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.