Hermite域基于预测器的子空间辨识方法的渐近方差
The asymptotic variance of the Hermite-Domain Predictor-Based Subspace Identification method
浏览论文内容
中文总结 AI 辅助
本文推导了HD-PBSID方法渐近方差的解析表达式，提供系统特征值的不确定性界，并在理想Hermite域和含噪时域数据上验证了其准确性。
中文摘要 AI 辅助
本文推导了Hermite域基于预测器的子空间辨识（HD-PBSID）方法渐近方差的解析表达式。与依赖中间域变换的连续时间子空间方法不同，HD-PBSID直接辨识连续时间状态空间矩阵。推导首先建立估计的状态空间矩阵的不确定性，然后利用这些结果获得渐近方差表达式。这些表达式为系统特征值提供了解析不确定性界，这些界在相似变换下不变，因此唯一地表征了所辨识的动态。所提出的公式首先在理想的Hermite域设置中验证，该设置满足推导所依据的条件，然后通过蒙特卡罗模拟在含噪时域数据上进行评估。预测的界在理想设置中与特征值分布非常吻合，在强制创新序列为白噪声的时域情况下也表现出可接受的吻合度。
英文摘要
This paper derives analytical expressions for the asymptotic variance of the Hermite-Domain Predictor-Based Subspace Identification (HD-PBSID) method. Unlike continuous-time subspace approaches that rely on intermediate-domain transformations, HD-PBSID identifies continuous-time state-space matrices directly. The derivation first establishes the uncertainty of the estimated state-space matrices and then exploits these results to obtain asymptotic variance expressions. These expressions provide analytical uncertainty bounds for system eigenvalues, which are invariant under similarity transformations and therefore uniquely characterize the identified dynamics. The proposed formulas are first validated in an ideal Hermite-domain setting, where the conditions underlying the derivation are satisfied, and then assessed on noisy time-domain data through Monte Carlo simulations. The predicted bounds show very good agreement with the eigenvalue distributions in the ideal setting and acceptable agreement in the time-domain case when the innovation sequence is enforced to be white.
发表机构
- Politecnico di Milano（米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。
