Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length s...

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Main Authors:	Hu, Jin-yan, Yan, Gang, Wang, Tao
Format:	Online
Language:	English
Published:	Hindawi Publishing Corporation 2015
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4385604/

id	pubmed-4385604
recordtype	oai_dc
spelling	pubmed-43856042015-04-13 Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences Hu, Jin-yan Yan, Gang Wang, Tao Research Article The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method. Hindawi Publishing Corporation 2015 2015-03-22 /pmc/articles/PMC4385604/ /pubmed/25873988 http://dx.doi.org/10.1155/2015/454638 Text en Copyright © 2015 Jin-yan Hu et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Hu, Jin-yan Yan, Gang Wang, Tao
spellingShingle	Hu, Jin-yan Yan, Gang Wang, Tao Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences
author_facet	Hu, Jin-yan Yan, Gang Wang, Tao
author_sort	Hu, Jin-yan
title	Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences
title_short	Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences
title_full	Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences
title_fullStr	Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences
title_full_unstemmed	Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences
title_sort	identifying odd/even-order binary kernel slices for a nonlinear system using inverse repeat m-sequences
description	The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method.
publisher	Hindawi Publishing Corporation
publishDate	2015
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4385604/
_version_	1613207709749870592

Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

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