{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T20:43:20Z","timestamp":1777149800051,"version":"3.51.4"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,11]],"date-time":"2019-11-11T00:00:00Z","timestamp":1573430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61531013"],"award-info":[{"award-number":["61531013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science and Technology Major Project of China","award":["2018ZX03001016"],"award-info":[{"award-number":["2018ZX03001016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The generalized maximum correntropy criterion (GMCC) algorithm is computationally simple and robust against impulsive noise but it suffers from slow convergence speed as it is derived and based on stochastic gradient, which only use the current data sample. In order to deal with this issue, a smoothed GMCC algorithm (SGMCC) is proposed. In the SGMCC algorithm, instead of taking the exponential weighted average of gradient vector to approximate the expectation of the gradient vector, we take the exponential weighted average of the variable step-size so that the SGMCC algorithm can be viewed as a sign GMCC algorithm with smoothed variable step-size. Moreover, convergence performance analyses are derived in terms of variable step-size, mean-square stability and steady-state behavior to demonstrate the robustness of the proposed algorithm. At last, simulation comparisons show that the proposed algorithm is robust against impulsive noise and converges fast with lower computational complexity. Also, for the steady-state behavior, simulation results verify that the simulated value matches well with the theoretical one.<\/jats:p>","DOI":"10.3390\/e21111099","type":"journal-article","created":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T04:07:07Z","timestamp":1573531627000},"page":"1099","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference"],"prefix":"10.3390","volume":"21","author":[{"given":"Hua","family":"Qu","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2018an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youwei","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2018an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jihong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2018an 710049, China"},{"name":"School of Telecommunication and Information Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Principe, J.C. 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