Robust Adaptive Filtering Algorithm Design for Improving the Performance in Impulsive-noise Environment

Abstract

This thesis proposes the various methods to improve the robustness against impulsive measurement noise of various adaptive filtering algorithms, which are the normalized least-mean-square (NLMS) algorithm, the affine projection (AP) algorithm (APA), the normalized subband adaptive filter (SAF), and the robust recursive least-squares (RLS) algorithm.First, we introduce the concept of the step-size scaler by investigating and modifying the tanh-type 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. To reduce the computational complexity, the simplified version of the step-size scaler, which is obtained by investigating and modifying the ln-type cost function, also is proposed. We perform several representative NLMS-type algorithms without or with the step-size scaler in impulsive-noise environments. The simulation results show that the step-size scaler improves the robustness against impulsive measurement whether the cost functions of the NLMS-type algorithms are adapted in impulsive-noise environments or not.Second, we propose a variable step-size (VSS) APA associated with a step-size scaler, which is suitable for application in the APA, to improve the robustness of APA against impulsive measurement noise. In the proposed VSS APA, the step-size scaler is applied to the equations for updating the step size, which are developed by interpreting the behavior of the mean square deviation (MSD) of the conventional APA. To reduce the computational complexity of the step-size scaler, a simplified version of the step-size scaler is introduced. By simulations in impulsive-noise environments, we confirm the proposed VSS APA leads to an excellent transient and steady-state behavior with in colored inputs.Third, we propose a variable step-size (VSS) normalized SAF (NSAF) using a step-size scaler, which is suitable for application in the NSAF. In the NSAF, since impulsive-type noise contains all frequencies in equal amounts, theoretically, every subbnad output errors can be influenced by impulsive measurement noise. Therefore the step-size scalers use the sum of the normalized subband output errors with respect to the subband input vectors. In the proposed VSS NSAF, the equations for updating the step size are constructed by interpreting the behavior of the MSD of the NSAF and applying the step-size scalers. Simulations using the proposed VSS NSAF show an excellent transient and steady-state behavior with colored input in impulsive-noise environments.Finally, we proposed a robust recursive least-squares (RLS) algorithm using the gain scaler which is developed by the step-size scaler. When impulsive measurement noise occurs, the gain vector of the proposed RLS algorithm is scaled down by the gain scaler. This suppresses the updating weight estimates using undesirable the output error due to impulsive measurement noise. Simulation results show the convergence and steady-state performance the proposed RLS algorithm and the compared robust RLS-type algorithms in impulsive-noise environments.