Sampling in Parametric and Nonparametric System Identification

Aliasing, Input Conditions, and Consistency

Journal article (2024)

Authors

Rodrigo A. González Eindhoven University of Technology
Max van Haren Eindhoven University of Technology
Tom Oomen Team Jan-Willem van Wingerden - Mechanical, Maritime and Materials Engineering , Eindhoven University of Technology
Cristian R. Rojas KTH Royal Institute of Technology
Research Group
Team Jan-Willem van Wingerden (Mechanical, Maritime and Materials Engineering) (TU Delft)
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Published Date

2024

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Jan-Willem van Wingerden

Abstract

The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for perfect signal reconstructability, careful consideration is required when identifying parametric and nonparametric models. In this letter, a comprehensive statistical analysis of estimators under slow sampling is performed. Necessary and sufficient conditions are obtained for unbiased estimates of the frequency response function beyond the Nyquist frequency, and it is shown that consistency of parametric estimators can be achieved even if input frequencies overlap after aliasing. Monte Carlo simulations confirm the theoretical properties.

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