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 ${\ell }_2$-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.

提出了一种仿射投影（AP）和鲁棒混合范数算法（RMNA）相结合的自适应滤波算法，称为APRMNA。AP方法具有在彩色输入下收敛速度快的特点，RMNA具有稳定的抗噪声干扰性能。提出的APRMNA算法不仅结合了AP和RMNA的优点，而且还利用了APRMNA算法的优势。${\ell }_{\mathrm{2个}}$-权重向量上的范数约束，以避免矩阵求逆。然后，将广义最大熵（GMC）准则应用于APRMNA，我们还开发了APRMNA-GMC。最后，推导了所提出的APRMNA-GMC（S-APRMNA-GMC）的简化版本，以降低计算复杂度。用于系统识别的数值模拟表明，所提出的算法优于其他AP型算法。