{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:30:38Z","timestamp":1762432238905,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,8,6]],"date-time":"2022-08-06T00:00:00Z","timestamp":1659744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62101340","61771316","62171292","2020A1515010410","2022A1515010188"],"award-info":[{"award-number":["62101340","61771316","62171292","2020A1515010410","2022A1515010188"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["62101340","61771316","62171292","2020A1515010410","2022A1515010188"],"award-info":[{"award-number":["62101340","61771316","62171292","2020A1515010410","2022A1515010188"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>With the rapid development of vibration and noise reduction technologies, underwater target detection is facing great challenges. Particularly, the task of high-resolution direction of arrival (DOA) estimation with sonar array is becoming more and more tough. In recent years, unmanned underwater vehicles (UUVs) have been developed considerably, with the improvements of target localization performance in terms of adaptability, detection range, operation efficiency, and anti-interference ability. Nevertheless, in general, the size of UUV is small such that current passive sonar systems usually have relatively limited localization accuracy, detection distance, and environmental robustness in complex ocean noise. This motivates us to present a new approach to construct a large-aperture virtual array with multiple small-aperture arrays of unmanned underwater vehicle swarm (UUVS) which consists of multiple UUVs in this paper. However, for the UUVS array, the received data could suffer from unobserved and corrupted samples. This makes it challenging to analyze and process large-aperture array data. Towards this end, the matrix completion technique is employed to recover the unobserved and corrupted data for virtual array construction based on the low rank property of array data matrix. The recovered matrix is then exploited for underwater target bearing estimation using the traditional DOA estimation approach. Numerical results verify that the proposed method is capable of detecting underwater targets with high precision and resolution.<\/jats:p>","DOI":"10.3390\/rs14153790","type":"journal-article","created":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T04:16:55Z","timestamp":1660018615000},"page":"3790","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Direction of Arrival Estimation of Acoustic Sources with Unmanned Underwater Vehicle Swarm via Matrix Completion"],"prefix":"10.3390","volume":"14","author":[{"given":"Liya","family":"Xu","sequence":"first","affiliation":[{"name":"Guangdong Key Laboratory of Intelligent Information Processing, College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7040-3591","authenticated-orcid":false,"given":"Jianjun","family":"Huang","sequence":"additional","affiliation":[{"name":"Guangdong Key Laboratory of Intelligent Information Processing, College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Hao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4636-4339","authenticated-orcid":false,"given":"Bin","family":"Liao","sequence":"additional","affiliation":[{"name":"Guangdong Key Laboratory of Intelligent Information Processing, College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,6]]},"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","first-page":"124","article-title":"Generalized MUSIC-Like array processing for underwater environments","volume":"42","author":"Lim","year":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_3","first-page":"8890","article-title":"A modified differential beamforming and its application for DOA estimation of low frequency underwater signal","volume":"20","author":"Xu","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H., and Tolstoy, A. (2011). Computational Ocean Acoustics, Springer.","DOI":"10.1007\/978-1-4419-8678-8"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, F., Chen, Y., and Wan, J. (2019). In-depth exploration of signal self-cancellation phenomenon to achieve DOA estimation of underwater acoustic sources. Appl. Sci., 9.","DOI":"10.3390\/app9030570"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5302","DOI":"10.1109\/TSP.2011.2164072","article-title":"Maximum likelihood direction-of-arrival estimation of underwater acoustic signals containing sinusoidal and random components","volume":"59","author":"Li","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3439","DOI":"10.1109\/TVT.2021.3064279","article-title":"A passive DOA estimation algorithm of underwater multipath signals via spatial time-frequency distributions","volume":"70","author":"Han","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/MRA.2019.2908063","article-title":"Underwater robots: From remotely operated vehicles to intervention-autonomous underwater vehicles","volume":"26","author":"Petillot","year":"2019","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jiang, W., Yang, X., Tong, F., Yang, Y., and Zhou, T. (2022). A low-complexity underwater acoustic coherent communication system for small AUV. Remote Sens., 14.","DOI":"10.3390\/rs14143405"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s13344-019-0054-0","article-title":"Identification of pitch dynamics of an autonomous underwater vehicle using sensor fusion","volume":"33","author":"Abtahi","year":"2019","journal-title":"China Ocean. