  In this paper we study a discrete time consensus model on a connected graph
with monotonically increasing peer-pressure and noise perturbed outputs masking
a hidden state. We assume that each agent maintains a constant hidden state and
a presents a dynamic output that is perturbed by random noise drawn from a
mean-zero distribution. We show consensus is ensured in the limit as time goes
to infinity under certain assumptions on the increasing peer-pressure term and
also show that the hidden state cannot be exactly recovered even when model
dynamics and outputs are known. The exact nature of the distribution is
computed for a simple two vertex graph and results found are shown to
generalize (empirically) to more complex graph structures.
