{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:55:48Z","timestamp":1777658148309,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2011,9,2]],"date-time":"2011-09-02T00:00:00Z","timestamp":1314921600000},"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>The practical deployment of wireless positioning systems requires minimizing the calibration procedures while improving the location estimation accuracy. Received Signal Strength localization techniques using propagation channel models are the simplest alternative, but they are usually designed under the assumption that the radio propagation model is to be perfectly characterized a priori. In practice, this assumption does not hold and the localization results are affected by the inaccuracies of the theoretical, roughly calibrated or just imperfect channel models used to compute location. In this paper, we propose the use of weighted multilateration techniques to gain robustness with respect to these inaccuracies, reducing the dependency of having an optimal channel model. In particular, we propose two weighted least squares techniques based on the standard hyperbolic and circular positioning algorithms that specifically consider the accuracies of the different measurements to obtain a better estimation of the position. These techniques are compared to the standard hyperbolic and circular positioning techniques through both numerical simulations and an exhaustive set of real experiments on different types of wireless networks (a wireless sensor network, a WiFi network and a Bluetooth network). The algorithms not only produce better localization results with a very limited overhead in terms of computational cost but also achieve a greater robustness to inaccuracies in channel modeling.<\/jats:p>","DOI":"10.3390\/s110908569","type":"journal-article","created":{"date-parts":[[2011,9,2]],"date-time":"2011-09-02T10:41:14Z","timestamp":1314960074000},"page":"8569-8592","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":116,"title":["Weighted Least Squares Techniques for Improved Received Signal Strength Based Localization"],"prefix":"10.3390","volume":"11","author":[{"given":"Paula","family":"Tarr\u00edo","sequence":"first","affiliation":[{"name":"Data Processing and Simulation Group, Universidad Polit\u00e9cnica de Madrid, ETSI. Telecomunicaci\u00f3n, Avda. Complutense 30, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ana M.","family":"Bernardos","sequence":"additional","affiliation":[{"name":"Data Processing and Simulation Group, Universidad Polit\u00e9cnica de Madrid, ETSI. Telecomunicaci\u00f3n, Avda. Complutense 30, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 R.","family":"Casar","sequence":"additional","affiliation":[{"name":"Data Processing and Simulation Group, Universidad Polit\u00e9cnica de Madrid, ETSI. Telecomunicaci\u00f3n, Avda. Complutense 30, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/SURV.2009.090103","article-title":"A survey of indoor positioning systems for wireless personal networks","volume":"11","author":"Gu","year":"2009","journal-title":"IEEE Commun. Surv. & Tutor"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s11277-007-9375-z","article-title":"A survey on wireless position estimation","volume":"44","author":"Gezici","year":"2008","journal-title":"Wirel. Person. Commun"},{"key":"ref_3","unstructured":"Alippi, C, and Vanini, G (2006, January 13\u201317). A RSSI-Based and Calibrated Centralized Localization Technique for Wireless Sensor Networks. Pisa, Italy."},{"key":"ref_4","unstructured":"Wang, C, Chiou, Y, and Yeh, S (June, January 30). 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