An Improved Variable Kernel Width for Maximum Correntropy Criterion Algorithm

Abstract

The maximum correntropy criterion (MCC) algorithm has attracted much attention due to its capability of combating impulsive noise. However, its performance depends on choice of the kernel width, which is a hard issue. Several variable kernel width schemes based on various error functions have been proposed to address this problem. Nevertheless, these methods may not provide an optimal kernel width because they do not contain any knowledge of the background noise that actually has influence on the optimization of the kernel width. This paper proposes an improved variable kernel width MCC algorithm, which is derived by minimizing the squared deviation at each iteration. We also design a reset mechanism for the proposed algorithm to improve its tracking capability when the estimated vector encounters a sudden change. Simulations for system identification and echo cancellation scenarios show that the proposed scheme outperforms other variable kernel width algorithms.

A Variable Step Size for Maximum Correntropy Criterion Algorithm with Improved Variable Kernel Width

“…The IVKW-MCC replaces σ in (5) with a time-varying kernel with σ (k ) [21] and obtains the design of the variable kernel width…”

“…If the impulsive noise is the alpha-stable noise model, the δ 2 should be estimated by adopting the moving average strategy between the error power and the output-noise power in Ref. [21]. IVKW-MCC has done an outstanding job in terms of kernel width, and we now discuss the proposed variable step size algorithm.…”

“…The MCC algorithm also can be written as w(k + 1) = w(k ) + μ (e(k ))e(k )u(k ) (20) where μ (e(k )) = μ(e(k )) exp − e 2 (k ) 2σ 2 (k ) . From the limitation of the step size factor in the LMS algorithm [20] 0 < μ (e(k )) < 2 3tr(R) (21) where tr(•) is the trace operator, and R is the autocorrelation matrix of the input vector and is given by…”

“…The unknown system vector w 0 changes to −w 0 at iteration 2 × 10 4 . GSNR = 1,3,5,7,9,11,13,15,17,19,21,23,25,27, 29…”

Robust adaptive filtering with variable risk‐sensitive parameter and kernel width

“…Nevertheless, the performance surface of correntropy is markedly nonconvex, which may give rise to inferior convergence speed. Recent work in information theoretic learning [2][3][4][5][6][7] has shown that kernel risksensitive loss (KRSL) has a more convex performance surface, and the corresponding minimum KRSL (MKRSL) algorithm can produce a faster convergence speed and higher accuracy without impairing the robustness against outliers [4]. However, the MKRSL algorithm is limited to adaptive filtering of the real domain.…”