  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.
