Robust Adaptive Filter Algorithms Against Impulsive Noise

This paper proposes a prefiltered observation-based adaptive filter algorithm that is robust against impulsive noise. Previous impulsive noise rejection algorithms were based on output error stochastic, so there was a trade-off relationship between impulsive noise detection and tracking performances. The proposed rejection algorithm is derived by using the statistics of the observed signal and the inequality such as the Schwarz and Young inequality in the absence of impulsive noise. From this, the proposed algorithm updates the weight vector only when the observed signal is not corrupted by impulsive noise. The proposed algorithm achieves the good tracking performance because it distinguishes between the system change and interruption of impulsive noise. In addition, the proposed algorithm has same performance without impulsive noise, compared with the normalized least-mean-square-type algorithm. Further, the proposed rejection algorithm could expand to various adaptive filtering structures, which suffer the performance degradation with impulsive noise, because it is easy to implement. Hence, the proposed algorithm is combined with the NLMS algorithm for dispersive systems and the proportionate NLMS algorithm for sparse systems. Simulation results show that the proposed algorithm achieves fast convergence rate, good tracking performance, and robustness under the impulsive noise environment.