{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T15:56:52Z","timestamp":1776182212847,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T00:00:00Z","timestamp":1724025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62171337"],"award-info":[{"award-number":["62171337"]}]},{"name":"National Natural Science Foundation of China","award":["62201434"],"award-info":[{"award-number":["62201434"]}]},{"name":"National Natural Science Foundation of China","award":["62101396"],"award-info":[{"award-number":["62101396"]}]},{"name":"National Natural Science Foundation of China","award":["62301391"],"award-info":[{"award-number":["62301391"]}]},{"name":"National Natural Science Foundation of China","award":["GZC20233512"],"award-info":[{"award-number":["GZC20233512"]}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["62171337"],"award-info":[{"award-number":["62171337"]}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["62201434"],"award-info":[{"award-number":["62201434"]}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["62101396"],"award-info":[{"award-number":["62101396"]}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["62301391"],"award-info":[{"award-number":["62301391"]}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["GZC20233512"],"award-info":[{"award-number":["GZC20233512"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>When the near-field and far-field information of a target is uncertain, it is necessary to choose a suitable localization method. The modified polar representation (MPR) method integrates the two scenarios and achieves a unified localization with direction of arrival (DOA) estimation in the far field and position estimation in the near field. Previous studies have only proposed solutions for stationary environments and have not considered the motion factor. Therefore, this paper proposes a new unified positioning algorithm using multi-sensor time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements without prior target source information. The method represents the position of the target source using MPR and describes the localization problem as a weighted least squares (WLS) problem with two constraints. We first obtain the initial estimates by WLS without considering the constraints and then investigate a two-step error correction method based on the constraints. The first step corrects the initial estimate using the Taylor series expansion technique, and the second step corrects the DOA estimate in the previous step using the direct error compensation technique based on the properties of the second constraint. Simulation experiments show that the method is effective for the unified positioning of moving targets and can achieve the Cramer\u2013Rao lower bound (CRLB).<\/jats:p>","DOI":"10.3390\/rs16163047","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T10:11:28Z","timestamp":1724062288000},"page":"3047","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Closed-Form Method for Unified Far-Field and Near-Field Localization Based on TDOA and FDOA Measurements"],"prefix":"10.3390","volume":"16","author":[{"given":"Weishuang","family":"Gong","sequence":"first","affiliation":[{"name":"Hangzhou Institute of Technology, Xidian University, Hangzhou 311231, China"}]},{"given":"Xuan","family":"Song","sequence":"additional","affiliation":[{"name":"School of Astronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Chunyu","family":"Zhu","sequence":"additional","affiliation":[{"name":"Hangzhou Institute of Technology, Xidian University, Hangzhou 311231, China"}]},{"given":"Qi","family":"Wang","sequence":"additional","affiliation":[{"name":"Hangzhou Institute of Technology, Xidian University, Hangzhou 311231, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6672-367X","authenticated-orcid":false,"given":"Yachao","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TASSP.1982.1163855","article-title":"Optimal source localization and tracking from passive array measurements","volume":"30","author":"Weinstein","year":"1982","journal-title":"IEEE Trans. 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