Tensor-Based Recursive Least-Squares Adaptive Algorithms with Low-Complexity and High Robustness Features

Ionuț-Dorinel Fîciu,Camelia Elisei-Iliescu,Cristian Anghel,Cristian-Lucian Stanciu

doi:10.3390/electronics11020237

Ionuț-Dorinel Fîciu, Camelia Elisei-Iliescu + Show 2 more

Open Access

https://doi.org/10.3390/electronics11020237

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Journal: Electronics	Publication Date: Jan 12, 2022
Citations: 3	License type: CC BY 4.0

Affiliation: Polytechnic University of Bucharest

Abstract

The recently proposed tensor-based recursive least-squares dichotomous coordinate descent algorithm, namely RLS-DCD-T, was designed for the identification of multilinear forms. In this context, a high-dimensional system identification problem can be efficiently addressed (gaining in terms of both performance and complexity), based on tensor decomposition and modeling. In this paper, following the framework of the RLS-DCD-T, we propose a regularized version of this algorithm, where the regularization terms are incorporated within the cost functions. Furthermore, the optimal regularization parameters are derived, aiming to attenuate the effects of the system noise. Simulation results support the performance features of the proposed algorithm, especially in terms of its robustness in noisy environments.

Highlights

Nowadays, tensor-based signal processing methods are employed in many important real-world applications [1]
Our purpose is to change the scope of this parameter in order to have more significance in practice. By adjusting it in real-time, we aim to improve the performance of the recursive least-squares (RLS)-dichotomous coordinate descent (DCD)-T in low signal-to-noise ratio (SNR) conditions, when the reference signal is affected by an undesired additive noise
We verify that the VR-RLSDCD-T works well in tracking situations, when the unknown global system g changes suddenly

Summary

Introduction

Tensor-based signal processing methods are employed in many important real-world applications [1]. Among the most popular adaptive filters, the recursive least-squares (RLS) algorithm represents a notable choice [6,7] This algorithm is well-known for its fast convergence rate, especially when processing correlated input signals, and for its high computational complexity. Despite their prohibitive nature, in classical and tensor-based structures, the RLS methods outperform their popular counterparts, such as the affine projection algorithm (APA) [8] and the algorithms based on the least-mean-square (LMS) method [9,10,11,12,13,14,15], which have been preferred in real-world applications due to their low arithmetic requirements. The high-dimensional system identification problem can be solved by using a decomposition into lower-dimensional structures, tensorized together

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