  In this paper we propose a Kronecker-based modeling for identifying the
spatial-temporal dynamics of large sensor arrays. The class of Kronecker
networks is defined for which we formulate a Vector Autoregressive model. Its
coefficient-matrices are decomposed into a sum of Kronecker products. For a
two-dimensional array of size $N \times N$, and when the number of terms in the
sum is small compared to $N$, exploiting the Kronecker structure leads to high
data compression. We propose an Alternating Least Squares algorithm to identify
the coefficient matrices with $\mathcal{O}(N^3N_t)$, where $N_t$ is the number
of temporal samples, instead of $\mathcal{O}(N^6)$ in the unstructured case.
This framework moreover allows for a convenient integration of more structure
(e.g sparse, banded, Toeplitz) on the factor matrices. Numerical examples on
atmospheric turbulence data has shown comparable performances with the
unstructured least-squares estimation while the number of parameters is growing
only linearly w.r.t. the number of nodes instead of quadratically in the full
unstructured matrix case.
