{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T06:49:05Z","timestamp":1772779745439,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T00:00:00Z","timestamp":1675641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003399","name":"Key Project of Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["20JC1416504"],"award-info":[{"award-number":["20JC1416504"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Key Project of Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["2022B01009"],"award-info":[{"award-number":["2022B01009"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Special Projects for Key R&amp;D Tasks in the Autonomous Region","award":["20JC1416504"],"award-info":[{"award-number":["20JC1416504"]}]},{"name":"Special Projects for Key R&amp;D Tasks in the Autonomous Region","award":["2022B01009"],"award-info":[{"award-number":["2022B01009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In recent years, frequency-modulated continuous wave (FMCW) radar has been widely used in automatic driving, settlement monitoring and other fields. The range accuracy is determined by the estimation of the signal beat frequency. The existing algorithms are unable to distinguish between signal components with similar frequencies. To address this problem, this study proposed an enhanced root-MUSIC algorithm based on matrix reconstruction. Firstly, based on the sparsity of a singular value vector, a convex optimization problem was formulated to identify a singular value vector. Two algorithms were proposed to solve the convex optimization problem according to whether the standard deviation of noise needed to be estimated, from which an optimized singular value vector was obtained. Then, a signal matrix was reconstructed using an optimized singular value vector, and the Hankel structure of the signal matrix was restored by utilizing the properties of the Hankel matrix. Finally, the conventional root-MUSIC algorithm was utilized to estimate the signal beat frequency. The simulation results showed that the proposed algorithm improved the frequency resolution of multi-frequency signals in a noisy environment, which is beneficial to improve the multi-target range accuracy and resolution capabilities of FMCW radar.<\/jats:p>","DOI":"10.3390\/s23041829","type":"journal-article","created":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T01:35:17Z","timestamp":1675733717000},"page":"1829","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Enhanced Root-MUSIC Algorithm Based on Matrix Reconstruction for Frequency Estimation"],"prefix":"10.3390","volume":"23","author":[{"given":"Yingjie","family":"Zhu","sequence":"first","affiliation":[{"name":"Key Laboratory of Science and Technology on Micro-System, Shanghai Institute of Microsystem and Information Technology Chinese Academy of Sciences, Shanghai 200050, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5084-3351","authenticated-orcid":false,"given":"Wuxiong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Science and Technology on Micro-System, Shanghai Institute of Microsystem and Information Technology Chinese Academy of Sciences, Shanghai 200050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8795-2201","authenticated-orcid":false,"given":"Huiyue","family":"Yi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Science and Technology on Micro-System, Shanghai Institute of Microsystem and Information Technology Chinese Academy of Sciences, Shanghai 200050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Science and Technology on Micro-System, Shanghai Institute of Microsystem and Information Technology Chinese Academy of Sciences, Shanghai 200050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Figueroa, A., Al-Qudsi, B., Joram, N., and Ellinger, F. 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