{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T16:15:56Z","timestamp":1776528956897,"version":"3.51.2"},"reference-count":26,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T00:00:00Z","timestamp":1689724800000},"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":["62171468"],"award-info":[{"award-number":["62171468"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In passive localization techniques, as the scale of the array of the sensors used increases, the source distribution may be a coexistence of near-field (NF) and far-field (FF) sources. Most of the existing algorithms dedicated to the localization of mixed-field sources are based on a simplified model, which has model errors and cannot make good use of non-circular properties when non-circular signals are present in the sources. In this paper, we present a mixed-field circular and non-circular source localization algorithm based on exact spatial propagation geometry. First, we make an initial estimate of the source parameters using exact spatial geometry relations. The MUSIC algorithm is then used in combination with the non-circular properties of the signal to achieve an accurate estimate. The algorithm does not lose performance due to model mismatch and is able to make good use of the non-circular properties of the sources to improve the estimation accuracy. The simulation results show that the proposed algorithm can effectively distinguish between sources and that the algorithm performs satisfactorily.<\/jats:p>","DOI":"10.3390\/s23146516","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T21:22:58Z","timestamp":1689801778000},"page":"6516","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Mixed-Field Circular and Non-Circular Source Localization Algorithm Based on Exact Spatial Propagation Geometry"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2705-5218","authenticated-orcid":false,"given":"Wei","family":"Lin","sequence":"first","affiliation":[{"name":"Institute of Information Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weijia","family":"Cui","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Ba","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8630-9049","authenticated-orcid":false,"given":"Haiyun","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2947-0239","authenticated-orcid":false,"given":"Jingjing","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/B978-0-12-811887-0.00011-0","article-title":"Sparse methods for direction-of-arrival estimation","volume":"Volume 7","author":"Yang","year":"2018","journal-title":"Academic Press Library in Signal Processing"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2002). Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory, John Wiley & Sons.","DOI":"10.1002\/0471221104"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4925","DOI":"10.1109\/TVT.2018.2817638","article-title":"A high-resolution doa estimation method with a family of nonconvex penalties","volume":"67","author":"Wu","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2270","DOI":"10.1109\/25.901896","article-title":"A multistatic microwave radar sensor for short range anticollision warning","volume":"49","author":"Giubbolini","year":"2000","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1109\/29.32276","article-title":"Esprit-estimation of signal parameters via rotational invariance techniques","volume":"37","author":"Roy","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/TSP.2009.2029723","article-title":"Passive localization of mixed near-field and far-field sources using two-stage music algorithm","volume":"58","author":"Liang","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.1109\/TSP.2011.2180902","article-title":"Efficient application of music algorithm under the coexistence of far-field and near-field sources","volume":"60","author":"He","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7671","DOI":"10.1109\/JSEN.2018.2863749","article-title":"Localization of mixed far-field and near-field sources via cumulant matrix reconstruction","volume":"18","author":"Zheng","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1109\/LSP.2013.2245503","article-title":"Mixed-order music algorithm for localization of far-field and near-field sources","volume":"20","author":"Wang","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7059","DOI":"10.1109\/TAP.2019.2925199","article-title":"Localization of mixed near-field and far-field sources using symmetric double-nested arrays","volume":"67","author":"Zheng","year":"2019","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"102879","DOI":"10.1016\/j.dsp.2020.102879","article-title":"Localization for mixed far-field and near-field sources utilizing improved symmetric nested array","volume":"107","author":"Shen","year":"2020","journal-title":"Digit. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1109\/TAP.2020.3005203","article-title":"Symmetric displaced coprime array configurations for mixed near-and far-field source localization","volume":"69","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1752","DOI":"10.1049\/rsn2.12294","article-title":"Symmetric flipped nested array for mixed near-field and far-field non-circular source localisation","volume":"16","author":"Wang","year":"2022","journal-title":"IET Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107665","DOI":"10.1016\/j.sigpro.2020.107665","article-title":"Localization of far-field and near-field signals with mixed sparse approach: A generalized symmetric arrays perspective","volume":"175","author":"Wu","year":"2020","journal-title":"Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"102899","DOI":"10.1016\/j.dsp.2020.102899","article-title":"A one-step algorithm for mixed far-field and near-field sources localization","volume":"108","author":"Molaei","year":"2021","journal-title":"Digit. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6111","DOI":"10.1109\/TAP.2022.3161269","article-title":"An efficient maximum-likelihood-like algorithm for near-field coherent source localization","volume":"70","author":"Cheng","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3540","DOI":"10.1109\/TVT.2021.3065954","article-title":"Mixed near-field and far-field source localization based on exact spatial propagation geometry","volume":"70","author":"He","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2105","DOI":"10.1109\/TSP.2022.3168975","article-title":"Mixed near-field and far-field localization and array calibration with partly calibrated arrays","volume":"70","author":"He","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5183","DOI":"10.1007\/s00034-022-02029-z","article-title":"Near-field doa-range and polarization estimation based on exact propagation model with cold arrays","volume":"41","author":"Yin","year":"2022","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.dsp.2019.06.003","article-title":"An effective localization method for mixed far-field and near-field strictly non-circular sources","volume":"94","author":"Wang","year":"2019","journal-title":"Digit. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.dsp.2018.11.006","article-title":"Rare-based localization for mixed near-field and far-field rectilinear sources","volume":"85","author":"Chen","year":"2019","journal-title":"Digit. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1109\/78.382404","article-title":"Applications of cumulants to array processing. i. aperture extension and array calibration","volume":"43","author":"Dogan","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1040","DOI":"10.1109\/LSP.2020.3002148","article-title":"Localization of near-field sources for exact source-sensor spatial geometry","volume":"27","author":"He","year":"2020","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1109\/TAES.2012.6129676","article-title":"Doa estimation and tracking of ulas with mutual coupling","volume":"48","author":"Liao","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6516\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:14:43Z","timestamp":1760127283000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6516"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,19]]},"references-count":26,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23146516"],"URL":"https:\/\/doi.org\/10.3390\/s23146516","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,19]]}}}