A Robust Adaptive Filtering Algorithm Against Impulsive Noise

A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we will derive a robust variable step-size NLMS algorithm which optimizes the square norm of the a posteriori error subject to the constraint on the norm of the filter change. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications.