Kronecker-ARX models in identifying (2D) spatial-temporal systems * * The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 339681.

摘要

In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-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 matrix, such a Kronecker representation leads to high data compression. Estimating in least-squares sense the coefficient-matrices gives rise to a bilinear estimation problem, which is tackled using a three-stage algorithm. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable performances with the unstructured least-squares estimation of VAR models. However, the number of parameters in the new modeling paradigm grows linearly w.r.t. the number of nodes in the 2D sensor network instead of quadratically in the full unstructured matrix case.