ELA Medical (Sorin Group), C.A. La Boursidiere, Le Plesis Robinson, France.
IEEE Trans Ultrason Ferroelectr Freq Control. 2010 May;57(5):1011-28. doi: 10.1109/TUFFC.2010.1513.
We analyze the Allan variance estimator as the combination of discrete-time linear filters. We apply this analysis to the different variants of the Allan variance: the overlapping Allan variance, the modified Allan variance, the Hadamard variance and the overlapping Hadamard variance. Based upon this analysis, we present a new method to compute a new estimator of the Allan variance and its variants in the frequency domain. We show that the proposed frequency domain equations are equivalent to extending the data by periodization in the time domain. Like the total variance, which is based on extending the data manually in the time domain, our frequency domain variance estimators have better statistics than the estimators of the classical variances in the time domain. We demonstrate that the previous well-know equation that relates the Allan variance to the power spectrum density (PSD) of continuous-time signals is not valid for real world discrete-time measurements and we propose a new equation that relates the Allan variance to the PSD of the discrete-time signals and allows computation of the Allan variance and its different variants in the frequency domain.
我们将 Allan 方差估计器分析为离散时间线性滤波器的组合。我们将此分析应用于不同的 Allan 方差变体：重叠 Allan 方差、修正 Allan 方差、Hadamard 方差和重叠 Hadamard 方差。基于此分析，我们提出了一种新的方法来计算 Allan 方差及其变体在频域中的新估计量。我们表明，所提出的频域方程等效于在时域中通过周期性扩展数据。像基于手动在时域中扩展数据的总方差一样，我们的频域方差估计量比时域中的经典方差估计量具有更好的统计特性。我们证明，先前将 Allan 方差与连续时间信号的功率谱密度 (PSD) 相关联的著名方程对于实际的离散时间测量并不有效，并且我们提出了一个新的方程，将 Allan 方差与离散时间信号的 PSD 相关联，并允许在频域中计算 Allan 方差及其不同变体。
