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.