Enhanced ${q}$-Least Mean Square

TL;DR

This paper introduces an enhanced $q$-LMS algorithm that employs a time-varying $q$ parameter and adaptive error-correlation energy normalization, resulting in improved convergence and stability in system identification tasks.

Contribution

The paper presents a novel $Eq$-LMS algorithm that fully utilizes $q$-calculus with a dynamic $q$ parameter and a parameterless error-correlation energy concept, advancing adaptive filtering methods.

Findings

Better convergence and stability than standard $q$-LMS

Lower steady-state error in system identification

Automatic adaptation of learning rate based on error

Abstract

In this work, a new class of stochastic gradient algorithm is developed based on $q$-calculus. Unlike the existing $q$-LMS algorithm, the proposed approach fully utilizes the concept of $q$-calculus by incorporating time-varying $q$ parameter. The proposed enhanced $q$-LMS ($Eq$-LMS) algorithm utilizes a novel, parameterless concept of error-correlation energy and normalization of signal to ensure high convergence, stability and low steady-state error. The proposed algorithm automatically adapts the learning rate with respect to the error. For the evaluation purpose the system identification problem is considered. Extensive experiments show better performance of the proposed $Eq$-LMS algorithm compared to the standard $q$-LMS approach.