近似协方差插值
Approximative Covariance Interpolation
AI总结：
本文提出两种正则化方法，用于在协方差估计不准确或模型类与过程不一致时进行近似协方差插值，以从无限族中选出最代表性的谱密度。
摘要：
当使用矩方法识别功率谱密度时，将模型与估计的二阶统计量（例如协方差估计）进行匹配。如果估计良好，则存在无限族的功率谱与该估计一致，在诸如识别等应用中，我们希望选出最具代表性的谱。我们选择一个先验谱密度来表示先验信息，并确定在给定拟距离下最接近它的谱。然而，如果估计基于少量数据，或者考虑的模型类与所考虑的过程不一致，则可能需要使用近似协方差插值。本文考虑了两种不同类型的正则化，它们可以应用于许多基于协方差插值的估计方法。
英文摘要：
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power spectra consistent with such an estimate and in applications, such as identification, we want to single out the most representative spectrum. We choose a prior spectral density to represent a priori information, and the spectrum closest to it in a given quasi-distance is determined. However, if the estimates are based on few data, or the model class considered is not consistent with the process considered, it may be necessary to use an approximative covariance interpolation. Two different types of regularizations are considered in this paper that can be applied on many covariance interpolation based estimation methods.
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