Enhanced ${q}$-Least Mean Square
For researchers in adaptive filtering, this is an incremental improvement over existing q-LMS with automatic learning rate adaptation.
The paper introduces an enhanced q-Least Mean Square (Eq-LMS) algorithm that uses time-varying q parameter and error-correlation energy to improve convergence and reduce steady-state error. Experiments on system identification show better performance than standard q-LMS.
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.