结构化CPD估计的统计效率及其在Wiener-Hammerstein建模中的应用
Statistical efficiency of structured cpd estimation applied to Wiener-Hammerstein modeling
AI总结：
本文研究了结构化CPD估计在非线性系统建模中的统计效率，通过Wiener-Hammerstein模型结合高阶Volterra核，推导出CRB并验证估计器的性能。
摘要：
结构化 canonical polyadic decomposition (CPD) 的计算对解决现实应用中的重要建模问题具有帮助。本文考虑通过 Wiener-Hammerstein 模型识别非线性系统，假设该系统的高阶 Volterra 核已预先估计。此类核视为张量，允许具有带状循环因子的 CPD，这些因子包含模型参数。为估计这些参数，我们基于最近提出的结构化 CPD 计算算法制定专用估计器。然后，考虑加性白高斯噪声的存在，我们推导出与此估计问题相关的 Cramer-Rao bound (CRB) 的闭式表达式。最后，通过蒙特卡洛模拟评估所提估计器的统计性能，通过将其均方误差与 CRB 进行比较来验证。
英文摘要：
The computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously estimated. Such a kernel, viewed as a tensor, admits a CPD with banded circulant factors which comprise the model parameters. To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs. Then, considering the presence of additive white Gaussian noise, we derive a closed-form expression for the Cramer-Rao bound (CRB) associated with this estimation problem. Finally, we assess the statistical performance of the proposed estimators via Monte Carlo simulations, by comparing their mean-square error with the CRB.
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