Robust Diffusion Affine Projection Algorithm with Variable Step-Size over Distributed Networks

The estimation performance of the standard diffusion affine projection algorithm may be degraded when the distributed network nodes are disturbed by impulsive noise. To overcome the limitation, a diffusion affine projection M-estimate (DAPM) algorithm is proposed for distributed estimation in the adaptive diffusion networks. This algorithm uses a robust cost function based on M-estimate function to eliminate the adverse effects of impulsive noise on distributed diffusion network nodes. In order to further enhance the performance of the DAPM algorithm, namely fast convergence rate and low steady-state error, a variable step-size diffusion affine projection M-estimate (VSS-DAPM) algorithm is presented. In addition, the convergence range of the step-size is deduced to ensure the convergence of the proposed algorithms. Computer simulations show that the proposed DAPM and VSS-DAPM algorithms have good convergence performance for distributed estimation in the adaptive diffusion networks. More importantly, the proposed VSS-DAPM algorithm improves convergence rate and the network mean square deviation (MSD) as compared to the DAPM algorithm in the distributed estimation.