{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:35:39Z","timestamp":1774053339112,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T00:00:00Z","timestamp":1645401600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T00:00:00Z","timestamp":1645401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"the nsfc","award":["51375087"],"award-info":[{"award-number":["51375087"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mobile Netw Appl"],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s11036-021-01898-z","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T10:05:42Z","timestamp":1645437942000},"page":"794-805","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Novel Calibration Method for Tri-axial Magnetometers Based on an Expanded Error Model and a Two-step Total Least Square Algorithm"],"prefix":"10.1007","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1770-8529","authenticated-orcid":false,"given":"Xiyuan","family":"Chen","sequence":"first","affiliation":[]},{"given":"Xiaotian","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Min","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Caiping","family":"Lv","sequence":"additional","affiliation":[]},{"given":"Yuan","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Hang","family":"Guo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,21]]},"reference":[{"key":"1898_CR1","doi-asserted-by":"publisher","first-page":"2053","DOI":"10.1109\/TIM.2011.2115330","volume":"60","author":"J Fang","year":"2011","unstructured":"Fang J, Sun H, Cao J, Zhang X, Tao Y (2011) A novel calibration method of magnetic compass based on ellipsoid fitting. IEEE Inst Meas 60:2053\u20132061","journal-title":"IEEE Inst Meas"},{"key":"1898_CR2","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1016\/j.robot.2013.06.003","volume":"61","author":"D Grivon","year":"2013","unstructured":"Grivon D, Vezzetti E, Violante M (2013) Development of an innovative low-cost MARG sensors alignment and distortion compensation methodology for 3D scanning applications. Robot Auton Syst 61:1710\u20131716","journal-title":"Robot Auton Syst"},{"key":"1898_CR3","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.jbiomech.2005.11.011","volume":"40","author":"H Luinge","year":"2007","unstructured":"Luinge H, Veltink P, Baten C (2007) Ambulatory measurement of arm orientation. J Biomech 40:78\u201385","journal-title":"J Biomech"},{"key":"1898_CR4","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1109\/TAES.2011.5751259","volume":"47","author":"F Vasconcelos","year":"2011","unstructured":"Vasconcelos F, Elkaim G, Silvestre C, Oliveira P, Cardeira B (2011) Geometric approach to strapdown magnetometer calibration in sensor frame. IEEE Aerospace Electron Syst 47:1293\u20131306","journal-title":"IEEE Aerospace Electron Syst"},{"key":"1898_CR5","unstructured":"Gebre-Egziabher D, Elkaim H, Powell D, Parkinson W (2001) A non-linear, two-step estimation algorithm for calibrating solid-state strapdown magnetometers. In 8th International St Petersburg Conference on Navigation Systems IEEE\/AIAA"},{"key":"1898_CR6","doi-asserted-by":"crossref","unstructured":"Lv C, Chen X, Huang H et al (2015) Study on calibration method for tri-axial accelerometers, in Metrology for Aerospace conference IEEE: 15\u201320","DOI":"10.1109\/MetroAeroSpace.2015.7180619"},{"key":"1898_CR7","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1061\/(ASCE)0893-1321(2006)19:2(87)","volume":"19","author":"D Gebre-Egziabher","year":"2006","unstructured":"Gebre-Egziabher D, Elkaim H, Powell D, Parkinson W, Parkinson W (2006) Calibration of strapdown magnetometers in magnetic field domain. J Aerosp Eng 19:87\u2013102","journal-title":"J Aerosp Eng"},{"key":"1898_CR8","doi-asserted-by":"publisher","first-page":"1070","DOI":"10.1109\/TAES.2008.4655364","volume":"44","author":"C Foster","year":"2008","unstructured":"Foster C, Elkaim G (2008) Extension of a two-step calibration methodology to include nonorthogonal sensor axes. IEEE Aerospace Electron Syst 44:1070\u20131078","journal-title":"IEEE Aerospace Electron Syst"},{"key":"1898_CR9","first-page":"3714","volume":"62","author":"Z Zhang","year":"2015","unstructured":"Zhang Z (2015) Two-step calibration methods for miniature inertial and magnetic sensor units. IEEE Trans Ind Electron 62:3714\u20133723","journal-title":"IEEE Trans Ind Electron"},{"key":"1898_CR10","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.patrec.2021.06.021","volume":"150","author":"Y Zhang","year":"2021","unstructured":"Zhang Y (2021) A multiple input deep convolutional attention network for Covid-19 diagnosis based on chest CT and chest X-ray. Pattern Recogn Lett 150:8\u201316","journal-title":"Pattern Recogn Lett"},{"key":"1898_CR11","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/j.sna.2005.12.001","volume":"127","author":"R Zhu","year":"2006","unstructured":"Zhu R, Zhou Z (2006) Calibration of three-dimensional