Abstract
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.
Highlights
Tensor decomposition is an important topic for the development of modern technologies such as big data, machine learning, communication systems with multiple inputs and/or multiple outputs, respectively source separation/beamforming [1,2,3]
This paper proposes a tensorial decomposition for multilinear forms based on the recursive least-squares (RLS)-dichotomous coordinate descent (DCD)
We propose to use the combination between the dichotomous coordinate descent (DCD) iterations and the RLS method as an alternative solution for the systems of equations in (21)
Summary
Tensor decomposition is an important topic for the development of modern technologies such as big data, machine learning, communication systems with multiple inputs and/or multiple outputs, respectively source separation/beamforming [1,2,3]. Considerable recent research was dedicated to identify multilinear forms [4,5,6] with two, three, or even more components using the Wiener filter [7,8,9] and adaptive algorithms based on the least-meansquare (LMS) method [10,11,12,13] or on the recursive least-squares (RLS) systems [10,14,15]. Despite its prohibitive nature in terms of required chip area, the decorrelation properties of the RLS (translated in practice into superior convergence speeds and overall performance) pushed researchers to develop new corresponding versions with attractive compromise between complexity and performance. For some algorithms, such as Fast-RLS (FRLS) [16], the negative aspects still tend to overtake the value brought by the reduction in terms of complexity and deny the practical applications a reliable least-squares algorithm
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