Linear System Identification Based on a Third-Order Tensor Decomposition

A wide variety of system identification problems can be efficiently addressed based on the Kronecker product decomposition of the impulse response, together with low-rank approximations. Such an approach solves the original system identification problem using a combination of two shorter filters. In this letter, targeting a higher dimensionality reduction, we develop a solution based on a third-order tensor decomposition. In addition, the problem of approximating the rank of a tensor is avoided thanks to the control of a matrix rank. Then, an iterative Wiener filter is developed, which outperforms both the conventional benchmark and the previously developed counterpart that exploits the second-order decomposition.