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Open AccessArticle

A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference

by Hua Qu 1, Youwei Shi 1,* and Jihong Zhao 1,2
1
School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi‘an 710049, China
2
School of Telecommunication and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710061, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(11), 1099; https://doi.org/10.3390/e21111099
Received: 18 October 2019 / Revised: 1 November 2019 / Accepted: 8 November 2019 / Published: 11 November 2019
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. View Full-Text
Keywords: generalized correntropy; exponential weighted average; robust adaptive filtering algorithm; impulsive noise generalized correntropy; exponential weighted average; robust adaptive filtering algorithm; impulsive noise
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Qu, H.; Shi, Y.; Zhao, J. A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference. Entropy 2019, 21, 1099.

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