Spectral estimation: An overdetermined rational model equation approach
Spectral estimation: An overdetermined rational model equation approach
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DOI：
10.1109/proc.1982.12424
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发表时间：
1982-09
影响因子：
20.6
通讯作者：
James A. Cadzow
中科院分区：
文献类型：
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作者：
James A. Cadzow
在寻求时间序列的合理模型时，经常显式或隐式地引用近似二阶统计关系(即Yule-Walker方程)的概念。假设的Rational模型的参数通常被选择，以便这些关系“最佳地表示”从时间序列观测计算出的一组自相关滞后估计。本文的目标之一将是建立这一生成理性模型的基本方法。对当代许多流行的谱估计方法的研究表明，假设的有理模型的参数是通过使用一组最小的Yule-Walker方程评估来估计的。这导致了不希望看到的参数过敏性以及随后估计性能的下降。为了抵消这种参数过敏性，这里提倡使用多于最小次数的Yule-Walker方程求值的概念。结果表明，通过采用这种超定参数估计方法，降低了数据诱导的模型参数超敏感度，并相应地改善了建模性能。此外，将扩展阶自相关矩阵估计的奇异值分解表示应用于该过程，获得了所需的模型阶数确定方法，并且进一步显著改善了建模性能。这种方法使得从短数据长度生成低阶高质量有理谱估计成为可能。
In seeking rational models of time series, the concept of approximating second-order statistical relationships (i.e., the Yule-Walker equations) is often explicitly or implicitly invoked. The parameters of the hypothesized rational model are typically selected so that these relationships "best represent" a set of autocorrelation lag estimates computed from time series observations. One of the objectives of this paper will be that of establishing this fundamental approach to the generation of rational models. An examination of many popular contemporary spectral estimation methods reveals that the parameters of a hypothesized rational model are estimated upon using a "minimal" set of Yule-Walker equation evaluations. This results in an undesired parameter hypersensitivity and a subsequent decrease in estimation performance. To counteract this parameter hypersensitivity, the concept of using more than the minimal number of Yule-Walker equation evaluations is herein advocated. It is shown that by taking this overdetermined parametric evaluation approach, a reduction in data-induced model parameter hypersensitivity is obtained, and a corresponding improvement in modeling performance results. Moreover, upon adapting a singular value decomposition representation of an extended-order autocorrelation matrix estimate to this procedure, a desired model order determination method is obtained and a further significant improvement in modeling performance is achieved. This approach makes possible the generation of low-order high-quality rational spectral estimates from short data lengths.