{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:32:28Z","timestamp":1760239948680,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T00:00:00Z","timestamp":1550620800000},"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 paper proposes an improved method for calculating the position of a movable tag whose distance to a (redundant) set of fixed beacons is measured by some suitable physical principle (typically ultra wide band or ultrasound propagation). The method is based on the multilateration technique, where the contribution of each individual beacon is weighed on the basis of a recurring, self-supported calibration of the measurement repeatability of each beacon at a given distance range. The work outlines the method and its implementation, and shows the improvement in measurement quality with respect to the results of a commercial Ultra-Wide-Band (UWB) system when tested on the same set of raw beacon-to-tag distances. Two versions of the algorithm are proposed: one-dimensional, or isotropic, and 3D. With respect to the standard approach, the isotropic solution managed to reduce the maximum localization error by around 25%, with a maximum error of     0.60     m, while the 3D version manages to improve even further the localization accuracy, with a maximum error of     0.45     m.<\/jats:p>","DOI":"10.3390\/s19040872","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T11:45:39Z","timestamp":1550663139000},"page":"872","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Self-Weighted Multilateration for Indoor Positioning Systems"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6008-4566","authenticated-orcid":false,"given":"Alberto","family":"Fornaser","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123 Trento, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2110-6360","authenticated-orcid":false,"given":"Luca","family":"Maule","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123 Trento, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Luchetti","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123 Trento, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Bosetti","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123 Trento, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariolino","family":"De Cecco","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123 Trento, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1109\/COMST.2016.2632427","article-title":"Recent advances in indoor localization: A survey on theoretical approaches and applications","volume":"19","author":"Yassin","year":"2016","journal-title":"IEEE Commun. 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Proceedings of the 2006 Radio and Wireless Symposium, San Diego, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kuhn, M., Zhang, C., Merkl, B., Yang, D., Wang, Y., Mahfouz, M., and Fathy, A. (2008, January 10\u201312). High accuracy UWB localization in dense indoor environments. Proceedings of the 2008 IEEE International Conference on Ultra-Wideband, Hannover, Germany.","DOI":"10.1109\/ICUWB.2008.4653368"},{"key":"ref_10","first-page":"84963","article-title":"UWB localization system for indoor applications: Concept, realization and analysis","volume":"2012","author":"Zwirello","year":"2012","journal-title":"J. Electr. Comput. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Jourdan, D.B., Dardari, D., and Win, M.Z. (2006, January 11\u201315). Position error bound for UWB localization in dense cluttered environments. Proceedings of the 2006 IEEE International Conference on Communications, Istanbul, Turkey.","DOI":"10.1109\/ICC.2006.255648"},{"key":"ref_12","unstructured":"Vapnyarskii, I. (2001). Lagrange multipliers. Encyclopedia of Mathematics, Springer."},{"key":"ref_13","unstructured":"Lasdon, L.S. (2002). Optimization Theory for Large Systems, Dover Publications, Inc."},{"key":"ref_14","unstructured":"Kanaan, M., and Pahlavan, K. (2004, January 21\u201325). A comparison of wireless geolocation algorithms in the indoor environment. Proceedings of the 2004 IEEE Wireless Communications and Networking Conference, Atlanta, GA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1113\/jphysiol.2006.118786","article-title":"The frequency of human, manual adjustments in balancing an inverted pendulum is constrained by intrinsic physiological factors","volume":"577","author":"Loram","year":"2006","journal-title":"J. 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