A Khatri-Rao product tensor network for efficient symmetric MIMO Volterra identification

Abstract

The identification of symmetric tensor network MIMO Volterra models has been studied earlier via the computation of a Moore-Penrose pseudoinverse in tensor network form. The current state of the art requires the construction of a tensor network of a repeated Khatri-Rao product of a matrix with itself. This construction has a computational complexity that is dominated by one singular value decomposition (SVD) of an RI × IN matrix, where N is the number of measurements, I depends linearly on the number of inputs and input lags and R is the maximal tensor network rank. In this article, we prove an alternative method for constructing this tensor network without any computation whatsoever. The pseudoinverse can then be computed through an orthogonalization of the newly proposed tensor network. Furthermore, the proposed algorithm allows for the recursive identification of symmetric Volterra models of increasing degree D, which reduces the computation to one SVD of a RI × N matrix per step. Through numerical experiments we demonstrate how the proposed algorithm enables up to ten times faster identification of symmetric tensor network MIMO Volterra systems.