":"first","affiliation":[{"name":"School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingtong","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanrui","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunqi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, The University of Sydney, Camperdown, NSW 2006, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaolong","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Engineering Management, Shenzhen Yuhu Power Co., Ltd., Shenzhen 518111, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Computer Science, Northeast Electric Power University, Jilin 132012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,29]]},"reference":[{"key":"ref_1","first-page":"24","article-title":"Multi-position static test of the magnetometer from IMU","volume":"61","author":"Hudak","year":"2010","journal-title":"J. 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