title: Identifying odd/even-order binary kernel slices for a nonlinear system using inverse repeat m-sequences.
abstract: 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.
authors: School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China.
authors: Jin-Yan
authors: JY
authors: Hu
authors: School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China.
authors: Gang
authors: G
authors: Yan
authors: School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China.
authors: Tao
authors: 0000-0002-9715-9389
authors: T
authors: Wang
mesh_terms: D000465:Algorithms; D019295:Computational Biology; D003198:Computer Simulation; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D012984:Software; D049490:Systems Biology