{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:38:29Z","timestamp":1760243909263,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2011,10,31]],"date-time":"2011-10-31T00:00:00Z","timestamp":1320019200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate coordinates for active beacons placed in the environment are required in Local Positioning Systems (LPS). These coordinates and the distances (or differences of distances) measured between the beacons and the mobile node to be localized are inputs to most trilateration algorithms. As a first approximation, such coordinates are obtained by means of manual measurements (a time-consuming and non-flexible method), or by using a calibration algorithm (i.e., automatic determination of beacon coordinates from ad hoc measurements). This paper presents a method to calibrate the beacons\u2019 positions in a LPS using a mobile receiver. The method has been developed for both, spherical and hyperbolic trilateration. The location of only three test points must be known a priori, while the position of the other test points can be unknown. Furthermore, the paper describes a procedure to estimate the optimal positions, or approximate areas in the coverage zone, where the test-points necessary to calibrate the ultrasonic LPS should be placed. Simulation and experimental results show the improvement achieved when these optimal test-points are used instead of randomly selected ones.<\/jats:p>","DOI":"10.3390\/s111110398","type":"journal-article","created":{"date-parts":[[2011,10,31]],"date-time":"2011-10-31T11:59:28Z","timestamp":1320062368000},"page":"10398-10414","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["LPS Auto-Calibration Algorithm with Predetermination of Optimal Zones"],"prefix":"10.3390","volume":"11","author":[{"given":"Francisco Daniel","family":"Ruiz","sequence":"first","affiliation":[{"name":"Electronics Department, University of Alcal\u00e1 de Henares, Escuela Polit\u00e9cnica. Ctra. Madrid-Barcelona, Km. 33,600, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Ure\u00f1a","sequence":"additional","affiliation":[{"name":"Electronics Department, University of Alcal\u00e1 de Henares, Escuela Polit\u00e9cnica. Ctra. Madrid-Barcelona, Km. 33,600, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9367-9475","authenticated-orcid":false,"given":"Juan C.","family":"Garc\u00eda","sequence":"additional","affiliation":[{"name":"Electronics Department, University of Alcal\u00e1 de Henares, Escuela Polit\u00e9cnica. Ctra. Madrid-Barcelona, Km. 33,600, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ana","family":"Jim\u00e9nez","sequence":"additional","affiliation":[{"name":"Electronics Department, University of Alcal\u00e1 de Henares, Escuela Polit\u00e9cnica. Ctra. Madrid-Barcelona, Km. 33,600, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c1lvaro","family":"Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Electronics Department, University of Alcal\u00e1 de Henares, Escuela Polit\u00e9cnica. Ctra. Madrid-Barcelona, Km. 33,600, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan J.","family":"Garc\u00eda","sequence":"additional","affiliation":[{"name":"Electronics Department, University of Alcal\u00e1 de Henares, Escuela Polit\u00e9cnica. Ctra. Madrid-Barcelona, Km. 33,600, 28871 Alcal\u00e1 de Henares, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,10,31]]},"reference":[{"key":"ref_1","unstructured":"Manley, E.D., Nahas, H.A., and Deogun, J.S. (2006, January 5\u20137). Localization and Tracking in Sensor Systems. Taichung, Taiwan."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Huang, Y., Brennan, P.V., and Seeds, A. (2008, January 15\u201318). Active RFID Location System Based on Time-Difference Measurement Using a Linear FM Chirp Tag Signal. Cannes, France.","DOI":"10.1109\/PIMRC.2008.4699805"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1552","DOI":"10.1016\/j.comcom.2009.05.013","article-title":"Tracking mobile targets indoors using WLAN and time of arrival","volume":"32","author":"Ciurana","year":"2009","journal-title":"Comput. Commun"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0921-8890(99)00042-1","article-title":"An automatic self-installation and calibration method for a 3D position sensing system using ultrasonics","volume":"28","author":"Mahajan","year":"1999","journal-title":"Robot. Auton. Syst"},{"key":"ref_5","unstructured":"Nishitani, A., Nishida, Y., Hori, T., and Mizoguchi, H. (2004, January 10\u201313). Portable Ultrasonic 3D Tag System Based on a Quick Calibration Method. the Hague, The Netherlands."},{"key":"ref_6","unstructured":"Duff, P., and Muller, H. (2003, January 21\u201323). Autocalibration Algorithm for Ultrasonic Location Systems. New York, NY, USA."},{"key":"ref_7","first-page":"123","article-title":"A new method for auto-calibrated object tracking","volume":"3660","author":"Duff","year":"2005","journal-title":"Engineering"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"P\u00e9rez, M.C., Ure\u00f1a, J., Hern\u00e1ndez, A., Jim\u00e9nez, A., Ruiz, D., \u00c1lvarez, F.J., and De Marziani, C. (2009, January 26\u201328). Performance Comparison of Different Codes in an Ultrasonic Positioning System Using DS-CDMA. Budapest, Hungary.","DOI":"10.1109\/WISP.2009.5286574"},{"key":"ref_9","unstructured":"Neering, J. Optimization and Estimation Techniques for Acoustic Source Localization. Mines ParisTech, Paris, France, 2009. Available online: http:\/\/hal.archives-ouvertes.fr\/docs\/00\/42\/67\/32\/PDF\/Neering_Dissertation.pdf (accessed on 24 October 2011)."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1137\/0806023","article-title":"An interior, trust region approach for nonlinear minimization subject to bounds","volume":"6","author":"Coleman","year":"1996","journal-title":"SIAM J. Optim"},{"key":"ref_11","unstructured":"Watson, G.A. (1977). Numerical Analysis, Berlin\/Heidelberg, Germany. Lecture Notes in Mathematics 630,."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Villadangos, J.M., Ure\u00f1a, J., Mazo, M., Hernandez, A., De Marziani, C., Perez, M.C., Alvarez, F., Garcia, J.J., Jimenez, A., and Gude, I. (2007, January 3\u20135). Ultrasonic Local Positioning System with Large Covered Area. Alcal\u00e1 de Henares, Spain.","DOI":"10.1109\/WISP.2007.4447508"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Villadangos, J.M., Ure\u00f1a, J., Mazo, M., Hern\u00e1ndez, A., De Marziani, C., Jim\u00e9nez, A., and \u00c1lvarez, F. (2007, January 4\u20137). Improvement of Cover Area in Ultrasonic Local Positioning System Using Cylindrical PVDF Transducer. Vigo, Spain.","DOI":"10.1109\/ISIE.2007.4374819"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/11\/10398\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:57:53Z","timestamp":1760219873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/11\/10398"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,31]]},"references-count":13,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11]]}},"alternative-id":["s111110398"],"URL":"https:\/\/doi.org\/10.3390\/s111110398","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2011,10,31]]}}}