On the Distributed Estimation from Relative Measurements: a Graph-based Convergence Analysis

For a multi-agent system state estimation restingupon noisy measurements constitutes a problem related toseveral application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized)analytic solution to this issue and two distributed iterativeschemes, which allow to establish a connection between theconvergence behavior of consensus algorithm toward the op-timal estimate and the theory of the stochastic matrices thatdescribe the network system dynamics. This study on the onehand highlights the role of the topological links that definethe neighborhood of agent nodes, while on the other allows tooptimize the convergence rate by easy parameter tuning. Thetheoretical findings are validated considering different networktopologies by means of numerical simulations.