  Classical distributed estimation scenarios typically assume timely and
reliable exchange of information over the multi-agent network. This paper, in
contrast, considers single time-scale distributed estimation of (potentially)
unstable full-rank dynamical systems via a multi-agent network subject to
transmission time-delays. The proposed networked estimator consists of two
steps: (i) consensus on (delayed) a-priori estimates, and (ii) measurement
update. The agents only share their a-priori estimates with their in-neighbors
over time-delayed transmission links. Considering the most general case, the
delays are assumed to be time-varying, arbitrary, unknown, but upper-bounded.
In contrast to most recent distributed observers assuming system observability
in the neighborhood of each agent, our proposed estimator makes no such
assumption. This may significantly reduce the communication/sensing loads on
agents in large-scale, while making the (distributed) observability analysis
more challenging. Using the notions of augmented matrices and Kronecker
product, the geometric convergence of the proposed estimator over
strongly-connected networks is proved irrespective of the bound on the
time-delay. Simulations are provided to support our theoretical results.
