{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:05:48Z","timestamp":1760241948670,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T00:00:00Z","timestamp":1539907200000},"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":["61671453"],"award-info":[{"award-number":["61671453"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To increase the number of estimable signal sources, two-parallel nested arrays are proposed, which consist of two subarrays with    M    sensors, and can estimate the two-dimensional (2-D) direction of arrival (DOA) of      M 2      signal sources. To solve the problem of direction finding with two-parallel nested arrays, a 2-D DOA estimation algorithm based on sparse Bayesian estimation is proposed. Through a vectorization matrix, smoothing reconstruction matrix and singular value decomposition (SVD), the algorithm reduces the size of the sparse dictionary and data noise. A sparse Bayesian learning algorithm is used to estimate one dimension angle. By a joint covariance matrix, another dimension angle is estimated, and the estimated angles from two dimensions can be automatically paired. The simulation results show that the number of DOA signals that can be estimated by the proposed two-parallel nested arrays is much larger than the number of sensors. The proposed two-dimensional DOA estimation algorithm has excellent estimation performance.<\/jats:p>","DOI":"10.3390\/s18103553","type":"journal-article","created":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T11:51:15Z","timestamp":1539949875000},"page":"3553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Two-Dimensional Angle Estimation of Two-Parallel Nested Arrays Based on Sparse Bayesian Estimation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6845-0580","authenticated-orcid":false,"given":"Lu","family":"Chen","sequence":"first","affiliation":[{"name":"Electronic Countermeasures College, National University of Defense Technology, Hefei 230037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daping","family":"Bi","sequence":"additional","affiliation":[{"name":"Electronic Countermeasures College, National University of Defense Technology, Hefei 230037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jifei","family":"Pan","sequence":"additional","affiliation":[{"name":"Electronic Countermeasures College, National University of Defense Technology, Hefei 230037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2678","DOI":"10.1109\/TSP.2006.873505","article-title":"MUSIC-like estimation of direction of arrival for noncircular sources","volume":"54","author":"Abeida","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1016\/j.sigpro.2007.11.012","article-title":"Extended 2q-MUSIC algorithm for noncircular signals","volume":"88","author":"Liu","year":"2008","journal-title":"Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1049\/iet-rsn.2009.0003","article-title":"Performance analysis of MUSIC for non-circular signals in the presence of mutual coupling","volume":"4","author":"Huang","year":"2010","journal-title":"IET Radar Sonar Navig."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/LSP.2017.2704612","article-title":"On time-reversal imaging by statistical testing","volume":"24","author":"Ciuonzo","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1109\/TAP.2005.846723","article-title":"Time reversal imaging of obscured targets from multistatic data","volume":"53","author":"Devaney","year":"2005","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.1109\/78.143447","article-title":"A performance analysis of subspace-based methods in the presence of model errors, Part I: The MUSIC algorithm","volume":"40","author":"Swindlehurst","year":"1992","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","unstructured":"Swindlehurst, A., Otterstein, B., and Kailath, T. (November, January 30). An analysis of MUSIC and root-MUSIC in the presence of sensor perturbations. Proceedings of the Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2650","DOI":"10.1109\/TSP.2015.2417507","article-title":"Performance analysis of time-reversal MUSIC","volume":"63","author":"Ciuonzo","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","first-page":"509","article-title":"A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection","volume":"49","author":"Zhu","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","unstructured":"Harter, M., Ziroff, A., and Zwick, T. (2011, January 12\u201314). Three-dimensional radar imaging by digital beamforming. Proceedings of the 2011 8th European Radar Conference, Manchester, UK."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1109\/TMTT.2009.2017254","article-title":"A 77-GHz FMCW MIMO radar based on an SiGe single-chip transceiver","volume":"57","author":"Feger","year":"2009","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMTT.2018.2869565","article-title":"A portable K-band 3-D MIMO radar with nonuniformly spaced array for short-range localization","volume":"99","author":"Peng","year":"2018","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2056","DOI":"10.1016\/j.sigpro.2012.01.017","article-title":"Real-valued DOA estimation for uniform linear array with unknown mutual coupling","volume":"92","author":"Dai","year":"2012","journal-title":"Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4683","DOI":"10.1109\/TSP.2012.2203125","article-title":"Joint 2-D DOA estimation and phase calibration for uniform rectangular arrays","volume":"60","author":"Heidenreich","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, Z., Ding, Y., and Ren, S. (2018). A Novel Noncircular MUSIC Algorithm Based on the Concept of the Difference and Sum Coarray. Sensors, 18.","DOI":"10.3390\/s18020344"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/LAWP.2007.907913","article-title":"Joint SVD of two cross-correlation matrices to achieve automatic pairing in 2-D angle estimation problems","volume":"6","author":"Gu","year":"2007","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Shi, H., Wen, L., and Guan, Z. (2017). Two Novel Two-Stage Direction