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

TL;DR

This paper analyzes how slow sampling affects system identification, providing conditions for unbiased and consistent estimators beyond the Nyquist frequency, supported by theoretical analysis and simulations.

Contribution

It offers a comprehensive statistical analysis of estimators under slow sampling, including necessary and sufficient conditions for unbiasedness and consistency beyond the Nyquist frequency.

Findings

Conditions for unbiased estimates beyond Nyquist frequency

Consistency of parametric estimators with overlapping input frequencies

Monte Carlo simulations confirm theoretical results

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.