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In this paper we propose a Kronecker-based modeling for identifying thespatial-temporal dynamics of large sensor arrays. The class of Kroneckernetworks is defined for which we formulate a Vector Autoregressive model. Itscoefficient-matrices are decomposed into a sum of Kronecker products. For atwo-dimensional array of size $N \times N$, and when the number of terms in thesum is small compared to $N$, exploiting the Kronecker structure leads to highdata compression. We propose an Alternating Least Squares algorithm to identifythe coefficient matrices with $\mathcal{O}(N^3N_t)$, where $N_t$ is the numberof 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 onatmospheric turbulence data has shown comparable performances with theunstructured least-squares estimation while the number of parameters is growingonly linearly w.r.t. the number of nodes instead of quadratically in the fullunstructured matrix case.

QUARKS: Identification of large-scale Kronecker Vector-AutoRegressive models