{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:20:11Z","timestamp":1762341611652,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,13]],"date-time":"2021-02-13T00:00:00Z","timestamp":1613174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National key Research Program of China","award":["2016YFB0501900"],"award-info":[{"award-number":["2016YFB0501900"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41674022"],"award-info":[{"award-number":["41674022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Under mixed sparse line-of-sight\/non-line-of-sight (LOS\/NLOS) conditions, how to quickly achieve high positioning accuracy is still a challenging task and a critical problem in the last dozen years. To settle this problem, we propose a constrained L1 norm minimization method which can reduce the effects of NLOS bias for improve positioning accuracy and speed up calculation via an iterative method. We can transform the TOA-based positioning problem into a sparse optimization one under mixed sparse LOS\/NLOS conditions if we consider NLOS bias as outliers. Thus, a relatively good method to deal with sparse localization problem is L1 norm. Compared with some existing methods, the proposed method not only has the advantages of simple and intuitive principle, but also can neglect NLOS status and corresponding NLOS errors. Experimental results show that our algorithm performs well in terms of computational time and positioning accuracy.<\/jats:p>","DOI":"10.3390\/s21041321","type":"journal-article","created":{"date-parts":[[2021,2,13]],"date-time":"2021-02-13T20:48:38Z","timestamp":1613249318000},"page":"1321","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Constrained L1-Norm Minimization Method for Range-Based Source Localization under Mixed Sparse LOS\/NLOS Environments"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3310-0529","authenticated-orcid":false,"given":"Chengwen","family":"He","sequence":"first","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunbin","family":"Yuan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingfeng","family":"Tan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1109\/TAP.2017.2784442","article-title":"Toward Near-Ground Localization: Modeling and Applications for TOA Ranging Error","volume":"66","author":"Xu","year":"2018","journal-title":"IEEE Trans. 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