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This paper proposes robust diffusion maximum versoria criterion algorithms to enhance the performance of the distributed estimation in a network of agents under impulsive noise environment. The diffusion maximum versoria criterion is a novel algorithm, under time-dependent constraint on the squared norm of the intermediate update at each node. To develop the robust version of the algorithm, the constraints are calculated by shared information which are collected from connected neighbors. The stability and steady-state performance of the proposed algorithms are also analyzed. We further exploit an altered dichotomous coordinate-descent (DCD) method to improve the performance and to reduce the complexity of the proposed algorithms in shifted-structure input regressors environment. Performance analysis and simulation results show the effectiveness and robustness of the proposed algorithms in various impulsive noise scenarios. [ABSTRACT FROM AUTHOR]