Variable step-size diffusion least mean fourth algorithm for distributed estimation

•The diffusion LMS may suffer from high misalignment with non-Gaussian noise.•The diffusion LMF has low misalignment in some non-Gaussian environments.•Variable step-sizes are presented to improve the performance of the diffusion LMF.

The diffusion LMS (DLMS) is one of the most popular online distributed estimation algorithms, due to its simplicity and ease of implementation. However, it may suffer from large steady-state misalignment in some strong, non-Gaussian noise environments. To address this problem, this paper introduces a diffusion least mean fourth (DLMF) algorithm by using the mean-fourth error cost function in a diffusion strategy. Moreover, a variable step-size (VSS) method is developed to further reduce the steady-state misalignment of the DLMF. Simulation results show that the DLMF outperforms the DLMS with uniform or binary noise, and that the VSS-DLMF has a superior steady-state performance as compared to the DLMF.