Affine projection mixed-norm algorithms for robust filtering.

• A novel robust mixed-norm algorithm with affine projection (APRMNA) is proposed. • The APRMNA based on the generalized maximum correntropy criterion (APRMNA-GMC) is proposed. • The simplified APRMNA-GMC (S-APRMNA-GMC) is proposed. In this paper, a novel adaptive filtering algorithm combining both affine projection (AP) method and robust mixed-norm algorithm (RMNA) is proposed, which is called APRMNA. The AP method has the feature of fast convergence speed under colored inputs and the RMNA exhibits stable performance against noise interference. The proposed APRMNA algorithm not only combines the advantages of both AP and RMNA but also utilizes the ℓ 2 -norm constraint on the weight vector to avoid matrix inversion. Then, applying the generalized maximum correntropy (GMC) criterion to APRMNA, we also develop the APRMNA-GMC. Finally, a simplified version of the proposed APRMNA-GMC (S-APRMNA-GMC) is derived to reduce the computation complexity. Numerical simulations for system identification show that the proposed algorithms outperform other AP-type algorithms. [ABSTRACT FROM AUTHOR]