{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:41:13Z","timestamp":1760233273561,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T00:00:00Z","timestamp":1672272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"STU Scientific Research Foundation for Talents","award":["NTF19036"],"award-info":[{"award-number":["NTF19036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper investigates the problem of elliptic localization in the absence of transmitter position. An efficient iterative method is developed to jointly evaluate the target and transmitter positions. Using the measurement information from the indirect paths reflected from the target and the direct paths between the transmitter and receivers, a non-convex maximum likelihood estimation (MLE) problem is formulated. Owing to the non-convex nature of the issue, we apply the majorization\u2013minimization (MM) principle to address the MLE problem, which iteratively minimizes a convex surrogate function instead of the original objective function. Moreover, the proposed MM method is further extended to tackle a general scenario where both multiple unknown transmitters and receiver position errors are considered. Finally, numerical simulations demonstrate that the proposed MM method outperforms the state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/s23010373","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T03:19:46Z","timestamp":1672370386000},"page":"373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Majorization-Minimization Method for Elliptic Localization in the Absence of Transmitter Position"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6193-3793","authenticated-orcid":false,"given":"Liehu","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Electronic and Information Engineering, Shantou University, Shantou 515063, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1034-9719","authenticated-orcid":false,"given":"Yanbin","family":"Zou","sequence":"additional","affiliation":[{"name":"Department of Electronic and Information Engineering, Shantou University, Shantou 515063, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6638","DOI":"10.1109\/TWC.2016.2586844","article-title":"RSSI-based distributed self-localization for wireless sensor networks used in precision agriculture","volume":"15","author":"Abouzar","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1684","DOI":"10.1109\/TSP.2015.2505689","article-title":"A Bayesian perspective on multiple source localization in wireless sensor networks","volume":"64","author":"Nguyen","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/LCOMM.2020.2968434","article-title":"TDOA localization with unknown signal propagation speed and sensor position errors","volume":"24","author":"Zou","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6149","DOI":"10.1109\/TWC.2018.2855126","article-title":"EM-based localization of noncooperative multicarrier communication sources with noncoherent subarrays","volume":"17","author":"Ikuma","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1388","DOI":"10.1109\/TVT.2015.2397312","article-title":"Blind selection of representative observations for sensor radar networks","volume":"64","author":"Bartoletti","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1109\/LSP.2016.2582043","article-title":"Moving target localization in multistatic sonar by differential delays and doppler shifts","volume":"23","author":"Yang","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1109\/JSEN.2019.2944957","article-title":"Closed-form localization method for moving target in passive multistatic radar network","volume":"20","author":"Zhang","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"8790","DOI":"10.1109\/TVT.2019.2928638","article-title":"Direct position determination in asynchronous sensor networks","volume":"68","author":"Ma","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1109\/LCOMM.2016.2589930","article-title":"Asynchronous time-of-arrival-based source localization with sensor position uncertainties","volume":"20","author":"Zou","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2221","DOI":"10.1109\/LCOMM.2021.3061014","article-title":"A 1-D search approach for single sensor passive localization based on signal periodicity","volume":"25","author":"Feng","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4751","DOI":"10.1109\/TSP.2016.2569465","article-title":"Closed-form and near closed-form solutions for TOA-based joint source and sensor localization","volume":"64","author":"Le","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1109\/LSP.2020.2965822","article-title":"Semidefinite programming methods for alleviating clock synchronization bias and sensor position errors in TDOA localization","volume":"27","author":"Zou","year":"2020","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3741","DOI":"10.1109\/JSEN.2019.2892652","article-title":"Wireless sensor network-based localization method using TDOA measurements in MPR","volume":"19","author":"Sun","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6969","DOI":"10.1109\/TVT.2021.3089161","article-title":"RSS-based target localization with unknown model parameters and sensor position errors","volume":"70","author":"Zou","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2256","DOI":"10.1109\/TSP.2020.2981773","article-title":"Eigenspace solution for AOA localization in modified polar