scholarly journals Low-Complexity Recursive Least-Squares Adaptive Algorithm Based on Tensorial Forms

2021 ◽  
Vol 11 (18) ◽  
pp. 8656
Author(s):  
Ionuț-Dorinel Fîciu ◽  
Cristian-Lucian Stanciu ◽  
Cristian Anghel ◽  
Camelia Elisei-Iliescu
Keyword(s):  
System Identification ◽  
Least Squares ◽  
Adaptive Systems ◽  
Stable Solution ◽  
Tensor Decomposition ◽  
Low Complexity ◽  
Recursive Least Squares ◽  
Rls Algorithm ◽  
Multilinear Forms ◽  
Single Output

Modern solutions for system identification problems employ multilinear forms, which are based on multiple-order tensor decomposition (of rank one). Recently, such a solution was introduced based on the recursive least-squares (RLS) algorithm. Despite their potential for adaptive systems, the classical RLS methods require a prohibitive amount of arithmetic resources and are sometimes prone to numerical stability issues. This paper proposes a new algorithm for multiple-input/single-output (MISO) system identification based on the combination between the exponentially weighted RLS algorithm and the dichotomous descent iterations in order to implement a low-complexity stable solution with performance similar to the classical RLS methods.

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

Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 237
Author(s):  
Ionuț-Dorinel Fîciu ◽  
Cristian-Lucian Stanciu ◽  
Camelia Elisei-Iliescu ◽  
Cristian Anghel
Keyword(s):  
Least Squares ◽  
Tensor Decomposition ◽  
Identification Problem ◽  
Low Complexity ◽  
Recursive Least Squares ◽  
Dimensional System ◽  
Multilinear Forms ◽  
Coordinate Descent Algorithm ◽  
Noise Simulation ◽  
The Cost

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.

scholarly journals A Recursive Least-Squares Algorithm for the Identification of Trilinear Forms

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 135
Author(s):  
Camelia Elisei-Iliescu ◽  
Laura-Maria Dogariu ◽  
Constantin Paleologu ◽  
Jacob Benesty ◽  
Andrei-Alexandru Enescu ◽  
...  
Keyword(s):  
Least Squares ◽  
Impulse Response ◽  
Recursive Least Squares ◽  
Dimensional System ◽  
Third Order ◽  
Rls Algorithm ◽  
Tensor Decompositions ◽  
Rank One ◽  
The Individual ◽  
Least Mean Squares Algorithm

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.

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