  In a Networked Dynamical System (NDS), each node is a system whose dynamics
are coupled with the dynamics of neighboring nodes. The global dynamics
naturally builds on this network of couplings and it is often excited by a
noise input with nontrivial structure. The underlying network is unknown in
many applications and should be inferred from observed data. We assume: i)
Partial observability -- time series data is only available over a subset of
the nodes; ii) Input noise -- it is correlated across distinct nodes while
temporally independent, i.e., it is spatially colored. We present a feasibility
condition on the noise correlation structure wherein there exists a consistent
network inference estimator to recover the underlying fundamental dependencies
among the observed nodes. Further, we describe a structure identification
algorithm that exhibits competitive performance across distinct regimes of
network connectivity, observability, and noise correlation.
