通过频域方法从重复测量中精准识别低阶系统，误差可控且可推广。
Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis
- 用核范数正则化洛弗勒矩阵，结合凸稳定性约束估计系统
- 给出采样频率下的有限样本误差界，并通过有理插值推广至全频段
- 适用于多输入多输出系统，适合关注模型精度与鲁棒性的研究者
本文提出一种基于重复噪声测量的低阶系统频域估计算法。该方法最小化二次数据拟合项，并以洛弗勒矩阵的核范数作为正则项，同时通过半定规划施加凸稳定性约束。我们证明了在采样频率上的有限样本误差界，并通过有理插值将其扩展到所有频率。误差界揭示了实验重复次数、频率点数、系统阶数和噪声水平的影响关系。针对SISO和MIMO系统的数值实验验证了该方法的低阶促进效果，并确认了预测的尺度律。
原文摘要 · Abstract (English)
This paper proposes a frequency-domain estimator for low-order systems from repeated noisy measurements. The estimator minimizes a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint enforced via a semidefinite program. We prove a finite-sample error bound at the sampled frequencies and extend it to all frequencies through rational interpolation. The bound characterizes the dependence on the number of repeated experiments, number of frequency points, system order, and noise level. Numerical experiments on SISO and MIMO systems demonstrate the low-order-promoting effect of the method and validate the predicted scaling laws.
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