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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >A Bayesian method for long AR spectral estimation: a comparativestudy
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A Bayesian method for long AR spectral estimation: a comparativestudy

机译：长时间AR光谱估计的贝叶斯方法：对比研究

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摘要

We address the problem of smooth power spectral density estimationnof zero-mean stationary Gaussian processes when only a short observationnset is available for analysis. The spectra are described by a longnautoregressive model whose coefficients are estimated in a Bayesiannregularized least squares (RLS) framework accounting the spectralnsmoothness prior. The critical computation of the tradeoff parameters isnaddressed using both maximum likelihood (ML) and generalizedncross-validation (GCV) criteria in order to automatically tune thenspectral smoothness. The practical interest of the method isndemonstrated by a computed simulation study in the field of Dopplernspectral analysis. In a Monte Carlo simulation study with a knownnspectral shape, investigation of quantitative indexes such as bias andnvariance, but also quadratic, logarithmic, and Kullback distances showsninteresting improvements with respect to the usual least squares method,nwhatever the window data length and the signal-to-noise ration(SNR)
机译：当只有短的观测值n可以用于分析时，我们解决了零均值平稳高斯过程的平稳功率谱密度估计n的问题。光谱由longn自回归模型描述，该模型的系数是在考虑了光谱平滑度的贝叶斯正则最小二乘（RLS）框架中估算的。使用最大似然（ML）和广义交叉验证（GCV）标准来解决权衡参数的关键计算问题，以便自动调整频谱平滑度。该方法的实际意义由多普勒光谱分析领域的计算机模拟研究证明。在具有已知光谱形状的蒙特卡罗模拟研究中，对定量指标（例如偏差和方差）以及二次，对数和Kullback距离的定量研究显示，与通常的最小二乘法相比，无论窗口数据长度和信号到噪声比（SNR）

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