  System state estimation constitutes a key problem in several applications
involving multi-agent system architectures. This rests upon the estimation of
the state of each agent in the group, which is supposed to access only relative
measurements w.r.t. some neighbors state. Exploiting the standard least-squares
paradigm, the system state estimation task is faced in this work by deriving a
distributed Proximal Point-based iterative scheme. This solution entails the
emergence of interesting connections between the structural properties of the
stochastic matrices describing the system dynamics and the convergence behavior
toward the optimal estimate. A deep analysis of such relations is provided,
jointly with a further discussion on the penalty parameter that characterizes
the Proximal Point approach.
