Scalar-gain distributed estimators for Hermitian systems

In this paper, we consider distributed estimation of discrete-time, LTI state-spaces, restricted to Hermitian (or symmetric) system matrices. We assume that the underlying system is monitored by a group of agents, sparsely connected via an undirected communication graph, and no agent may possess enough measurements (in its neighborhood) to estimate the entire state-vector. In this context, we analyze an estimation protocol that only requires a single design parameter: a scalar-gain, α ∈ R. We design this scalar-gain, α, with the help of some eigenvalue (Weyl´s) inequalities and derive the conditions under which a scalar-gain is sufficient to estimate the underlying system with bounded estimation error.