{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:19Z","timestamp":1760060659594,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T00:00:00Z","timestamp":1758067200000},"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>Hammerstein adaptive filters (HAFs) are widely used for nonlinear system identification due to their structural simplicity and modeling effectiveness. However, their performance can degrade significantly in the presence of impulsive disturbance or other more complex non-Gaussian noise, which are common in real-world scenarios. To address this limitation, this paper proposes a robust HAF algorithm based on the kernel mean p-power error (KMPE) criterion. By extending the p-power loss into the kernel space, KMPE preserves its symmetry while providing enhanced robustness against non-Gaussian noise in adaptive filter design. In addition, random Fourier features are employed to flexibly and efficiently model the nonlinear component of the system. A theoretical analysis of steady-state excess mean square error is presented, and our simulation results validate the superior robustness and accuracy of the proposed method over the classical HAF and its robust variants.<\/jats:p>","DOI":"10.3390\/sym17091556","type":"journal-article","created":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T11:00:00Z","timestamp":1758106800000},"page":"1556","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Kernel Mean p-Power Loss-Enhanced Robust Hammerstein Adaptive Filter and Its Performance Analysis"],"prefix":"10.3390","volume":"17","author":[{"given":"Yan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-8653-1664","authenticated-orcid":false,"given":"Chuanliang","family":"Tu","sequence":"additional","affiliation":[{"name":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Yong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Yu","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Semiconductors (College of Integrated Circuits), Hunan University, Changsha 410082, China"}]},{"given":"Chenggan","family":"Wen","sequence":"additional","affiliation":[{"name":"College of Semiconductors (College of Integrated Circuits), Hunan University, Changsha 410082, China"}]},{"given":"Banghui","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Central South University, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7268","DOI":"10.1109\/TIE.2022.3199931","article-title":"Bias-Correction Errors-in-Variables Hammerstein Model Identification","volume":"70","author":"Hou","year":"2023","journal-title":"IEEE Trans. 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