  In this note, the distributed consensus corrupted by relative-state-dependent
measurement noises is considered. Each agent can measure or receive its
neighbors' state information with random noises, whose intensity is a vector
function of agents' relative states. By investigating the structure of this
interaction and the tools of stochastic differential equations, we develop
several small consensus gain theorems to give sufficient conditions in terms of
the control gain, the number of agents and the noise intensity function to
ensure mean square (m. s.) and almost sure (a. s.) consensus and quantify the
convergence rate and the steady-state error. Especially, for the case with
homogeneous communication and control channels, a necessary and sufficient
condition to ensure m. s. consensus on the control gain is given and it is
shown that the control gain is independent of the specific network topology,
but only depends on the number of nodes and the noise coefficient constant. For
symmetric measurement models, the almost sure convergence rate is estimated by
the Iterated Logarithm Law of Brownian motions.
