  This paper considers the identification of large-scale 1D networks consisting
of identical LTI dynamical systems. A new subspace identification method is
developed that only uses local input-output information and does not rely on
knowledge about the local state interaction. The identification of the local
system matrices (up to a similarity transformation) is done via a low
dimensional subspace retrieval step that enables the estimation of the Markov
parameters of a locally lifted system. Using the estimated Markov parameters,
the state-space realization of a single subsystem in the network is determined.
The low dimensional subspace retrieval step exploits various key structural
properties that are present in the data equation such as a low rank property
and a {\em two-layer} Toeplitz structure in the data matrices constructed from
products of the system matrices. For the estimation of the system matrices of a
single subsystem, it is formulated as a structured low-rank matrix
factorization problem. The effectiveness of the proposed identification method
is demonstrated by a simulation example.
