Identifying odd/even-order binary kernel slices for a nonlinear system using inverse repeat m-sequences

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.