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Statistical biases and very-long-term time stability analysis

机译：统计偏差和非常长期的时间稳定性分析

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摘要

The prediction of very-long-term time stability is a key issue in various fields, such as time keeping, obviously, but also navigation and spatial applications. This is usually performed by extrapolating the measurement data obtained by estimators such as the Allan variance, modified Allan variance, Hadamard variance, etc. This extrapolation may be assessed from a fit over the variance estimates. However, this fit should be performed on the log-log graph of the estimates, which corresponds to a least-squares minimization of the relative difference between the variance estimates and the fitting curve. However, a bias exists between the average of the log of the estimates and the log of the true value of the estimated variance. This paper presents the theoretical calculation of this log-log bias based on the number of equivalent degrees of freedom of the estimates, shows simulations over a large number of realizations, and provides a reliable method of unbiased logarithmic fit. Extrapolating this fit yields a more confident assessment of the very-long-term time stability.
机译：长期时间稳定性的预测是各个领域的关键问题，例如，计时，显然，也是导航和空间应用中的一个关键问题。这通常是通过外推估算器（例如艾伦方差，修正的艾伦方差，哈达玛方差等）获得的测量数据来执行的。可以根据方差估算值的拟合来估算这种外推。但是，应该在估计的对数-对数图上执行此拟合，这对应于方差估计和拟合曲线之间的相对差的最小二乘最小化。但是，在估计的对数的平均值与估计的方差的真实值的对数之间存在偏差。本文介绍了基于估计的等效自由度数量的对数-对数偏差的理论计算，并显示了许多实现的仿真，并提供了一种可靠的无偏对数拟合方法。通过外推这种拟合，可以对长期时间稳定性进行更可靠的评估。

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