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yokota, Y., and Matsuda, T. (2021). Underwater communication using UAVs to realize high-speed AUV deployment. Remote Sens., 13.","DOI":"10.20944\/preprints202108.0330.v1"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Verdun, J., Roussel, C., Cali, J., Maia, M., D\u2019Eu, J.-F., Kharbou, O., Poitou, C., Ammann, J., Durand, F., and Bouhier, M.-\u00c9. (2022). Development of a Lightweight Inertial Gravimeter for Use on Board an Autonomous Underwater Vehicle: Measurement Principle, System Design and Sea Trial Mission. Remote Sens., 14.","DOI":"10.3390\/rs14112513"},{"key":"ref_13","unstructured":"Button, R.W., Kamp, J., Curtin, T.B., and Dryden, J. (2009). A Survey of Missions for Unmanned Undersea Vehicles, RAND Corporation."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1109\/TVT.2021.3053456","article-title":"Joint design of communication, wireless energy transfer, and control for swarm autonomous underwater vehicles","volume":"70","author":"Guo","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","first-page":"21","article-title":"Research on the application of unmanned system cluster in marine combat applications","volume":"39","author":"Wang","year":"2019","journal-title":"Ship Electron. Eng."},{"key":"ref_16","first-page":"88","article-title":"A review on unmanned aerial vehicle remote sensing and its application","volume":"1","author":"Jin","year":"2009","journal-title":"Remote Sens. Inf."},{"key":"ref_17","first-page":"1492","article-title":"Overview of development of unmanned-surface-vehicle sensing technology","volume":"41","author":"Zhu","year":"2020","journal-title":"J. Harbin Eng. Univ."},{"key":"ref_18","first-page":"1","article-title":"Research on the development and combat application of foreign underwater unmanned vehicle","volume":"42","author":"Liu","year":"2020","journal-title":"Ship Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1007\/s13344-020-0063-z","article-title":"Multiple unmanned underwater vehicles consensus control with unmeasurable velocity information and environmental disturbances under switching directed topologies","volume":"34","author":"Yan","year":"2020","journal-title":"China Ocean. Eng."},{"key":"ref_20","unstructured":"Nichols, R.K., Ryan, J.J., Mumm, H.C.M., Lonstein, W.D., Carter, C.M., Shay, J., Mai, R., Hood, J.P., and Jackson, M. (2021). Unmanned Vehicle Systems & Operations on Air, Sea, Land, New Prairie Press."},{"key":"ref_21","unstructured":"Trees, H.L.V. (2002). Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory, John Wiley & Sons, Inc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3866","DOI":"10.1016\/j.eswa.2008.02.046","article-title":"An evolutionary computing approach for the target motion analysis (TMA) problem for underwater tracks","volume":"36","author":"Ince","year":"2009","journal-title":"Exp. Syst. Appl."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","unstructured":"Balzano, L., Recht, B., and Nowak, R. (2010, January 13\u201318). High-dimensional matched subspace detection when data are missing. Proceedings of the 2010 IEEE International Symposium on Information Theory, Austin, TX, USA.","DOI":"10.1109\/ISIT.2010.5513344"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kim, Y.G., Kim, Y., Lee, S.H., Moon, S.T., Jeon, M., and Kim, H.K. (2016, January 6\u20138). Underwater acoustic sensor fault detection for passive sonar systems. Proceedings of the 2016 First International Workshop on Sensing, Processing and Learning for Intelligent Machines (SPLINE), Aalborg, Denmark.","DOI":"10.1109\/SPLIM.2016.7528395"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3213","DOI":"10.1109\/TSP.2019.2912882","article-title":"Robustness of difference coarrays of sparse arrays to sensor failures\u2014Part I: A theory motivated by coarray MUSIC","volume":"67","author":"Liu","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/TIT.2005.860430","article-title":"Stable recovery of sparse overcomplete representations in the presence of noise","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2580","DOI":"10.1109\/TSP.2019.2904021","article-title":"Correction of corrupted columns through fast robust Hankel matrix completion","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1109\/JPROC.2009.2035722","article-title":"Matrix completion with noise","volume":"98","author":"Candes","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1145\/2184319.2184343","article-title":"Exact matrix completion via convex optimization","volume":"55","author":"Candes","year":"2012","journal-title":"Commun. ACM"},{"key":"ref_31","first-page":"3413","article-title":"A simpler approach to matrix completion","volume":"12","author":"Recht","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","article-title":"The power of convex relaxation: Near-optimal matrix completion","volume":"56","author":"Tao","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","article-title":"Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information","volume":"52","author":"Romberg","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","article-title":"Near-optimal signal recovery from random projections: Universal encoding strategies?","volume":"52","author":"Candes","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"8504","DOI":"10.1109\/TVT.2018.2850305","article-title":"Compressed sensing of underwater acoustic signals via structured approximation l0-norm","volume":"67","author":"Wu","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1109\/TIT.2010.2046205","article-title":"Matrix completion from a few entries","volume":"56","author":"Keshavan","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Darsena, D., and Verde, F. (2022). Anti-jamming beam alignment in millimeter-wave MIMO systems. IEEE Trans. Commun., Early Access.","DOI":"10.1109\/TCOMM.2022.3184158"},{"key":"ref_39","unstructured":"Karatzoglou, A., and Weimer, M. (September, January ). Quantile Matrix Factorization for Collaborative Filtering. Proceedings of the International Conference on Electronic Commerce and Web Technologies, Bilbao, Spain."