The present study proposes the Robust DLMS -RDLMS- algorithm for a robust estimation over adaptive networks. Instead of minimizing the mean square error -MSE-, the RDLMS algorithm is derived from minimizing the pseudo-Huber function which is a continuous derivative and smooth approximation of the Huber function. Performance of the RDLMS algorithm is examined in the presence of Gaussian and α-stable non-Gaussian noise, in stationary and non-stationary environments. The results show that in the presence of non-Gaussian noise the proposed algorithm is robust and outperforms the diffusion LMS, the diffusion maximum correntropy criteria, and the diffusion least mean fourth algorithms. In addition, RDLMS is similar to the diffusion sign-error LMS and diffusion robust LMS. On the other hand, when the environment noise is Gaussian, the performance of RDLMS is similar to the DLMS while outperforms the other aforementioned algorithms.

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