{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T21:52:16Z","timestamp":1783115536349,"version":"3.54.6"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T00:00:00Z","timestamp":1675728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Defense Science Foundation for Distinguished Young Scholars","award":["2020-JCJQ-ZQ-014"],"award-info":[{"award-number":["2020-JCJQ-ZQ-014"]}]},{"name":"National Defense Science Foundation for Distinguished Young Scholars","award":["18-JCJQ-QT-015"],"award-info":[{"award-number":["18-JCJQ-QT-015"]}]},{"name":"Young Elite Scientists Sponsorship Program by CAST","award":["2020-JCJQ-ZQ-014"],"award-info":[{"award-number":["2020-JCJQ-ZQ-014"]}]},{"name":"Young Elite Scientists Sponsorship Program by CAST","award":["18-JCJQ-QT-015"],"award-info":[{"award-number":["18-JCJQ-QT-015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Multi-station joint localization has important practical significance. In this paper, phase difference of arrival (PDOA) information is introduced into the joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) localization method to improve the target localization accuracy. First, the Cramer\u2013Rao lower bound (CRLB) of the joint TDOA, FDOA and PDOA localization approach with multi-station precise phase synchronization is derived. Then, the CRLB of the joint TDOA, FDOA and differential PDOA (dPDOA) localization method for the case of phase asynchronization between observation stations is also presented. Furthermore, the authors analyze the influence of the phase wrapping problem on localization accuracy and propose solutions to solve the phase wrapping problem based on cost functions of grid search. Finally, iterative localization algorithms based on maximum likelihood (ML) are proposed for both TDOA\/FDOA\/PDOA and TDOA\/FDOA\/dPDOA scenarios, respectively. Simulation results demonstrate the localization performance of the proposed approaches.<\/jats:p>","DOI":"10.3390\/rs15040915","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T05:37:31Z","timestamp":1675834651000},"page":"915","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Joint TDOA, FDOA and PDOA Localization Approaches and Performance Analysis"],"prefix":"10.3390","volume":"15","author":[{"given":"Jinzhou","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Spaceborne Information Intelligent Interpretation, Beijing Institute of Remote Sensing Information, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shouye","family":"Lv","sequence":"additional","affiliation":[{"name":"Key Laboratory of Spaceborne Information Intelligent Interpretation, Beijing Institute of Remote Sensing Information, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liujie","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sheng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Spaceborne Information Intelligent Interpretation, Beijing Institute of Remote Sensing Information, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Nie","sequence":"additional","affiliation":[{"name":"Key Laboratory of Spaceborne Information Intelligent Interpretation, Beijing Institute of Remote Sensing Information, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying","family":"Jin","sequence":"additional","affiliation":[{"name":"Sergeant School, Space Engineering University, Beijing 101416, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenglin","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Spaceborne Information Intelligent Interpretation, Beijing Institute of Remote Sensing Information, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,7]]},"reference":[{"key":"ref_1","first-page":"462","article-title":"Time Delay Estimation for Passive Sonar Signal Processing","volume":"29","author":"Cater","year":"1981","journal-title":"IEEE Trans. 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