Variable step-size Griffiths’ algorithm for improved performance of feedforward/feedback active noise control

A new robust computationally efficient variable step-size LMS algorithm is proposed and it is applied for secondary path (SP) identification of feedforward and feedback active noise control (ANC) systems. The proposed variable step-size Griffiths’ LMS (VGLMS) algorithm not only uses a step-size, but also the gradient itself, based on the cross-correlation between input and the desired signal. This makes the algorithm robust to both stationary and non-stationary observation noise and the additional computational load involved for this is marginal. Further, in terms of convergence speed and error, it is better than those by the Normalized LMS (NLMS) and the Zhang’s method (Zhang in EURASIP J. Adv. Signal Process. 2008(529480):1–9, 2008). The convergence rate of the feedforward and feedback ANC systems with the VGLMS algorithm for SP identification is faster (by a factor of 2 and 3, respectively) compared with that using NLMS algorithm. For feedforward ANC, its convergence rate is faster (3 times) compared with Akhtar’s algorithm (Akhtar in IEEE Trans Audio Speech Lang Process 14(2), 2006). Also, for higher main path lengths compared with SP, the proposed algorithm is computationally efficient compared with Akhtar’s algorithm.