In this paper, we study a distributed constrained consensus problem for multi-agent systems in the presence of distance-dependent noises. Given a convex set constraint which can only be accessed by part of agents, all agents are required to achieve state agreement within the set by relative state measurements of their neighbors. These measurements are corrupted by noises whose intensities are proportional to the relative distance. Based on weighted averaging and projection, a two-step update scheme is proposed to achieve the mean square consensus within the constraint set. We show that the stochastic constrained consensus in the mean square sense can be achieved in two different cases, namely a switching and balanced multi-agent network which frequently contains a joint spanning tree and connects to the constraint set (considered as a virtual node), and a fixed and strongly connected network with at least one agent that can access the convex constraint.
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