A Weighted Exponential Bilinear Functional Link Artificial Neural Network Filter And Weighted Filtered-s LMS algorithm For Saturation Nonlinearity

In the field of nonlinear noise, when the output of the system no longer increases linearly with the input after reaching a certain threshold but tends to be stable, this characteristic is called saturated nonlinearity. In response to it, various bilinear functional link artificial neural network (BFLANN) filters have been proposed. Most of these related filters aim to enhance the adaptive algorithm while preserving the bilinear expansion mode, in which there may still be some room for improvement. Moreover, a universal variable step-size scheme applicable to all nonlinear filters has yet to be developed. To improve noise reduction performance, both in terms of expansion mode and variable step-size scheme, this paper introduces an innovative approach that integrates a weighted exponential bilinear functional link artificial neural network nonlinear filter (WEB-FLANN) with the weighted filtered-s least mean square (WFsLMS) algorithm. And the stable boundedness and computational complexity of the filter are analyzed. Simulation results and real-world ambient noise trials indicate that WEB-FLANN filter can improve the steady MSE by 2-3dB in saturated nonlinear environment, and has good noise reduction effect in common nonlinear environment. The adaptive variable step-size scheme does not need manual debugging and has high application value.