{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T14:51:16Z","timestamp":1786114276017,"version":"3.56.0"},"reference-count":48,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T00:00:00Z","timestamp":1712448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior\u2014Brasil (CAPES)"},{"name":"Brazilian Navy"},{"name":"Brazilian Army"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate direction of arrival (DoA) estimation is paramount in various fields, from surveillance and security to spatial audio processing. This work introduces an innovative approach that refines the DoA estimation process and demonstrates its applicability in diverse and critical domains. We propose a two-stage method that capitalizes on the often-overlooked secondary peaks of the cross-correlation function by introducing a reduced complexity DoA estimation method. In the first stage, a low complexity cost function based on the zero cyclic sum (ZCS) condition is used to allow for an exhaustive search of all combinations of time delays between pairs of microphones, including primary peak and secondary peaks of each cross-correlation. For the second stage, only a subset of the time delay combinations with the lowest ZCS cost function need to be tested using a least-squares (LS) solution, which requires more computational effort. To showcase the versatility and effectiveness of our method, we apply it to the challenging acoustic-based drone DoA estimation scenario using an array of four microphones. Through rigorous experimentation with simulated and actual data, our research underscores the potential of our proposed DoA estimation method as an alternative for handling complex acoustic scenarios. The ZCS method demonstrates an accuracy of 89.4%\u00b12.7%, whereas the ZCS with the LS method exhibits a notably higher accuracy of 94.0%\u00b13.1%, showcasing the superior performance of the latter.<\/jats:p>","DOI":"10.3390\/s24072344","type":"journal-article","created":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T06:04:58Z","timestamp":1712556298000},"page":"2344","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Reduced Complexity Acoustic-Based 3D DoA Estimation with Zero Cyclic Sum"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5269-2342","authenticated-orcid":false,"given":"Rigel Proc\u00f3pio","family":"Fernandes","sequence":"first","affiliation":[{"name":"Program of Defense Engineering, Military Institute of Engineering (IME), Rio de Janeiro 22290-270, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1426-9636","authenticated-orcid":false,"suffix":"Jr.","given":"Jos\u00e9 Antonio","family":"Apolin\u00e1rio","sequence":"additional","affiliation":[{"name":"Program of Defense Engineering, Military Institute of Engineering (IME), Rio de Janeiro 22290-270, Brazil"},{"name":"Department of Electrical Engineering, Military Institute of Engineering (IME), Rio de Janeiro 22290-270, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5148-7363","authenticated-orcid":false,"given":"Jos\u00e9 Manoel","family":"de Seixas","sequence":"additional","affiliation":[{"name":"Signal Processing Lab, COPPE\/POLI, Technology Center, Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro 21941-914, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Isiaka, F. 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