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/TPAMI.2008.79","article-title":"Robust face recognition via sparse representation","volume":"31","author":"Wright","year":"2008","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/TFUZZ.2006.879996","article-title":"Control design for fuzzy systems based on relaxed nonquadratic stability and performance conditions","volume":"15","author":"Zhou","year":"2007","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1109\/JSAC.2011.110206","article-title":"Collaborative spectrum sensing from sparse observations in cognitive radio networks","volume":"29","author":"Meng","year":"2011","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Tachwali, Y., Barnes, W.J., Basma, F., and Refai, H. (2010, January 15\u201319). The feasibility of a fast fourier sampling technique for wireless microphone detection in IEEE 802.22 air interface. Proceedings of the 2010 Infocom IEEE Conference on Computer Communications Workshops, San Diego, CA, USA.","DOI":"10.1109\/INFCOMW.2010.5466621"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1109\/JSTSP.2010.2042410","article-title":"Compressive estimation of doubly selective channels in multicarrier systems: Leakage effects and sparsity-enhancing processing","volume":"4","author":"Taubock","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"HesamMohseni, A., Babaie Zadeh, M., and Jutten, C. (2009, January 19\u201324). Inflating compressed samples: A joint source-channel coding approach for noise-resistant compressed sensing. Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, Taipei, Taiwan.","DOI":"10.1109\/ICASSP.2009.4960244"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Chen, Y., Lei, C., and Wu, Y.C. (2022). Bayesian low-rank matrix completion with dual-graph embedding: Prior analysis and tuning-free inference. arXiv.","DOI":"10.2139\/ssrn.4063431"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Liao, B., Guo, C., Huang, L., and Wen, J. (2016, January 16\u201318). Matrix completion based direction-of-arrival estimation in nonuniform noise. Proceedings of the 2016 IEEE International Conference on Digital Signal Processing (DSP), Beijing, China.","DOI":"10.1109\/ICDSP.2016.7868517"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Ji, H., Liu, C.Q., Shen, Z.W., and Xu, Y.H. (2010, January 5). Robust video denoising using low rank matrix completion. Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA.","DOI":"10.1109\/CVPR.2010.5539849"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Wang, M., and Wang, W. (2013, January 5\u20138). DOA estimation of array radar via random interval sub-Nyquist-sampling. Proceedings of the 2013 IEEE International Conference on Signal Processing, Communication and Computing (ICSPCC 2013), Kunming, China.","DOI":"10.1109\/ICSPCC.2013.6664017"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1109\/JSTSP.2019.2937392","article-title":"Irregular array manifold aided channel estimation in massive MIMO communications","volume":"13","author":"Cheng","year":"2019","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_51","unstructured":"Cherapanamjeri, Y., Gupta, K., and Jain, P. (2017, January 6\u201311). Nearly-optimal robust matrix completion. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","article-title":"A singular value thresholding algorithm for matrix completion","volume":"20","author":"Cai","year":"2010","journal-title":"SIAM J. Optim."},{"key":"ref_53","unstructured":"Keshavan, R.H., and Oh, S. (2009). A gradient descent algorithm on the grassman manifold for matrix completion. arXiv."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1109\/TSP.2017.2784361","article-title":"Outlier-robust matrix completion via \u2113p-minimization","volume":"66","author":"Zeng","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1109\/78.376849","article-title":"Probability of resolution of the MUSIC algorithm","volume":"43","author":"Zhang","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1109\/78.136540","article-title":"Statistical characterization of the MUSIC null spectrum","volume":"39","author":"Lee","year":"1991","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3790\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:05:10Z","timestamp":1760141110000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3790"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,6]]},"references-count":56,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14153790"],"URL":"https:\/\/doi.org\/10.3390\/rs14153790","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,8,6]]}}}