The least squares based affine projection algorithm (APA) is sensitive to outliers/impulsive noise in the desired data. A novel robust APA over distributed networks scenario is proposed in this manuscript, which is based on the rank based robust estimator named Wilcoxon norm. The proposed diffusion Wilcoxon affine projection algorithm (DWx-APA) based on pseudo least squares formulation is robust against outliers in the desired data and converges faster than the diffusion minimum Wilcoxon norm algorithm (DWx). The QR based diffusion minimum Wilcoxon norm (QR-DWx) algorithm is also robust against outliers in the desired data and converges faster than the DWx and the proposed DWx-APA, but the computational complexity is very high in comparison to its counterparts. The proposed DWx-APA is a compromise between DWx and QR-DWx in terms of computational complexity and convergence speed. The mean stability, tracking capability and computational complexity of the proposed algorithm are investigated. The simulation based experiments and analysis validate that the proposed algorithm performs better than the state-of-the-art algorithms in the presence of color data.

基于最小二乘的仿射投影算法（APA）对所需数据中的异常值/脉冲噪声敏感。该手稿提出了一种新颖的基于分布式网络的鲁棒APA方案，该方案基于名为Wilcoxon范数的基于秩的鲁棒估计量。拟议的基于伪最小二乘公式的扩散Wilcoxon仿射投影算法（DWx-APA）对期望数据中的离群值具有鲁棒性，并且收敛速度比扩散最小Wilcoxon范数算法（DWx）快。基于QR的扩散最小Wilcoxon范数（QR-DWx）算法对于所需数据中的离群值也很鲁棒，并且收敛速度比DWx和提出的DWx-APA快，但是与之相比，计算复杂度很高。就计算复杂度和收敛速度而言，提出的DWx-APA是DWx和QR-DWx之间的折衷方案。研究了该算法的平均稳定性，跟踪能力和计算复杂度。基于仿真的实验和分析证明，在存在彩色数据的情况下，该算法的性能优于最新算法。