Abstract
High-dimensional system identification problems can be efficiently addressed based on tensor decompositions and modelling. In this paper, we design a recursive least-squares (RLS) algorithm tailored for the identification of trilinear forms, namely RLS-TF. In our framework, the trilinear form is related to the decomposition of a third-order tensor (of rank one). The proposed RLS-TF algorithm acts on the individual components of the global impulse response, thus being efficient in terms of both performance and complexity. Simulation results indicate that the proposed solution outperforms the conventional RLS algorithm (which handles only the global impulse response), but also the previously developed trilinear counterparts based on the least-mean- squares algorithm.
Highlights
There is an increasing interest in developing methods and algorithms that exploit tensor decompositions and modelling [1,2]
Simulations were performed in the framework of a tensor-based system identification problem, which resulted following the multiple-input single-output (MISO) model defined by (12) and (20) and was similar to the setup used in [17]
We explored the identification of trilinear forms using the recursive least-squares (RLS) algorithm
Summary
There is an increasing interest in developing methods and algorithms that exploit tensor decompositions and modelling [1,2]. Many important applications rely on such tensor-based techniques, which can be successfully used in the fields of big data [3], source separation [4], machine learning [5], multiple-input multiple-output (MIMO) communication systems [6], and beamforming [7]. Tensor decompositions and their related applications are frequently addressed based on multilinear signal processing techniques [8,9]. Among the recent related works, we can mention the iterative Wiener filter for bilinear forms [10] and the subsequent adaptive filtering methods [11,12,13], together with their extensions to trilinear forms [14,15,16,17]
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