非高斯噪声下基于Wilcoxon范数的变步长符号扩散式仿射投影算法

扩散式仿射投影算法(DAPA)是实现分布式网络参数自适应估计的一种重要方法，该算法在输入信号存在相关性时仍快速收敛，但抑制具有脉冲特性的非高斯噪声能力弱，且固定步长对收敛性有所限制。为此，该文提出了基于Wilcoxon范数的变步长符号扩散式仿射投影算法(VSS-DWAPA)。首先，引入稳健估计理论中抗异常值能力强的Wilcoxon范数作为代价函数并根据其取值特点进行了符号量化，推导出了新的迭代方程；其次，针对固定步长的局限性，采用迭代方式实现了误差信号对步长的控制，在初始阶段和接近收敛阶段选择不同的步长，使算法具有更好的适应性。仿真结果表明，在非高斯噪声下本文的VSS-DWAPA算法在收敛性、跟踪性等方面均优于现有一些扩散式自适应滤波算法，同时在高斯噪声环境下也具有较好的性能。

Variable Step Size Sign Diffusion Affine Projection Algorithm Based on Wilcoxon Norm under Non-Gaussian Noise

Diffusion Affine Projection Algorithm (DAPA) is an important method to realize the adaptive estimation of distributed network parameters. The algorithm can converge rapidly even when the input signal has correlation. The disadvantage of DAPA is that the ability to suppress non-Gaussian noise with impulsive characteristics is weak, and the fixed step size limits the performance of the algorithm. In this paper, a Variable Step size Sign Diffusion Wilcoxon Affine Projection Algorithm (VSS-DWAPA) is proposed. Firstly, the Wilcoxon norm which has strong ability to resist outliers is introduced as the cost function, and sign quantization is carried out according to its value characteristics, and then a new iterative equation is derived. Secondly, considering the limitation of fixed step size, the control of error signal to step size is realized through iterative method. That is, in the initial stage and the almost convergent stage, the step size is selected differently, which effectively makes it have better adaptation. The simulation results show that the proposed VSS-DWAPA is superior to some existing diffusion adaptive filtering algorithms in convergence, stability and tracking. It can also work well in Gaussian noise environment.