{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T09:58:17Z","timestamp":1773741497848,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,19]],"date-time":"2020-12-19T00:00:00Z","timestamp":1608336000000},"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":["Grant 61701440 and Grant 11704248"],"award-info":[{"award-number":["Grant 61701440 and Grant 11704248"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Beamforming technology is an essential method in acoustic imaging or reconstruction, which has been widely used in sound source localization and noise reduction. The beamforming algorithm can be described as all microphones in a plane simultaneously recording the source signal. The source position is then localized by maximizing the result of the beamformer. Evidence has shown that the accuracy of the sound source localization in a 2D plane can be improved by the non-synchronous measurements of moving the microphone array. In this paper, non-synchronous measurements are applied to 3D beamforming, in which the measurement array envelops the 3D sound source space to improve the resolution of the 3D space. The entire radiated object is covered better by a virtualized large or high-density microphone array, and the range of beamforming frequency is also expanded. The 3D imaging results are achieved in different ways: the conventional beamforming with a planar array, the non-synchronous measurements with orthogonal moving arrays, and the non-synchronous measurements with non-orthogonal moving arrays. The imaging results of the non-synchronous measurements are compared with the synchronous measurements and analyzed in detail. The number of microphones required for measurement is reduced compared with the synchronous measurement. The non-synchronous measurements with non-orthogonal moving arrays also have a good resolution in 3D source localization. The proposed approach is validated with a simulation and experiment.<\/jats:p>","DOI":"10.3390\/s20247308","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T01:01:08Z","timestamp":1608512468000},"page":"7308","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Achieving 3D Beamforming by Non-Synchronous Microphone Array Measurements"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8079-4055","authenticated-orcid":false,"given":"Liang","family":"Yu","sequence":"first","affiliation":[{"name":"Institute of Vibration, Shock and Noise, State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China"}]},{"given":"Qixin","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Electronics and Information Engineering, Tongji University, Shanghai 201804, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1514-873X","authenticated-orcid":false,"given":"Ning","family":"Chu","sequence":"additional","affiliation":[{"name":"College of Energy Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, China"}]},{"given":"Rui","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronics and Information Engineering, Tongji University, Shanghai 201804, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Park, Y., Choi, A., and Kim, K. (2020). Parametric Estimations Based on Homomorphic Deconvolution for Time of Flight in Sound Source Localization System. Sensors, 20.","DOI":"10.3390\/s20030925"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cao, R., Yang, K., Yang, Q., Chen, P., Sun, Q., and Xue, R. (2019). Localization of Two Sound Sources Based on Compressed Matched Field Processing with a Short Hydrophone Array in the Deep Ocean. Sensors, 19.","DOI":"10.3390\/s19173810"},{"key":"ref_3","unstructured":"Siller, H., Drescher, M., Saueressig, G., and Lange, R. (2010, January 24\u201325). Fly-over Source Localisation on a Boeing 747-400. Proceedings of the Berlin Beamforming Conference, Berlin, Germany."},{"key":"ref_4","unstructured":"Dinsenmeyer, A., Antoni, J., Leclere, Q., and Pereira, A. (2018, January 5\u20136). On the Denoising of Cross-Spectral Matrices for (aero) Acoustic Applications. Proceedings of the Berlin Beamforming Conference, Berlin, Germany."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1177\/1475472X17718883","article-title":"A unified formalism for acoustic imaging based on microphone array measurements","volume":"16","author":"Pereira","year":"2017","journal-title":"Int. J. Aeroacoustics"},{"key":"ref_6","first-page":"66","article-title":"Identification of truck noise sources under passby condition based on wave beamforming method","volume":"31","author":"Chu","year":"2012","journal-title":"J. Vib. Shock"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1121\/1.392911","article-title":"Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH","volume":"78","author":"Maynard","year":"1985","journal-title":"JASA"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"EL34","DOI":"10.1121\/1.5116333","article-title":"Robust reconstruction of equivalent source method based near-field acoustic holography using an alternative regularization parameter determination approach","volume":"146","author":"Tan","year":"2019","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.jsv.2018.09.049","article-title":"Near-field acoustic holography with three-dimensional scanning measurements","volume":"439","author":"Luo","year":"2019","journal-title":"J. Sound Vibration."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1121\/1.404263","article-title":"Application of BEM (boundary element metliod)-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries","volume":"92","author":"Bai","year":"1992","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1121\/1.1529668","article-title":"Sound source reconstruction using inverse boundary element calculations","volume":"113","author":"Schuhmacher","year":"2003","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1121\/1.4973567","article-title":"Sound field reconstruction using compressed modal equivalent point source method","volume":"141","author":"Bi","year":"2017","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.ymssp.2018.04.006","article-title":"Wideband holography based spherical equivalent source method with rigid spherical arrays","volume":"111","author":"Ping","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.jsv.2015.02.023","article-title":"Identification of active sources inside cavities using the equivalent source method-based free-field recovery technique","volume":"346","author":"Bi","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_15","first-page":"107220","article-title":"The acoustic inverse problem in the framework of alternating direction method of multipliers","volume":"49","author":"Yu","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","first-page":"83","article-title":"Near-field acoustical holography without the errors and limitations caused by the use of spatial DFT","volume":"6","author":"Steiner","year":"2001","journal-title":"Int. J. Acoust. Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2105","DOI":"10.1121\/1.3079773","article-title":"Basic theory and properties of statistically optimized near-field acoustical holography","volume":"125","author":"Hald","year":"2009","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2020","DOI":"10.1121\/1.419691","article-title":"Helmholtz equation-least-squares method for reconstructing acoustic pressure fields","volume":"102","author":"Wang","year":"1997","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Sarradj, E. (2012). Three-dimensional acoustic source mapping with different beamforming steering vector formulations. Adv. Acoust. Vib., 2012.","DOI":"10.1155\/2012\/292695"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Brooks, T., and Humphreys, W. (2005, January 23\u201325). Three-dimensional applications of DAMAS methodology for aeroacoustic noise source definition. Proceedings of the 11th AIAA\/CEAS Aeroacoustics Conference, Monterey, CA, USA.","DOI":"10.2514\/6.2005-2960"},{"key":"ref_21","unstructured":"Legg, M., and Bradley, S. (2012, January 22\u201323). Comparison of CLEAN-SC for 2D and 3D scanning surfaces. Proceedings of the 4th Berlin Beamforming Conference., Berlin, Germany."},{"key":"ref_22","first-page":"1","article-title":"Localization and identification of three-dimensional sound source with beamforming based acoustic tomography","volume":"19","author":"Ding","year":"2013","journal-title":"Proc. Mtgs. Acoust."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1939","DOI":"10.1016\/j.jsv.2011.12.011","article-title":"Improving the resolution of three-dimensional acoustic imaging with planar phased arrays","volume":"331","author":"Xenaki","year":"2012","journal-title":"J. Sound Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.jsv.2015.01.047","article-title":"Deconvolution for three-dimensional acoustic source identification based on spherical harmonics beamforming","volume":"344","author":"Chu","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jsv.2016.06.009","article-title":"Three-dimensional acoustic imaging with planar microphone arrays and compressive sensing","volume":"380","author":"Ning","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_26","unstructured":"Battista, G., Chiariotti, P., Herold, G., Sarradj, E., and Castellini, P. (2018, January 5\u20136). Inverse methods for three-dimensional acoustic mapping with a single planar array. Proceedings of the 7th Berlin Beamforming Conference, Berlin, Germany."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Padois, T., Robin, O., and Berry, A. (2013, January 27\u201329). 3D Source localization in a closed wind-tunnel using microphone arrays. Proceedings of the 19th AIAA\/CEAS Aeroacoustics Conference, Berlin, Germany.","DOI":"10.2514\/6.2013-2213"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"392","DOI":"10.3813\/AAA.919069","article-title":"Two and Three-Dimensional Sound Source Localization with Beamforming and Several Deconvolution Techniques","volume":"103","author":"Padois","year":"2017","journal-title":"Acta Acust. United Acust."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jsv.2015.06.030","article-title":"Three-dimensional beamforming of dipolar aeroacoustic sources","volume":"355","author":"Porteous","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1121\/10.0001383","article-title":"Three-dimensional source localization using sparse Bayesian learning on a spherical microphone array","volume":"147","author":"Ping","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"82500","DOI":"10.1109\/ACCESS.2020.2991606","article-title":"A High-resolution and Low-frequency Acoustic Beamforming based on Bayesian Inference and Non-synchronous Measurements","volume":"8","author":"Chu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.jsv.2017.07.036","article-title":"Acoustical source reconstruction from non-synchronous sequential measurements by Fast Iterative Shrinkage Thresholding Algorithm","volume":"408","author":"Yu","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.jsv.2015.03.008","article-title":"Reconstruction of sound quadratic properties from non-synchronous measurements with insufficient or without references: Proof of concept","volume":"349","author":"Antoni","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"106309","DOI":"10.1016\/j.ymssp.2019.106309","article-title":"Fast iteration algorithms for implementing the acoustic beamforming of non-synchronous measurements","volume":"134","author":"Yu","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_35","unstructured":"Chu, N. (2013). Bayesian Approach in Acoustic Source Localization and Imaging. [Ph.D. Thesis, Universit\u00e9 Paris Sud-Paris XI]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"Ieee Trans. Antennas Propag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.jsv.2019.01.001","article-title":"Sparse acoustical holography from iterated Bayesian focusing","volume":"446","author":"Antoni","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Brillinger, D.R. (2001). Time Series: Data Analysis and Theory, SIAM.","DOI":"10.1137\/1.9780898719246"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.jsv.2003.06.031","article-title":"Optimal regularisation for acoustic source reconstruction by inverse methods","volume":"275","author":"Kim","year":"2004","journal-title":"J. Sound Vib."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.jsv.2016.02.031","article-title":"Spectral matrix completion by Cyclic Projection and application to sound source reconstruction from non-synchronous measurements","volume":"372","author":"Yu","year":"2016","journal-title":"J. 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