{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:29:19Z","timestamp":1774448959472,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"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":["62001507"],"award-info":[{"award-number":["62001507"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20210106"],"award-info":[{"award-number":["20210106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young Talent fund of University Association for Science and Technology in Shaanxi, China","award":["62001507"],"award-info":[{"award-number":["62001507"]}]},{"name":"Young Talent fund of University Association for Science and Technology in Shaanxi, China","award":["20210106"],"award-info":[{"award-number":["20210106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Deep unfolded networks have recently been regarded as an essential way to direction of arrival (DOA) estimation due to the fast convergence speed and high interpretability. However, few consider gridless DOA estimation. This paper proposes two deep unfolded gridless DOA estimation networks to resolve the above problem. We first consider the atomic norm-based 1D and decoupled atomic norm-based 2D gridless DOA models solved by the alternating iterative minimization of variables, respectively. Then, the corresponding deep networks are trained offline after constructing the corresponding complete training datasets. At last, the trained networks are applied to realize the 1D DOA and 2D estimation, respectively. Simulation results reveal that the proposed networks can secure higher 1D and 2D DOA estimation performances while maintaining a lower computational expenditure than typical methods.<\/jats:p>","DOI":"10.3390\/rs15010013","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T03:31:06Z","timestamp":1671593466000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Deep Unfolded Gridless DOA Estimation Networks Based on Atomic Norm Minimization"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8479-6514","authenticated-orcid":false,"given":"Hangui","family":"Zhu","sequence":"first","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4205-538X","authenticated-orcid":false,"given":"Weike","family":"Feng","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"given":"Cunqian","family":"Feng","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"given":"Teng","family":"Ma","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9765-9335","authenticated-orcid":false,"given":"Bo","family":"Zou","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2576","DOI":"10.1109\/TSP.2022.3173150","article-title":"Joint DoA-Range Estimation Using Space-Frequency Virtual Difference Coarray","volume":"70","author":"Mao","year":"2022","journal-title":"IEEE Trans. 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