Fractional-Based Stochastic Gradient Algorithms for Time-Delayed ARX Models

In this study, two fractional-based stochastic gradient (FSG) algorithms for time-delayed auto-regressive exogenous (ARX) models are proposed. By combining momentum and adaptive methods, a momentum-based FSG and an adaptive-based FSG algorithms are developed. These two FSG algorithms have faster con...

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Bibliographic Details
Published in:Circuits, systems, and signal processing Vol. 41; no. 4; pp. 1895 - 1912
Main Authors: Xu, Tianyang, Chen, Jing, Pu, Yan, Guo, Liuxiao
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2022
Springer Nature B.V
Subjects:
Adaptive algorithms
Algorithms
Autoregressive models
Circuits and Systems
Convergence
Electrical Engineering
Electronics and Microelectronics
Engineering
Instrumentation
Momentum
Signal,Image and Speech Processing
Momentum method
Parameter estimation
ARX model
Time delay
Adaptive method
Fractional derivative
ISSN:0278-081X, 1531-5878
Online Access:Get full text
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Summary:In this study, two fractional-based stochastic gradient (FSG) algorithms for time-delayed auto-regressive exogenous (ARX) models are proposed. By combining momentum and adaptive methods, a momentum-based FSG and an adaptive-based FSG algorithms are developed. These two FSG algorithms have faster convergence rates when compared with the stochastic gradient algorithm. The mechanism of the convergence is proved in theory. Furthermore, two simulated examples are presented to illustrate the efficiency of the new proposed algorithms.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-021-01874-8