Recursive Generalized Maximum Correntropy Criterion Algorithm with Sparse Penalty Constraints for System Identification

Abstract

To address the sparse system identification problem in a non‐Gaussian impulsive noise environment, the recursive generalized maximum correntropy criterion (RGMCC) algorithm with sparse penalty constraints is proposed to combat impulsive‐inducing instability. Specifically, a recursive algorithm based on the generalized correntropy with a forgetting factor of error is developed to improve the performance of the sparsity aware maximum correntropy criterion algorithms by achieving a robust steady‐state error. Considering an unknown sparse system, the l1‐norm and correntropy induced metric are employed in the RGMCC algorithm to exploit sparsity as well as to mitigate impulsive noise simultaneously. Numerical simulations are given to show that the proposed algorithm is robust while providing robust steady‐state estimation performance.

State of Charge Estimation of Lithium Battery Based on Improved Correntropy Extended Kalman Filter

“…Correntropy, as a measure of local similarity that is insensitive to outliers and noise, has been successfully applied in fields such as pattern recognition [38], machine learning [39] and signal processing [40]. Correntropy [22,[41][42][43] can be expressed as follows…”

Maximum Correntropy Criterion Based l1-Iterative Wiener Filter for Sparse Channel Estimation Robust to Impulsive Noise

“…To estimate the channel in nonGaussian noise, we define an MCC cost function with exponential forgetting factor λ shown in (1) [20,21] and minimize it adaptively.…”

“…Recently, the maximum correntropy criterion (MCC) [16][17][18][19] has been successfully applied to various adaptive algorithms robust to impulsive noise. Current studies in robust sparse adaptive methods have resulted in the development of CR-RLS-based algorithms with MCC [20,21], and showed strong robustness under impulsive noise. However, CR-RLS used in [20,21] is not practical when determining the regularization coefficient for the sparse regularization term because CR-RLS [6] needs information about the true channel when calculating the regularization coefficients.…”

“…Current studies in robust sparse adaptive methods have resulted in the development of CR-RLS-based algorithms with MCC [20,21], and showed strong robustness under impulsive noise. However, CR-RLS used in [20,21] is not practical when determining the regularization coefficient for the sparse regularization term because CR-RLS [6] needs information about the true channel when calculating the regularization coefficients. In addition, MCC CR-RLS algorithms (so called convex regularized recursive maximum correntropy (CR-RMC)) [20,21] include the inversion of the auto-covariance matrix, which is linked to the numerical instability in finite-precision environments [15].…”

Robust Matching Pursuit Extreme Learning Machines

“…It applies a kernel trick that nonlinearly maps the original space to a higher dimensional feature space. It can be shown that correntropy is directly related to the probability of how similar two random variables are in a neighborhood of the joint space controlled by the kernel bandwidth [17,25,26].…”