integrated sensors for improved system accuracy. Sensors Actuators A Phys 127:340\u2013344","journal-title":"Sensors Actuators A Phys"},{"key":"1898_CR12","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/j.sna.2007.05.008","volume":"138","author":"D Jurman","year":"2007","unstructured":"Jurman D, Jankovec M, Kamnik R, Topic M (2007) Calibration and data fusion solution for the miniature attitude and heading reference system. Sensors Actuators A Phys 138:411\u2013420","journal-title":"Sensors Actuators A Phys"},{"key":"1898_CR13","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1016\/j.sna.2009.10.008","volume":"156","author":"S Bonnet","year":"2009","unstructured":"Bonnet S, Bassompierre C, Godin C, Lesecq S, Barraud A (2009) Calibration methods for inertial and magnetic sensors. Sensors Actuators A Phys 156:302\u2013311","journal-title":"Sensors Actuators A Phys"},{"key":"1898_CR14","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1016\/j.sna.2005.02.040","volume":"123","author":"J V\u010del\u00e1k","year":"2005","unstructured":"V\u010del\u00e1k J, Ripka P, Kubik J, Platil A, Ka\u0161par P (2005) AMR navigation systems and methods of their calibration. Sensors Actuators A Phys 123:122\u2013128","journal-title":"Sensors Actuators A Phys"},{"key":"1898_CR15","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.sna.2005.09.048","volume":"129","author":"J V\u010del\u00e1k","year":"2006","unstructured":"V\u010del\u00e1k J, Ripka P, Kubik J, Platil A, Ka\u0161par P (2006) Errors of AMR compass and methods of their compensation. Sensors Actuators A Phys 129:53\u201357","journal-title":"Sensors Actuators A Phys"},{"key":"1898_CR16","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1109\/TCST.2017.2670527","volume":"26","author":"Y Wu","year":"2018","unstructured":"Wu Y, Zou D, Liu P et al (2018) Dynamic magnetometer calibration and alignment to inertial sensors by Kalman filtering. IEEE Trans Control Syst Technol 26:716\u2013723","journal-title":"IEEE Trans Control Syst Technol"},{"key":"1898_CR17","doi-asserted-by":"crossref","unstructured":"Renaudin V, Afzal H, Lachapelle G (2010) New method for magnetometers based orientation estimation. In Position Location and Navigation Symposium, IEEE: 348\u2013356","DOI":"10.1109\/PLANS.2010.5507301"},{"key":"1898_CR18","first-page":"2439","volume":"30","author":"X Zhang","year":"2009","unstructured":"Zhang X, Zhang Y (2009) New auto-calibration and compensation method for vehicle magnetic field based on ellipse restriction. Chin J Sci Instrum 30:2439\u20132443","journal-title":"Chin J Sci Instrum"},{"key":"1898_CR19","first-page":"23","volume":"1","author":"R Val\u00e9rie","year":"2010","unstructured":"Val\u00e9rie R, Afzal MH, G\u00e9rard L (2010) Complete triaxis magnetometer calibration in the magnetic domain. J Sensors 1:23\u201359","journal-title":"J Sensors"},{"key":"1898_CR20","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/j.measurement.2016.06.056","volume":"93","author":"H Pang","year":"2016","unstructured":"Pang H, Pan M, Chen J et al (2016) Integrated calibration and magnetic disturbance compensation of three-axis magnetometers. Measurement 93:409\u2013413","journal-title":"Measurement"},{"key":"1898_CR21","doi-asserted-by":"publisher","first-page":"1295","DOI":"10.1007\/s40747-020-00218-4","volume":"7","author":"Y Zhang","year":"2021","unstructured":"Zhang Y (2021) Improving ductal carcinoma in situ classification by convolutional neural network with exponential linear unit and rank-based weighted pooling. Complex Intell Syst 7:1295\u20131310","journal-title":"Complex Intell Syst"},{"key":"1898_CR22","doi-asserted-by":"publisher","first-page":"055106","DOI":"10.1088\/1361-6501\/aa58b9","volume":"28","author":"X Zhu","year":"2017","unstructured":"Zhu X, Zhao T, Cheng D et al (2017) A three-step calibration method for tri-axial field sensors in a 3D magnetic digital compass. Meas Sci Technol 28:055106","journal-title":"Meas Sci Technol"},{"key":"1898_CR23","doi-asserted-by":"publisher","first-page":"115","DOI":"10.2514\/1.6278","volume":"28","author":"L Crassidis","year":"2005","unstructured":"Crassidis L, Lai L, Harman R (2005) Real-time attitude-independent three-axis magnetometer calibration. J Guid Control Dyn 28:115\u2013120","journal-title":"J Guid Control Dyn"},{"key":"1898_CR24","doi-asserted-by":"publisher","first-page":"105754","DOI":"10.1016\/j.ast.2020.105754","volume":"99","author":"H Soken","year":"2020","unstructured":"Soken H, Sakai S (2020) Attitude estimation and magnetometer calibration using reconfigurable TRIAD+filtering approach. Aerosp Sci Technol 99:105754","journal-title":"Aerosp Sci Technol"},{"key":"1898_CR25","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.isatra.2020.08.030","volume":"108","author":"J Wang","year":"2021","unstructured":"Wang J, Chen X, Yang P (2021) Adaptive h-infinite kalman filter based on multiple fading factors and its