{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:37:25Z","timestamp":1760150245934,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2023,11,5]],"date-time":"2023-11-05T00:00:00Z","timestamp":1699142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["U20A20163","KZ202111232049"],"award-info":[{"award-number":["U20A20163","KZ202111232049"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003213","name":"Beijing Education Commission Projects","doi-asserted-by":"publisher","award":["U20A20163","KZ202111232049"],"award-info":[{"award-number":["U20A20163","KZ202111232049"]}],"id":[{"id":"10.13039\/501100003213","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability.<\/jats:p>","DOI":"10.3390\/s23218990","type":"journal-article","created":{"date-parts":[[2023,11,5]],"date-time":"2023-11-05T07:35:06Z","timestamp":1699169706000},"page":"8990","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fast DOA Estimation Algorithms via Positive Incremental Modified Cholesky Decomposition for Augmented Coprime Array Sensors"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-8474-2793","authenticated-orcid":false,"given":"Jing","family":"Song","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, China University of Mining and Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0875-1549","authenticated-orcid":false,"given":"Lin","family":"Cao","sequence":"additional","affiliation":[{"name":"Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, China"},{"name":"School of Information and Communication Engineering, Beijing Information Science and Technology University, Beijing 100101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongmin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, China"},{"name":"School of Information and Communication Engineering, Beijing Information Science and Technology University, Beijing 100101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing TransMicrowave Technology Company, Beijing 100080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4549-744X","authenticated-orcid":false,"given":"Chong","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110169, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.sigpro.2016.03.024","article-title":"An Efficient Off-Grid DOA Estimation Approach for Nested Array Signal Processing by Using Sparse Bayesian Learning Strategies","volume":"128","author":"Yang","year":"2016","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4959","DOI":"10.1109\/TSP.2014.2339792","article-title":"A Discretization-Free Sparse and Parametric Approach for Linear Array Signal Processing","volume":"62","author":"Yang","year":"2014","journal-title":"IEEE Trans. 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