text: abstract—in this paper we address the identification of 2d
  spatial-temporal dynamical systems described by the vectorauto-regressive (var) form. the coefficient-matrices of the var
  model are parametrized as sums of kronecker products. when
  the number of terms in the sum is small compared to the
  size of the matrices, such a kronecker representation efficiently
  models large-scale var models. estimating the coefficient matrices in least-squares sense gives rise to a bilinear estimation
  problem which is tackled using an alternating least squares
  (als) algorithm. regularization or parameter constraints on the
  coefficient-matrices allows to induce temporal network properties
  such as stability, as well as spatial properties such as sparsity or
  toeplitz structure. convergence of the regularized als is proved
  using fixed-point theory. a numerical example demonstrates the
  advantages of the new modeling paradigm. it leads to comparable
  variance of the prediction error with the unstructured leastsquares estimation of var models. however, the number of
  parameters grows only linearly with respect to the number of
  nodes in the 2d sensor network instead of quadratically in the
  case of fully unstructured coefficient-matrices.
  index terms—system identification, vector auto-regressive
  model, large-scale networks, kronecker product, alternating
  least squares.