  For a multi-agent system state estimation resting upon noisy measurements
constitutes a problem related to several application scenarios. Adopting the
standard least-squares approach, in this work we derive both the (centralized)
analytic solution to this issue and two distributed iterative schemes, which
allow to establish a connection between the convergence behavior of consensus
algorithm toward the optimal estimate and the theory of the stochastic matrices
that describe the network system dynamics. This study on the one hand
highlights the role of the topological links that define the neighborhood of
agent nodes, while on the other allows to optimize the convergence rate by easy
parameter tuning. The theoretical findings are validated considering different
network topologies by means of numerical simulations.
