This manuscript presents a new technique to improve the performance of adaptive filters in handling the non-Gaussian or impulsive noise environment. The conduct of the adaptive filter decays in the presence of impulsive noise or outliers. To improve the efficiency of the filtering technique, this work presents a robust exponential hyperbolic tangent Geman McClure function for nonlinear system identification. The algorithm utilizes the saturation properties of the hyperbolic tangent function to improve the performance under impulsive noise. The simulation results clearly illustrate the potency of the suggested technique.

The hybrid selective fixed-filter active noise control with filtered reference normalized least mean square (SFANC-FxNLMS) method struggles in dynamic noise environments due to its reliance on static filters, which limits effectiveness when noise characteristics change rapidly. The generative fixed-filter active noise control with Kalman filtering (GFANC-Kalman) approach offers improved adaptability by dynamically adjusting the filtering process but may still underperform in complex noise scenarios. The dynamic fixed-filter active noise control with extended Kalman filter (DFANC-EKF) method overcomes these limitations by integrating an extended Kalman filter with a 2D convolutional neural network for advanced feature extraction. This integration enables the system to better capture and adapt to intricate noise patterns, significantly enhancing noise reduction. Numerical simulations using real-world noise data validate the DFANC-EKF approach's superior performance across various challenging scenarios.

The noise cancellation performance of an active control system decreases when there are temporal variations in the primary and secondary paths. An active noise control (ANC) framework has been introduced in this work, which incorporates four adaptive filters and two decorrelation filters for online secondary path modelling. A novel adaptive algorithm for an active noise control filter has been developed with the combination of modified gain filtered-x recursive least square and normalised step size filtered-x least mean square. The aim is to improve the reduction of mean noise and decrease residual noise while maintaining consistent convergence rate. To update the decorrelation filters in the framework, an adaptive variable step size modified decorrelation normalised least mean square algorithm has been used. These filters are designed to maximize the efficiency of secondary path modelling. Compared to its counterparts, the simulation results illustrate the enhancements of the proposed framework without a substantial increase in overall computational complexity.

A new method is suggested to improve the effectiveness of adaptive filters in dealing with unexpected disturbances at the error sensor. This method focuses specifically on the difficult scenario of α-stable noise in feedback cancellation for hearing aids. α-stable noise, which is distinguished by its strong tails and abrupt behavior, poses considerable difficulties for conventional adaptive algorithms. In order to tackle this issue, we propose the implementation of a fractional order hyperbolic tangent (FOHT) algorithm. Fractional order systems, which utilize non-integer order derivatives to represent intricate dynamics, provide improved adaptability and precision, especially in settings where non-Gaussian noise, such as α-stable distributions, is prevalent. The algorithm utilizes the distinct characteristics of fractional calculus to enhance the resilience and adaptability of the system, thereby reducing the influence of α-stable noise. The results of extensive simulations indicate that the FOHT algorithm outperforms existing techniques in terms of steady-state convergence and robustness.

Recently, to mitigate the loudspeaker-based distortion in the acoustic system, the functional link adaptive filter – based nonlinear acoustic echo cancellation (NAEC) algorithm has been proposed. However, the usage of sine and cosine functions in nonlinear modeling coupled with the steepest descent based weight adaption limits the echo cancellation performance when the underlying distortion has faster time varying amplitude levels. Hence, in this paper, we propose a conjugate gradient (CG)-based algorithm referred to as nonlinear improved sparse conjugate algorithm. It employs the sine and cosine terms but, with time-varying coefficients to enhance distortion modeling and also an improved CG method in improving the echo cancellation performance of NAEC. The simulation results demonstrate the effectiveness of the proposed algorithm compared to the existing functional link-based NAEC.

This work proposes an improved variable-step FXLMS (IVS-FXLMS) adaptive algorithm for active noise control, which considers the effect of secondary path. A lower bound for the step size is obtained to establish a minimum adaptation-level and a range of step size values for breaking the trade-off between misadjustment and convergence time. Computer simulations are performed for a comparative assessment of the performances of the various adaptive algorithms based on the mean-square-error criteria, with respect to the proposed algorithm, in a high-noise environment. Comparison is done in terms of noise attenuation, reproduction of the original signal and mean square error. It is observed from the obtained results that the FXLMS algorithm, due to its ability to take secondary path into consideration, performs better than the LMS and NLMS adaptive algorithms. However, the proposed algorithm exhibits an improved performance over the FXLMS algorithm by effectively attenuating noise at the output and reproducing the original acoustic signal, which was corrupted with noise. Moreover, the proposed algorithm also incurs the least mean square error of all the considered algorithms.