In this study, we propose a diffusion robust recursive least squares (D-R2LS) algorithm over adaptive networks. Instead of conventional mean square error cost function, the suggested method is derived from the maximum correntropy criterion (MCC) cost function, being more suitable for non-Gaussian noise. Furthermore, to improve tracking ability when encountering sudden changes in unknown systems in non-stationary environments, a diversity-based extension of D-R2LS is developed by adaptive forgetting factor for each node. Also, to conduct performance analysis, we employ a half-quadratic optimization to approximate our model iteratively by a quadratic problem. The mean, mean-square convergence and stability of the D-R2LS are discussed theoretically. The simulation results show that the proposed methods outperform the other robust algorithms and enhance tracking quality in the presence of non-Gaussian noise in the stationary and non-stationary environments.

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