{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T17:34:05Z","timestamp":1767980045451,"version":"3.49.0"},"reference-count":16,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:00:00Z","timestamp":1551916800000},"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>One of the common ways for solving indoor navigation is known as Pedestrian Dead Reckoning (PDR), which employs inertial and magnetic sensors typically embedded in a smartphone carried by a user. Estimation of the pedestrian\u2019s heading is a crucial step in PDR algorithms, since it is a dominant factor in the positioning accuracy. In this paper, rather than assuming the device to be fixed in a certain orientation on the pedestrian, we focus on estimating the vertical direction in the sensor frame of an unconstrained smartphone. To that end, we establish a framework for gravity direction estimation and highlight the important role it has for solving the heading in the horizontal plane. Furthermore, we provide detailed derivation of several approaches for calculating the heading angle, based on either the gyroscope or the magnetic sensor, all of which employ the estimated vertical direction. These various methods\u2014both for gravity direction and for heading estimation\u2014are demonstrated, analyzed and compared using data recorded from field experiments with commercial smartphones.<\/jats:p>","DOI":"10.3390\/s19051170","type":"journal-article","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T04:58:35Z","timestamp":1552021115000},"page":"1170","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Gravity-Based Methods for Heading Computation in Pedestrian Dead Reckoning"],"prefix":"10.3390","volume":"19","author":[{"given":"Adi","family":"Manos","sequence":"first","affiliation":[{"name":"Technion-Israel Institute of Technology, Haifa 32000, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7846-0654","authenticated-orcid":false,"given":"Itzik","family":"Klein","sequence":"additional","affiliation":[{"name":"Technion-Israel Institute of Technology, Haifa 32000, Israel"}]},{"given":"Tamir","family":"Hazan","sequence":"additional","affiliation":[{"name":"Technion-Israel Institute of Technology, Haifa 32000, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,7]]},"reference":[{"key":"ref_1","unstructured":"Beauregard, S., and Haas, H. (2006, January 16). Pedestrian dead reckoning: A basis for personal positioning. Proceedings of the 3rd Workshop on Positioning, Navigation and Communication, Hannover, Germany."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1109\/TITS.2016.2617200","article-title":"A survey on approaches of motion mode recognition using sensors","volume":"18","author":"Elhoushi","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7577","DOI":"10.1109\/JSEN.2018.2861395","article-title":"Pedestrian Dead Reckoning With Smartphone Mode Recognition","volume":"18","author":"Klein","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Manos, A., Klein, I., and Hazan, T. (2018, January 24\u201327). Gravity Direction Estimation and Heading Determination for Pedestrian Navigation. 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J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"21518","DOI":"10.3390\/s150921518","article-title":"Heading estimation for indoor pedestrian navigation using a smartphone in the pocket","volume":"15","author":"Deng","year":"2015","journal-title":"Sensors"},{"key":"ref_9","unstructured":"Nguyen, P., Akiyama, T., Ohashi, H., Nakahara, G., Yamasaki, K., and Hikaru, S. (2016, January 4\u20137). User-friendly heading estimation for arbitrary smartphone orientations. Proceedings of the 2016 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Madrid, Spain."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.pmcj.2018.03.004","article-title":"Attitude estimation for indoor navigation and augmented reality with smartphones","volume":"46","author":"Michel","year":"2018","journal-title":"Pervasive Mob. Comput."},{"key":"ref_11","unstructured":"Groves, P.D. (2013). 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Proceedings of the NTM 2004 Conference (Session E3), San Diego, CA, USA."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1170\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:37:10Z","timestamp":1760186230000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,7]]},"references-count":16,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19051170"],"URL":"https:\/\/doi.org\/10.3390\/s19051170","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,7]]}}}