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In this paper we consider the issue of reliability of observations in distributed adaptive estimation problem. More specifically, we consider the distributed incremental least mean-square (DILMS) estimation in an inhomogeneous environment where some of nodes make unreliable observations (noisy nodes). First we show that these noisy nodes deteriorate considerably the performance of the DILMS algorithm. Then we propose a new distributed incremental LMS algorithm with reliability of observation considerations. The proposed algorithm contains two phases including a training phase in which the observation noise variance and unknown parameter are estimated in every node; and the estimating phase where the step-size parameter is adjusted for each node according to its observation noise variance. As our simulation results show, the proposed algorithm considerably improves the performance of the DILMS algorithm in the same condition.