{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T06:25:17Z","timestamp":1766298317644,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T00:00:00Z","timestamp":1685059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["2022NSFSC0953"],"award-info":[{"award-number":["2022NSFSC0953"]}],"id":[{"id":"10.13039\/501100018542","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The idea of variable step-size was introduced into the Hybrid Affine Projection Algorithm (H-APA) and we propose two variable step size algorithms based on H-APA, which are called the Variable Step-Size Hybrid Affine Projection Algorithm (VSS-H-APA) and the Modified Variable Step-Size Hybrid Affine Projection Algorithm (MVSS-H-APA). These are two variable-step algorithms aim to further improve the robust performance and convergence speed of H-APA under non-Gaussian noise. This allows for faster convergence while maintaining stability. The MVSS-H-APA goes further than VSS-H-APA to estimate the noise in order to achieve better convergence performance. The proposed algorithm performs better than the existing algorithms in system identification under symmetric non-Gaussian noise.<\/jats:p>","DOI":"10.3390\/sym15061158","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:10:53Z","timestamp":1685203853000},"page":"1158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Variable Step Size Methods of the Hybrid Affine Projection Adaptive Filtering Algorithm under Symmetrical Non-Gaussian Noise"],"prefix":"10.3390","volume":"15","author":[{"given":"Xingli","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 610056, China"},{"name":"School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China"}]},{"given":"Guoliang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 610056, China"}]},{"given":"Hongbin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 610056, China"}]},{"given":"Xin","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China"},{"name":"School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610056, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1002\/ecja.4400670503","article-title":"An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties","volume":"67","author":"Ozeki","year":"1984","journal-title":"Electron. 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