{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:36:27Z","timestamp":1760146587776,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,22]],"date-time":"2024-11-22T00:00:00Z","timestamp":1732233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Sichuan Science and Technology Program","award":["2024NSFSC1437","2024NSFSC0477","XZ202201ZD0006G02"],"award-info":[{"award-number":["2024NSFSC1437","2024NSFSC0477","XZ202201ZD0006G02"]}]},{"name":"Science and Technology Major Project of Tibetan Autonomous Region of China","award":["2024NSFSC1437","2024NSFSC0477","XZ202201ZD0006G02"],"award-info":[{"award-number":["2024NSFSC1437","2024NSFSC0477","XZ202201ZD0006G02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper introduces a reduced Gaussian kernel filtered-x least mean square (RGKxLMS) algorithm for a nonlinear active noise control (NANC) system. This algorithm addresses the computational and storage challenges posed by the traditional kernel (i.e., KFxLMS) algorithm. Then, we analyze the mean weight behavior and computational complexity of the RGKxLMS, demonstrating its reduced complexity compared to existing kernel filtering methods and its mean stable performance. To further enhance noise reduction, we also develop the historical error correction RGKxLMS (HECRGKxLMS) algorithm, incorporating historical error information. Finally, the effectiveness of the proposed algorithms is validated, using Lorenz chaotic noise, non-stationary noise environments, and factory noise.<\/jats:p>","DOI":"10.3390\/e26121010","type":"journal-article","created":{"date-parts":[[2024,11,22]],"date-time":"2024-11-22T10:17:23Z","timestamp":1732270643000},"page":"1010","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reduced Gaussian Kernel Filtered-x LMS Algorithm with Historical Error Correction for Nonlinear Active Noise Control"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-3424-3659","authenticated-orcid":false,"given":"Jinhua","family":"Ku","sequence":"first","affiliation":[{"name":"College of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4043-8987","authenticated-orcid":false,"given":"Hongyu","family":"Han","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weixi","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0247-3317","authenticated-orcid":false,"given":"Sheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1109\/5.763310","article-title":"Active noise control: A tutorial review","volume":"87","author":"Kuo","year":"1999","journal-title":"Proc. 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