An augmented observer for the distributed estimation problem for LTI systems

This paper studies a network of observers for a distributed estimation problem, where each observer assesses a portion of output of a given LTI system. The goal of each observer is to compute a state estimate that asymptotically converges to the state of the LTI system. We consider there is a sparsity constraint that restricts interconnections between observers. We provide a sufficient condition for the existence of parameters for the observers which achieve the convergence of the state estimates to the state of the LTI system. In particular, this condition can be written in terms of the eigenvalues of the Laplacian matrix of the underlying communication graph and the spectral radius of the dynamic matrix of the LTI system.