  Fully distributed estimation and tracking solutions to large-scale
multi-agent networks suffer slow convergence and are vulnerable to network
failures. In this paper, we aim to speed up the convergence and enhance the
resilience of state estimation and tracking using a simple hierarchical system
architecture wherein agents are clusters into smaller networks, and a parameter
server exists to aid the information exchanges among networks. The information
exchange among networks is expensive and occurs only once in a while.
  We propose two consensus + innovation algorithms for the state estimation and
tracking problems, respectively. In both algorithms, we use a novel
hierarchical push-sum consensus component. For the state estimation, we use
dual averaging as the local innovation component. State tracking is much harder
to tackle in the presence of dropping-link failures and the standard
integration of the consensus and innovation approaches are no longer
applicable. Moreover, dual averaging is no longer feasible. Our algorithm
introduces a pair of additional variables per link and ensure the relevant
local variables evolve according to the state dynamics, and use projected local
gradient descent as the local innovation component. We also characterize the
convergence rates of both of the algorithms under linear local observation
model and minimal technical assumptions. We numerically validate our algorithm
through simulation of both state estimation and tracking problems.