of Arrival Estimation Algorithms for Two-Dimensional Mixed Noncircular and Circular Sources. Sensors, 17.","DOI":"10.3390\/s17061433"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1109\/PROC.1985.13324","article-title":"A new approach to array geometry for improved spatial spectrum estimation","volume":"73","author":"Pillai","year":"1985","journal-title":"Proc. IEEE"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2458","DOI":"10.1109\/78.709534","article-title":"Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. I. Fully augmentable arrays","volume":"46","author":"Abramovich","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1109\/78.765119","article-title":"Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays","volume":"47","author":"Abramovich","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","article-title":"Nested arrays: A novel approach to array processing with enhanced degrees of freedom","volume":"58","author":"Pal","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Pal, P., and Vaidyanathan, P.P. (2011, January 4\u20137). Coprime sampling and the music algorithm. Proceedings of the Digital Signal Processing and Signal Processing Education Meeting (DSP\/SPE), Sedona, AZ, USA.","DOI":"10.1109\/DSP-SPE.2011.5739227"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1049\/iet-spr.2015.0252","article-title":"Two-dimensional DOA estimation for L-shaped array with nested subarrays without pair matching","volume":"10","author":"Dong","year":"2017","journal-title":"IET Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2627","DOI":"10.1109\/TAP.2007.904143","article-title":"Decoupled estimation of 2-D angles of arrival using two parallel uniform linear arrays","volume":"55","author":"Xia","year":"2007","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1049\/el.2015.0293","article-title":"Two-dimensional DOA estimation algorithm with co-prime array via sparse representation","volume":"51","author":"Cheng","year":"2015","journal-title":"Electron. Lett."},{"key":"ref_26","first-page":"1","article-title":"DOA estimation based on sparse signal recovery utilizing double-threshold sigmoid penalty","volume":"9","author":"Wang","year":"2015","journal-title":"J. Electr. Comput. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Si, W., Peng, Z., Hou, C., and Zeng, F. (2018). Two-dimensional DOA estimation for three-parallel nested subarrays via sparse representation. Sensors, 18.","DOI":"10.3390\/s18061861"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","article-title":"Sparse sensing with co-prime samplers and arrays","volume":"59","author":"Vaidyanathan","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1109\/JSEN.2016.2637059","article-title":"Source Estimation using Coprime Array: A Sparse Reconstruction Perspective","volume":"17","author":"Shi","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3032","DOI":"10.1016\/j.sigpro.2012.06.010","article-title":"Improved two-dimensional DOA estimation algorithm for two-parallel uniform linear arrays using propagator method","volume":"92","author":"Li","year":"2012","journal-title":"Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2136","DOI":"10.1109\/TAP.2010.2046838","article-title":"Joint elevation and azimuth direction finding using L-shaped array","volume":"58","author":"Liang","year":"2010","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1622","DOI":"10.1109\/TAP.2005.846804","article-title":"L-shape 2-dimensional arrival angle estimation with propagator method","volume":"53","author":"Tayem","year":"2005","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1109\/TSP.2011.2144591","article-title":"Computationally efficient subspace-based method for two-dimensional direction estimation with L-shaped array","volume":"59","author":"Wang","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1016\/j.sigpro.2010.12.001","article-title":"L-shaped array-based elevation and azimuth direction finding in the presence of mutual coupling","volume":"91","author":"Liang","year":"2011","journal-title":"Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/LSP.2014.2321791","article-title":"A Computationally Efficient Subspace Algorithm for 2-D DOA Estimation with L-shaped Array","volume":"21","author":"Nie","year":"2014","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"8510","DOI":"10.1109\/ACCESS.2018.2805168","article-title":"An efficient dictionary learning-based 2-D DOA estimation without pair matching for co-prime parallel arrays","volume":"6","author":"Sun","year":"2018","journal-title":"IEEE Access"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1049\/iet-rsn.2014.0547","article-title":"Sparse representation based two-dimensional direction-of-arrival estimation method with L-shaped array","volume":"10","author":"Cheng","year":"2016","journal-title":"IET Radar Sonar Navig."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3997","DOI":"10.1109\/TSP.2016.2558159","article-title":"Super nested arrays: Linear sparse arrays with reduced mutual coupling-part I: Fundamentals","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4203","DOI":"10.1109\/TSP.2016.2558167","article-title":"Super nested arrays: Linear sparse arrays with reduced mutual coupling-part II:High-order extensions","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5549","DOI":"10.1109\/TSP.2017.2736493","article-title":"Augmented nested arrays with enhanced DOF and reduced mutual coupling","volume":"65","author":"Liu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/TSP.2015.2393838","article-title":"Generalized coprime array configurations for direction-of-arrival estimation","volume":"63","author":"Qin","year":"2015","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3553\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:50Z","timestamp":1760196410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,19]]},"references-count":41,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103553"],"URL":"https:\/\/doi.org\/10.3390\/s18103553","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,10,19]]}}}