Abstract
This paper provides a novel Newtonian-type optimization method for robust adaptive filtering inspired by information theory learning. With the traditional minimum mean square error (MMSE) criterion replaced by criteria like the maximum correntropy criterion (MCC) or generalized maximum correntropy criterion (GMCC), adaptive filters assign less emphasis on the outlier data, thus become more robust against impulsive noises. The optimization methods adopted in current MCC-based LMS-type and RLS-type adaptive filters are gradient descent method and fixed point iteration, respectively. However, in this paper, a Newtonian-type method is introduced as a novel method for enhancing the existing body of knowledge of MCC-based adaptive filtering and providing a fast convergence rate. Theoretical analysis of the steady-state performance of the algorithm is carried out and verified by simulations. The experimental results show that, compared to the conventional MCC adaptive filter, the MCC-based Newtonian-type method converges faster and still maintains a good steady-state performance under impulsive noise. The practicability of the algorithm is also verified in the experiment of acoustic echo cancellation.
Highlights
Adaptive filtering is widely used in many areas including system identification, channel equalization, interference cancelling, acoustic echo cancellation(AEC), etc. [1,2,3,4,5]
Traditional adaptive filtering methods based on minimum mean square error (MMSE) criterion perform well in the presence of Gaussian noise, and the optimization methods adopted are mostly least mean square (LMS)-type or recursive least square (RLS)-type [6]
LMS-type adaptive filtering uses gradient descent characterized with a low convergence speed and a very low arithmetic complexity, while RLS-type adaptive filtering, free from the selection problem of the optimal step size, converges much faster at the cost of higher complexity, and is afflicted with stability problems caused by error propagation and unregulated matrix inversion [7]
Summary
Adaptive filtering is widely used in many areas including system identification, channel equalization, interference cancelling, acoustic echo cancellation(AEC), etc. [1,2,3,4,5]. [28] implied that a Newtonian algorithm could be utilized in the MCC state estimation, as correntropy is a differentiable function Different methods such as Newton’s method and all its derivative algorithms that converge faster than gradient descent are seldom considered in MCC-based adaptive filtering. The main contributions of this paper are as follows: (1) the Newtonian-type optimization method is introduced in MCC-based adaptive filter and the recursive updating equation of the impulse response is derived. The experiments verifying the steady-state performance discussion is displayed, and there are experiments showing that the proposed algorithm is robust in the presence of impulsive noise and converges faster than the gradient descent-based adaptive filter algorithms.
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