{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:53:36Z","timestamp":1772448816769,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,17]],"date-time":"2018-03-17T00:00:00Z","timestamp":1521244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61201381"],"award-info":[{"award-number":["61201381"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61401513"],"award-info":[{"award-number":["61401513"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2016M592989"],"award-info":[{"award-number":["2016M592989"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Outstanding Youth foundation of Information Engineering University","award":["2016603201"],"award-info":[{"award-number":["2016603201"]}]},{"name":"Self-topic Foundation of Information Engineering University","award":["2016600701"],"award-info":[{"award-number":["2016600701"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A novel geolocation architecture, termed \u201cMultiple Transponders and Multiple Receivers for Multiple Emitters Positioning System (MTRE)\u201d is proposed in this paper. Existing Direct Position Determination (DPD) methods take advantage of a rather simple channel assumption (line of sight channels with complex path attenuations) and a simplified MUltiple SIgnal Classification (MUSIC) algorithm cost function to avoid the high dimension searching. We point out that the simplified assumption and cost function reduce the positioning accuracy because of the singularity of the array manifold in a multi-path environment. We present a DPD model for unknown signals in the presence of Multi-path Propagation (MP-DPD) in this paper. MP-DPD adds non-negative real path attenuation constraints to avoid the mistake caused by the singularity of the array manifold. The Multi-path Propagation MUSIC (MP-MUSIC) method and the Active Set Algorithm (ASA) are designed to reduce the dimension of searching. A Multi-path Propagation Maximum Likelihood (MP-ML) method is proposed in addition to overcome the limitation of MP-MUSIC in the sense of a time-sensitive application. An iterative algorithm and an approach of initial value setting are given to make the MP-ML time consumption acceptable. Numerical results validate the performances improvement of MP-MUSIC and MP-ML. A closed form of the Cram\u00e9r\u2013Rao Lower Bound (CRLB) is derived as a benchmark to evaluate the performances of MP-MUSIC and MP-ML.<\/jats:p>","DOI":"10.3390\/s18030892","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T06:57:11Z","timestamp":1521529031000},"page":"892","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Direct Position Determination of Unknown Signals in the Presence of Multipath Propagation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7091-3989","authenticated-orcid":false,"given":"Jianping","family":"Du","sequence":"first","affiliation":[{"name":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6533-9206","authenticated-orcid":false,"given":"Ding","family":"Wang","sequence":"additional","affiliation":[{"name":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1515-3179","authenticated-orcid":false,"given":"Wanting","family":"Yu","sequence":"additional","affiliation":[{"name":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongyi","family":"Yu","sequence":"additional","affiliation":[{"name":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,17]]},"reference":[{"key":"ref_1","unstructured":"Shen, Y., and Win, M.Z. 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