CramÉr–Rao Bounds for Multiple Poles and Coefficients of Quasi-Polynomials in Colored Noise
CramÉr–Rao Bounds for Multiple Poles and Coefficients of Quasi-Polynomials in Colored Noise
复制标题
有色噪声中拟多项式的多极点和系数的 CramÉr–Rao 界
DOI：
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发表时间：
2008
影响因子：
5.4
通讯作者：
G. Richard
中科院分区：
文献类型：
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作者：
R. Badeau;B. David;G. Richard
本文给出了色噪声中复指数函数的频率、阻尼因子、振幅和相位的Cramer-Rao界的解析表达式。这些表达式显示了每个不同参数的幅度和相位的界限的显式依赖性，导致容易解释的公式，然后在渐近的情况下简化。结果中提出的多项式振幅复指数（PACE）模型，也被称为准多项式模型在文献中，它占系统涉及多个极点，并表示一个信号作为一个混合物的多项式调制的复指数的一般框架。这项工作看起来更进一步，并概括了以前进行的指数和准多项式模型的研究。
In this paper, we provide analytical expressions of the Cramer-Rao bounds for the frequencies, damping factors, amplitudes, and phases of complex exponentials in colored noise. These expressions show the explicit dependence of the bounds of each distinct parameter with respect to the amplitudes and phases, leading to readily interpretable formulae, which are then simplified in an asymptotic context. The results are presented in the general framework of the polynomial amplitude complex exponentials (PACE) model, also referred to as the quasi-polynomial model in the literature, which accounts for systems involving multiple poles and represents a signal as a mixture of complex exponentials modulated by polynomials. This work looks further and generalizes the studies previously undertaken on the exponential and the quasi-polynomial models.