A Normalized Least Mean Squares Algorithm With a Step-Size Scaler Against Impulsive Measurement Noise

This brief introduces the concept of a step-size scaler by investigating and modifying the tanh cost function for adaptive filtering with impulsive measurement noise. The step-size scaler instantly scales down the step size of gradient-based adaptive algorithms whenever impulsive measurement noise appears, which eliminates a possibility of updating weight vector estimates based on wrong information due to impulsive noise. The most attractive feature of the step-size scaler is that this is easily applicable to various gradient-based adaptive algorithms. Several representative gradient-based adaptive algorithms are performed without or with the step-size scaler in impulsive-noise environments, which shows the improvement of robustness against impulsive noise.