Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter

TL;DR

This paper demonstrates that using very high sampling frequencies combined with a state variable filter approach significantly improves system identification accuracy, especially in challenging scenarios like closed-loop systems with noise and offsets.

Contribution

It introduces a novel approach combining high sampling rates with SVF-like least squares for robust system identification under noise and offsets, extending traditional guidelines.

Findings

Estimation error variance scales as O(h) with sampling interval h.

High sampling frequencies improve identification accuracy in closed-loop systems.

Method effectively handles colored noise and noise correlations.

Abstract

This paper investigates the effects of setting the sampling frequency significantly higher than conventional guidelines in system identification. Although continuous-time identification methods resolve the numerical difficulties encountered in discrete-time approaches when employing fast sampling (e.g., the problems caused by all poles approaching unity), the potential benefits of using sampling frequencies that far exceed traditional rules like the "ten times the bandwidth" guideline remained largely unexplored. We show that using a state variable filter (SVF)-like least squares approach, the variance of the estimation error scales as $O(h)$ with the sampling interval $h$. Importantly, this scaling holds even with colored noise or noise correlations between variables. Thus, increasing the sampling frequency and applying the SVF method offers a novel solution for challenging problems such as closed-loop system identification and measurements with offsets. Theoretical findings are supported by numerical examples, including the closed-loop identification of unstable multi-input multi-output (MIMO) systems.