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.
Highlights
Living systems usually exhibit complex and nonlinear behaviors [1,2,3], which can be characterized by a mathematical model carefully tuned to represent the relationship between the input and output data
The shift-and-product property of the m- and inverse repeat (IR) m-sequence is crucial in the derivation of new properties to address the overlap problem for short-length m-sequence
We alternatively propose an approach by introducing the IR m-sequence
Summary
Living systems usually exhibit complex and nonlinear behaviors [1,2,3], which can be characterized by a mathematical model carefully tuned to represent the relationship between the input and output data. The kernel estimation for such nonlinear system usually requires the input signal to be a long Gaussian white noise to completely activate the underlying system Under such conditions, Lee and Schetzen proposed a convenient cross-correlation method widely used to estimate the kernel functions [7, 8]. A straightforward approach to solve this problem is to multiply the length of the input msequence, which is unfavorable for living systems with more or less time-varying property Another approach to alleviate the overlap issue is to sparsify the impulse train of the msequence at risk of suffering the underestimation caused by the reduced number of available kernel slices [18]. A thirdorder nonlinear system is simulated to demonstrate the process of the proposed method
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