标题： 系统辨识的快速采样：利用状态变量滤波器克服噪声、偏移和闭环挑战 显示英文标题

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

摘要： 本文研究了在系统辨识中显著提高采样频率相对于传统准则的影响。尽管连续时间辨识方法解决了离散时间方法在采用快速采样时遇到的数值困难（例如，所有极点接近于1所导致的问题），但使用远远超过传统规则（如“带宽的十倍”准则）的采样频率所带来的潜在好处仍未被充分探索。 我们表明，使用类似状态变量滤波器（SVF）的最小二乘法，估计误差的方差与采样间隔 $h$ 成比例地变化为 $O(h)$。重要的是，这种比例关系即使在有色噪声或变量之间的噪声相关性存在的情况下仍然成立。 因此，提高采样频率并应用SVF方法为具有挑战性的难题（如闭环系统辨识和带偏移量的测量）提供了一种新颖的解决方案。理论发现通过数值例子得到了支持，包括不稳定多输入多输出（MIMO）系统的闭环辨识。 显示英文摘要

摘要： 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.