An Iterative Wiener Filter for the Identification of Multilinear Forms

Abstract

Multidimensional system identification problems can be encountered in many important fields, such as big data, machine learning, and source separation. Nevertheless, a large parameter space usually raises additional challenges in terms of system identification. In this context, there is a huge interest in exploiting the methods based on tensor decompositions and modelling. Recently, we focused on bilinear forms (i.e., two-dimensional decomposition), in the framework of identifying spatiotemporal models. Following this approach, we developed several solutions based on the Wiener filter and different adaptive algorithms. In this paper, in order to further exploit the decomposition of the global impulse response, we propose an iterative Wiener filter tailored for the identification of trilinear forms (where third-order tensors are involved). Simulation results indicate the good performance of the proposed solution, as compared to the conventional Wiener approach.