representation","volume":"68","author":"Sun","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1109\/JSEN.2018.2881892","article-title":"A novel localization method based on RSS-AOA combined measurements by using polarized identity","volume":"19","author":"Chang","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1109\/LCOMM.2018.2833544","article-title":"Performance metric on the best achievable accuracy for hybrid TOA\/AOA target localization","volume":"22","author":"Li","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9343","DOI":"10.1109\/JSEN.2018.2869762","article-title":"A novel hybrid RSS and TOA positioning algorithm for multi-objective cooperative wireless sensor networks","volume":"18","author":"Xiong","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2746","DOI":"10.1109\/TWC.2020.3044217","article-title":"Accurate semidefinite relaxation method for elliptic localization with unknown transmitter position","volume":"20","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4745","DOI":"10.1109\/TSP.2019.2929960","article-title":"Multistatic localization in the absence of transmitter position","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/TAES.1983.309339","article-title":"Position accuracy in netted monostatic and bistatic radar","volume":"19","author":"Farina","year":"1983","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1109\/LSP.2017.2697500","article-title":"An efficient weighted least squares estimator for elliptic localization in distributed MIMO radars","volume":"24","author":"Amiri","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1582","DOI":"10.1109\/TAES.2019.2934007","article-title":"Moving target localization in bistatic forward scatter radars: Performance study and efficient estimators","volume":"56","author":"Hamdollahzadeh","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1109\/LSP.2017.2747479","article-title":"Iterative target localization in distributed MIMO radar from bistatic range measurements","volume":"24","author":"Noroozi","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1049\/ip-rsn:20045082","article-title":"Passive coherent location radar systems. Part 1: Performance prediction","volume":"152","author":"Griffiths","year":"2005","journal-title":"IEE Proc.-Radar Sonar Navig."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1049\/iet-rsn.2011.0390","article-title":"Ambiguity function and Cram\u00e9r-Rao bounds for universal mobile telecommunications system-based passive coherent location systems","volume":"6","author":"Stinco","year":"2012","journal-title":"IET Radar Sonar Navig."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TWC.2012.040412.110697","article-title":"Accurate passive location estimation using TOA measurements","volume":"11","author":"Shen","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1109\/TVT.2017.2762631","article-title":"Exact solution for elliptic localization in distributed MIMO radar systems","volume":"67","author":"Amiri","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4425","DOI":"10.1109\/TWC.2019.2924626","article-title":"Efficient joint moving target and antenna localization in distributed MIMO radars","volume":"18","author":"Amiri","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3385","DOI":"10.1109\/TAES.2022.3149855","article-title":"Semidefinite programming solutions for elliptic localization in asynchronous radar networks","volume":"58","author":"Wu","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5919","DOI":"10.1109\/TII.2019.2909135","article-title":"Adaptive range-based target localization using diffusion Gauss\u2013Newton method in industrial environments","volume":"15","author":"Wu","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5824","DOI":"10.1109\/TSP.2020.3023972","article-title":"Localization of a moving object with sensors in motion by time delays and doppler shifts","volume":"68","author":"Jia","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1080\/10556788.2018.1510927","article-title":"Quasi\u2013Newton methods: Superlinear convergence without line searches for self-concordant functions","volume":"34","author":"Gao","year":"2019","journal-title":"Optim. Methods Softw."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"794","DOI":"10.1109\/TSP.2016.2601299","article-title":"Majorization-minimization algorithms in signal processing, communications, and machine learning","volume":"65","author":"Sun","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1109\/LSP.2022.3158592","article-title":"Maximum likelihood algorithm for time-delay based multistatic target localization","volume":"29","author":"Panwar","year":"2022","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1109\/TSP.2007.909342","article-title":"Exact and approximate solutions of source localization problems","volume":"56","author":"Beck","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zou, Y., Fan, J., Wu, L., and Liu, H. (2022). Fixed point iteration based algorithm for asynchronous TOA-based source localization. Sensors, 22.","DOI":"10.3390\/s22186871"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/373\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:55:38Z","timestamp":1760147738000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,29]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23010373"],"URL":"https:\/\/doi.org\/10.3390\/s23010373","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,12,29]]}}}