application in unmanned underwater vehicle. ISA Trans 108:295\u2013304","journal-title":"ISA Trans"},{"key":"1898_CR26","doi-asserted-by":"publisher","first-page":"3680","DOI":"10.1109\/JSEN.2020.3022934","volume":"21","author":"J Wang","year":"2021","unstructured":"Wang J, Ma Z, Chen X (2021) Generalized dynamic fuzzy nn model based on multiple fading factors sckf and its application in integrated navigation. IEEE Sensors J 21:3680\u20133693","journal-title":"IEEE Sensors J"},{"key":"1898_CR27","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.inffus.2020.07.006","volume":"64","author":"Y Zhang","year":"2020","unstructured":"Zhang Y (2020) Advances in multimodal data fusion in neuroimaging: overview, challenges, and novel orientation. Inf Fusion 64:149\u2013187","journal-title":"Inf Fusion"},{"key":"1898_CR28","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1007\/s40747-020-00161-4","volume":"7","author":"S Liu","year":"2021","unstructured":"Liu S, Liu D, Srivastava G et al (2021) Overview and methods of correlation filter algorithms in object tracking. Complex Intell Syst 7:1895\u20131917","journal-title":"Complex Intell Syst"},{"key":"1898_CR29","doi-asserted-by":"publisher","first-page":"2929","DOI":"10.1109\/TIM.2013.2263913","volume":"62","author":"S Tabatabaei","year":"2013","unstructured":"Tabatabaei S, Gluhak A, Tafazolli R (2013) A fast calibration method for triaxial magnetometers. IEEE Trans Instrum Meas 62:2929\u20132937","journal-title":"IEEE Trans Instrum Meas"},{"key":"1898_CR30","first-page":"1","volume":"15","author":"Y Wu","year":"2019","unstructured":"Wu Y, Zhu M, Yu W (2019) An efficient method for gyroscope-aided full magnetometer calibration. IEEE Sensors J 15:1\u20131","journal-title":"IEEE Sensors J"},{"key":"1898_CR31","doi-asserted-by":"publisher","first-page":"109092","DOI":"10.1016\/j.measurement.2021.109092","volume":"175","author":"J Liu","year":"2021","unstructured":"Liu J, Li X, Zhang Y et al (2021) A comprehensive strapdown triaxial magnetometer calibration method considering temporal misalignment error. Measurement 175:109092","journal-title":"Measurement"},{"key":"1898_CR32","volume-title":"The American Pratical Navigator","author":"N Bowditch","year":"1984","unstructured":"Bowditch N (1984) The American Pratical Navigator. Hydrographic \/Topographic Center, Defense Mapping Agency"},{"key":"1898_CR33","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1007\/s11036-019-01358-9","volume":"25","author":"S Liu","year":"2020","unstructured":"Liu S, Bai W, Srivastava G et al (2020) Property of self-similarity between baseband and modulated signals. Mobile Netw Appl 25:1537\u20131547","journal-title":"Mobile Netw Appl"},{"key":"1898_CR34","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1109\/34.765658","volume":"21","author":"A Fitzgibbon","year":"1999","unstructured":"Fitzgibbon A, Pilu M, Fisher R (1999) Direct least square fitting of ellipses. IEEE Patt Anal Mach Intell 21:476\u2013480","journal-title":"IEEE Patt Anal Mach Intell"},{"key":"1898_CR35","first-page":"40","volume":"21","author":"H Zhang","year":"1995","unstructured":"Zhang H, Huang J, Fan W (1995) Total least square method and its application to parameter estimation. Acta Automat Sin 21:40\u201347","journal-title":"Acta Automat Sin"},{"key":"1898_CR36","doi-asserted-by":"publisher","first-page":"1055","DOI":"10.1007\/s00521-020-05021-3","volume":"33","author":"S Liu","year":"2021","unstructured":"Liu S, Liu X, Wang S et al (2021) Fuzzy-aided solution for out-of-view challenge in visual tracking under IoT assisted complex environment. Neural Comput Applic 33:1055\u20131106","journal-title":"Neural Comput Applic"},{"key":"1898_CR37","doi-asserted-by":"publisher","first-page":"107690","DOI":"10.1016\/j.ymssp.2021.107690","volume":"159","author":"X Chen","year":"2021","unstructured":"Chen X, Ma Z, Yang P (2021) Integrated modeling of motion decoupling and flexure deformation of carrier in transfer alignment. Mech Syst Signal Process 159:107690","journal-title":"Mech Syst Signal Process"}],"container-title":["Mobile Networks and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11036-021-01898-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11036-021-01898-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11036-021-01898-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,16]],"date-time":"2022-06-16T13:25:28Z","timestamp":1655385928000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11036-021-01898-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,21]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["1898"],"URL":"https:\/\/doi.org\/10.1007\/s11036-021-01898-z","relation":{},"ISSN":["1383-469X","1572-8153"],"issn-type":[{"value":"1383-469X","type":"print"},{"value":"1572-8153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,21]]},"assertion":[{"value":"15 November 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}