Sampling in Parametric and Nonparametric System Identification: Aliasing, Input Conditions, and Consistency

Rodrigo González; Max van Haren; Tom A.E. Oomen; Cristian R. Rojas

doi:10.1109/LCSYS.2024.3487501

Sampling in Parametric and Nonparametric System Identification: Aliasing, Input Conditions, and Consistency

Rodrigo González (Corresponding author)
, Max van Haren
, Tom A.E. Oomen
, Cristian R. Rojas

Research output: Contribution to journal › Letter › Academic › peer-review

3 Citations (Scopus)

99 Downloads (Pure)

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.

Original language	English
Article number	10737126
Pages (from-to)	2415-2420
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	8
DOIs	https://doi.org/10.1109/LCSYS.2024.3487501
Publication status	Published - 4 Nov 2024

Funding

This work was partly supported by the Swedish Research Council under contract number 2023-05170, and by the ECSEL Joint Undertaking under grant agreement 101007311 (IMOCO4.E). The Joint Undertaking receives support from the European Union Horizon 2020 research and innovation programme.

Funders	Funder number
European Union's Horizon 2020 - Research and Innovation Framework Programme	101007311
Swedish Research Council	2023-05170

Keywords

Frequency-domain system identification
Undersampled systems
Frequency response function

Access to Document

10.1109/LCSYS.2024.3487501

[GonzalezvanHarenOomenRojas2024] Sampling in parametric and nonparametric system identification - aliasing input conditions and consistency-PureFinal author version , 546 KBLicence: CC BY-NC-ND
Sampling_in_Parametric_and_Nonparametric_System_Identification_Aliasing_Input_Conditions_and_ConsistencyFinal published version, 669 KBLicence: TAVERNE

Cite this

@article{83d876de2b614f87ab443a9f0805e362,

title = "Sampling in Parametric and Nonparametric System Identification: Aliasing, Input Conditions, and Consistency",

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.",

keywords = "Frequency-domain system identification, Undersampled systems, Frequency response function",

author = "Rodrigo Gonz{\'a}lez and \{van Haren\}, Max and Oomen, \{Tom A.E.\} and Rojas, \{Cristian R.\}",

year = "2024",

month = nov,

day = "4",

doi = "10.1109/LCSYS.2024.3487501",

language = "English",

volume = "8",

pages = "2415--2420",

journal = "IEEE Control Systems Letters",

issn = "2475-1456",

publisher = "Institute of Electrical and Electronics Engineers",

}

TY - JOUR

T1 - Sampling in Parametric and Nonparametric System Identification

T2 - Aliasing, Input Conditions, and Consistency

AU - González, Rodrigo

AU - van Haren, Max

AU - Oomen, Tom A.E.

AU - Rojas, Cristian R.

PY - 2024/11/4

Y1 - 2024/11/4

N2 - 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.

AB - 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.

KW - Frequency-domain system identification

KW - Undersampled systems

KW - Frequency response function

UR - https://www.scopus.com/pages/publications/85208225107

U2 - 10.1109/LCSYS.2024.3487501

DO - 10.1109/LCSYS.2024.3487501

M3 - Letter

AN - SCOPUS:85208225107

SN - 2475-1456

VL - 8

SP - 2415

EP - 2420

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

M1 - 10737126

ER -

Sampling in Parametric and Nonparametric System Identification: Aliasing, Input Conditions, and Consistency

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this