Quantized Tracking Capacity for Unstable Dynamics in Distributed Estimation under Data Rate Limitation

This paper considers the distributed estimation of an unstable system under data rate constraint. A quantized consensus-based distributed state estimation algorithm is designed. The Quantized Tracking Capacity (QTC) is proposed to describe an upper bound on the degree of instability of the dynamical system that can be estimated by the proposed distributed algorithm. A set of sufficient conditions is derived, guaranteeing the boundedness of estimation errors. It is shown that QTC reveals the fundamental limitation on distributed estimation induced by network connectivity, limited data rate, and system dynamics. Finally, numerical simulations show that the QTC decreases as the achievable end-to-end data rate decreases, verifying our theoretical results.