  In this paper, a novel diffusion estimation algorithm is proposed from a
probabilistic perspective by combining diffusion strategy and the probabilistic
least-mean-squares (PLMS) at all agents. The proposed method diffusion
probabilistic LMS (DPLMS) is more robust to input signal and impulsive
interference than the DSE-LMS, DRVSSLMS and DLLAD algorithms. Instead of
minimizing the estimate error, the DPLMS algorithm is derived from
approximating the posterior distribution with an isotropic Gaussian
distribution. The stability of mean performance and computational complexity
are analyzed theoretically. Results from the simulation indicate that the DPLMS
algorithm is more robust to input signal and impulsive interference than the
DSE-LMS, DRVSSLMS and DLLAD algorithms. These results suggest that the DPLMS
algorithm can perform better in identifying the unknown coefficients under the
complex and changeable impulsive interference environments.
