Short communicationDiffusion least mean square/fourth algorithm for distributed estimation

•A diffusion LMS/F algorithm is proposed for non-Gaussian noise environments.•Three diffusion sparse LMS/F algorithms are developed for sparse system estimation.•The proposed algorithms are derived from the mixed square/fourth error cost function.•Simulation results confirm the improvements of the proposed algorithms.

Proposed is a diffusion least mean square/fourth (LMS/F) algorithm, which is characterized by its fast convergence and low steady-state misalignment for distributed estimation in non-Gaussian noise environments. Instead of the conventional mean square error cost function, the diffusion LMS/F algorithm is derived from the mixed square/fourth error cost function, which is more suitable for non-Gaussian noise environments. Moreover, we incorporate the L1- and L0-norm constraints into the mixed square/fourth error cost function, and then a class of diffusion sparse LMS/F algorithms is developed which is able to exploit the sparsity of the considered system. Simulation results show that the diffusion LMS/F algorithm outperforms the conventional diffusion LMS and LMF algorithms in non-Gaussian noise environments. The improvements of diffusion sparse LMS/F algorithms in terms of steady-state misalignment are also demonstrated relative to the diffusion LMS/F algorithm.