{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:20:31Z","timestamp":1773800431463,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T00:00:00Z","timestamp":1663804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a novel variable matrix-type step-size affine projection sign algorithm (VMSS-APSA) characterized by robustness against impulsive noise. To mathematically derive a matrix-type step size, VMSS-APSA utilizes mean-square deviation (MSD) for the modified version of the original APSA. Accurately establishing the MSD of APSA is impossible. Therefore, the proposed VMSS-APSA derives the upper bound of the MSD using the upper bound of the L1-norm of the measurement noise. The optimal matrix-type step size is calculated at each iteration by minimizing the upper bound of the MSD, thereby improving the filter performance in terms of convergence rate and steady-state estimation error. Because a novel cost function of the proposed VMSS-APSA was designed to maintain a form similar to the original APSA, they have symmetric characteristics. Simulation results demonstrate that the proposed VMSS-APSA improves filter performance in a system-identification scenario in the presence of impulsive noise.<\/jats:p>","DOI":"10.3390\/sym14101985","type":"journal-article","created":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T04:07:07Z","timestamp":1663906027000},"page":"1985","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Variable Matrix-Type Step-Size Affine Projection Sign Algorithm for System Identification in the Presence of Impulsive Noise"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3765-6009","authenticated-orcid":false,"given":"Jaewook","family":"Shin","sequence":"first","affiliation":[{"name":"The Division of Electrical Engineering, Kumoh National Institute of Technology, Gumi 39177, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9490-0365","authenticated-orcid":false,"given":"Bum Yong","family":"Park","sequence":"additional","affiliation":[{"name":"The Division of Electrical Engineering, Department of IT Convergence Engineering, Kumoh National Institute of Technology, Gumi 39177, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0851-3113","authenticated-orcid":false,"given":"Won Il","family":"Lee","sequence":"additional","affiliation":[{"name":"The Division of Electrical Engineering, Kumoh National Institute of Technology, Gumi 39177, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1025-3784","authenticated-orcid":false,"given":"Jinwoo","family":"Yoo","sequence":"additional","affiliation":[{"name":"Department of Automobile and IT Convergence, Kookmin University, Seoul 02707, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/TSP.2019.2955831","article-title":"Performance Analysis of Deficient Length Quaternion Least Mean Square Adaptive Filters","volume":"68","author":"Xiang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, R., and Zhao, H. (2021). A Novel Method for Online Extraction of Small-Angle Scattering Pulse Signals from Particles Based on Variable Forgetting Factor RLS Algorithm. Sensors, 21.","DOI":"10.3390\/s21175759"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, Y., Wang, Y., and Sun, L. (2018). A Proportionate Normalized Maximum Correntropy Criterion Algorithm with Correntropy Induced Metric Constraint for Identifying Sparse Systems. Symmetry, 10.","DOI":"10.3390\/sym10120683"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dogariu, L.-M., Stanciu, C.L., Elisei-Iliescu, C., Paleologu, C., Benesty, J., and Ciochina, S. (2021). Tensor-Based Adaptive Filtering Algorithms. Symmetry, 13.","DOI":"10.3390\/sym13030481"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108276","DOI":"10.1016\/j.sigpro.2021.108276","article-title":"Robust and sparsity-aware adaptive filters: A Review","volume":"189","author":"Kumar","year":"2021","journal-title":"Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108731","DOI":"10.1016\/j.sigpro.2022.108731","article-title":"A variable regularization parameter widely linear complex-valued NLMS algorithm: Performance analysis and wind prediction","volume":"201","author":"Long","year":"2022","journal-title":"Signal Process."},{"key":"ref_7","first-page":"3934","article-title":"Sparsity-Aware Robust Normalized Subband Adaptive Filtering Algorithms With Alternating Optimization of Parameters","volume":"69","author":"Yu","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1007\/s00034-019-01209-8","article-title":"Robust Variable Step-Size Affine Projection Sign Algorithm Against Impulsive Noises","volume":"39","author":"Abadi","year":"2019","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1109\/LSP.2022.3166395","article-title":"Robust Sparsity-Aware RLS Algorithms With Jointly-Optimized Parameters Against Impulsive Noise","volume":"29","author":"Yu","year":"2022","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.1109\/TVT.2021.3061126","article-title":"Affine-Projection Lorentzian Algorithm for Vehicle Hands-Free Echo Cancellation","volume":"70","author":"Huang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1109\/TASLP.2022.3183935","article-title":"General Robust Subband Adaptive Filtering: Algorithms and Applications","volume":"30","author":"Yi","year":"2022","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"19","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. Commun. Jpn."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jiang, Z., Li, Y., Huang, X., and Jin, Z. (2019). A Sparsity-Aware Variable Kernel Width Proportionate Affine Projection Algorithm for Identifying Sparse Systems. Symmetry, 11.","DOI":"10.3390\/sym11101218"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"108153","DOI":"10.1016\/j.sigpro.2021.108153","article-title":"Affine projection mixed-norm algorithms for robust filtering","volume":"187","author":"Li","year":"2021","journal-title":"Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shin, J., Kim, J., Kim, T.K., and Yoo, J. (2021). Lp-Norm-like Affine Projection Sign Algorithm for Sparse System to Ensure Robustness against Impulsive Noise. Symmetry, 13.","DOI":"10.3390\/sym13101916"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1109\/LSP.2010.2040203","article-title":"An affine projection sign algorithm robust against impulsive interference","volume":"17","author":"Shao","year":"2010","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.1109\/TASL.2011.2125955","article-title":"Proportionate affine projection sign algorithm for network echo cancellation","volume":"19","author":"Yang","year":"2011","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1049\/el.2012.1563","article-title":"Improved affine projection sign algorithm for sparse system identification","volume":"48","author":"Yoo","year":"2012","journal-title":"Electron. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.sigpro.2014.06.006","article-title":"Affine projection sign algorithm with l1 minimization-based variable step-size","volume":"105","author":"Kim","year":"2014","journal-title":"Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1049\/el.2012.0751","article-title":"Variable step-size affine projection sign algorithm","volume":"48","author":"Shin","year":"2012","journal-title":"Electron. Lett."},{"key":"ref_21","first-page":"274","article-title":"Variable step-size affine projection sign algorithm","volume":"61","author":"Yoo","year":"2014","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2806","DOI":"10.1016\/j.sigpro.2010.03.029","article-title":"A robust variable step-size affine projection algorithm","volume":"90","author":"Rey","year":"2010","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1109\/TSP.2007.913142","article-title":"A new robust variable step-size NLMS algorithm","volume":"56","author":"Rey","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1049\/iet-spr.2014.0253","article-title":"Variable step-size sign algorithm against impulsive noises","volume":"9","author":"Yoo","year":"2015","journal-title":"IET Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/LSP.2012.2237166","article-title":"Variable step-size sign subband adaptive filter","volume":"20","author":"Shin","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.sigpro.2014.05.001","article-title":"A band-dependent variable step-size sign subband adaptive filter","volume":"104","author":"Yoo","year":"2014","journal-title":"Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1774","DOI":"10.1109\/LSP.2022.3195662","article-title":"A Variable Step Size Adaptive Algorithm With Simple Parameter Selection","volume":"29","author":"Tiglea","year":"2022","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1109\/97.873571","article-title":"A recursive least m-estimate (RLM) adaptive filter for robust filtering in impulse noise","volume":"7","author":"Zou","year":"2000","journal-title":"IEEE Signal Process. 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