Fractional normalised filtered‐error least mean squares algorithm for application in active noise control systems

A novel fractional normalised filtered‐error least mean squares (FN‐FeLMS) algorithm is designed for secondary path modelling in active noise control systems. The update is formed as a combination of the conventional LMS and a fractional update derived from the Riemann–Liouville differintegral operator. The algorithm is considered for (machine) noise reduction for a primary path with zero‐mean binary or Gaussian sources as inputs. An anti‐noise signal is generated to alleviate the effect of noise and to minimise the filtered error by improved secondary path modelling. The proposed arrangement is evaluated for a number of different scenarios by varying the step size and fractional orders. Simulation results show that the proposed technique is more robust to step size variation; it outperforms the traditional FeLMS approach in terms of convergence, model accuracy and steady‐state performance for a given signal‐to‐noise ratio.