On quantifying the uncertainty of stochastic process power spectrum estimates subject to missing data
On quantifying the uncertainty of stochastic process power spectrum estimates subject to missing data
复制标题
关于量化受缺失数据影响的随机过程功率谱估计的不确定性
DOI：
10.1504/ijsmss.2015.078358
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Beer
中科院分区：
文献类型：
--
作者：
Liam A. Comerford;I. Kougioumtzoglou;M. Beer
研究了基于缺失数据实现的随机过程功率谱估计中不确定性的量化问题。在这方面，依赖于相对宽松的假设缺失的数据，利用概率论的基本概念，并诉诸于傅立叶和谐波小波为基础的平稳和非平稳随机过程的表示，分别，一个封闭形式的表达式推导出对应于一个特定的频率的功率谱值的概率密度函数（PDF）。导出的PDF的意义涉及的情况下，不完整的过程实现可用于功率谱估计应用。在这种情况下，标准的功率谱估计技术受到丢失数据的影响，通常提供对功率谱的确定性估计。因此，没有提供关于估计数不确定性的资料。本文中的数值示例证明了任何给定的单个估计可能在很大程度上不代表目标光谱。
The issue of quantifying the uncertainty in stochastic process power spectrum estimates based on realisations with missing data is addressed. In this regard, relying on relatively relaxed assumptions for the missing data, utilising fundamental concepts from probability theory, and resorting to Fourier and harmonic wavelets based representations of stationary and non-stationary stochastic processes, respectively, a closed-form expression is derived for the probability density function (PDF) of the power spectrum value corresponding to a specific frequency. The significance of the derived PDF relates to cases where incomplete process realisations are available for power spectrum estimation applications. In this setting, standard power spectrum estimation techniques subject to missing data typically provide with a deterministic estimate for the power spectrum. Thus, no information is provided concerning the uncertainty in the estimates. Numerical examples herein demonstrate the large extent to which any given single estimate may be unrepresentative of the target spectrum.