Distributed state estimation in multi-agent networks

In this paper, we consider the problem of state estimation of a dynamical system in a multi-agent network. The agents are sparsely connected and each of them observes a strict subset of the state vector. The distributed algorithm that we propose enables each agent to estimate any arbitrary linear dynamical system with bounded mean-squared error. To achieve this, the ratio of the algebraic connectivity and the largest eigenvalue of the graph Laplacian has to be larger than a lower bound determined by the spectral radius of the system's dynamics matrix. This extends the notion of Network Tracking Capacity introduced by other authors in prior work. We accomplish this by introducing a new class of estimation algorithm of dynamical systems that, besides a (consensus + innovations) term, also includes consensus on the innovations.