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This study introduces a new method using inverse repeat (IR) maximum length sequences (m-sequences) to improve system identification for dynamic nonlinear systems. The technique effectively separates kernel slices, reducing overlap distortion for more accurate nonlinear system modeling.

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Area of Science:

  • System identification
  • Nonlinear dynamics
  • Signal processing

Background:

  • System identification of complex dynamic nonlinear systems is challenging.
  • Kernel-based methods using maximum length sequences (m-sequences) are established for estimating nonlinear system properties.
  • Cross-correlation analysis of m-sequence input and system output can reveal kernel slices but suffers from overlap distortion.

Purpose of the Study:

  • To investigate the mathematical properties of kernel slices, specifically the shift-and-product property and overlap distortion.
  • To propose a novel method using inverse repeat (IR) m-sequences to mitigate kernel-slice overlapping in system identification.
  • To validate the proposed method through simulation of a third-order Wiener nonlinear model.

Main Methods:

  • Analysis of kernel slice mathematical properties, including shift-and-product and overlap distortion.
  • Derivation of properties for inverse repeat (IR) m-sequences.
  • Development of a method employing IR m-sequences to separately estimate odd- and even-order kernel slices.
  • Simulation of a third-order Wiener nonlinear model to test the proposed identification technique.

Main Results:

  • Identified overlap distortion issues in traditional m-sequence based kernel slice estimation.
  • Demonstrated that IR m-sequences possess properties beneficial for kernel slice separation.
  • The proposed method successfully reduced kernel-slice overlapping in simulations.
  • Accurate estimation of odd- and even-order kernel slices was achieved.

Conclusions:

  • The proposed method utilizing IR m-sequences offers a significant improvement for identifying dynamic nonlinear discrete-time systems.
  • Separating odd- and even-order kernel slices effectively resolves overlap distortion problems.
  • This approach enhances the accuracy and reliability of system identification for complex nonlinear models.