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Recently distributed adaptive estimation algorithms have been proposed for distributed estimation over wireless sensor networks (WSN). Among them, diffusion based algorithms (like distributed least mean-square, DLMS) are widely considered in the literature duo to their robustness and steady-state performance. Nevertheless, diffusion based adaptive estimation algorithms suffer from low convergence problem. To address this problem, in this paper we propose a constrained DLMS algorithm. In the proposed algorithm the cost function is modified to consider the observation noise variance of each sensor. In fact, the knowledge of observation noise variance might be useful in selecting search directions in an adaptive algorithm. As our simulation results show, the proposed algorithm converges faster than the conventional DLMS algorithm.