KLMAT: A Kernel Least Mean Absolute Third Algorithm

TL;DR

This paper introduces the KLMAT algorithm, combining kernel methods with LMAT for robust adaptive prediction, and proposes a variable step-size version to improve convergence, with theoretical analysis and simulation validation.

Contribution

It presents a novel kernel-based LMAT algorithm and a variable step-size enhancement, along with stability analysis and empirical validation.

Findings

KLMAT outperforms traditional algorithms in noisy environments.

VSS-KLMAT accelerates convergence.

Algorithms are effective in time series prediction.

Abstract

In this paper, a kernel least mean absolute third (KLMAT) algorithm is developed for adaptive prediction. Combining the benefits of the kernel method and the least mean absolute third (LMAT) algorithm, the proposed KLMAT algorithm performs robustly against noise with different probability densities. To further enhance the convergence rate of the KLMAT algorithm, a variable step-size version (VSS-KLMAT algorithm) is proposed based on a Lorentzian function. Moreover, the stability and convergence property of the proposed algorithms are analyzed. Simulation results in the context of time series prediction demonstrate that the effectiveness of proposed algorithms.