Identification of Multilinear Systems: A Brief Overview

Nonlinear systems have been studied for a long time and have applications in numerous research fields. However, there is currently no global solution for nonlinear system identification, and different used approaches depend on the type of nonlinearity. An interesting class of nonlinear systems, with a wide range of popular applications, is represented by multilinear (or multidimensional) systems. These systems exhibit a particular property that may be exploited, namely that they can be regarded as linearly separable systems and can be modeled accordingly, using tensors. Examples of well-known applications of multilinear forms are multiple-input/single-output (MISO) systems and acoustic echo cancellers, used in multi-party voice communications, such as videoconferencing. Many important fields (e.g., big data, machine learning, and source separation) can benefit from the methods employed in multidimensional system identification. In this context, this chapter aims to briefly present the recent approaches in the identification of multilinear systems. Methods relying on tensor decomposition and modeling are used to address the large parameter space of such systems.