常均值非平稳过程Allan方差的研究
A Study of the Allan Variance for Constant-Mean Non-Stationary Processes
摘要：
Allan方差（AV）是一个广泛使用的量，在关注误差测量的领域以及在诸如工程和更具体地说计量学领域中的自相关过程的一般方差方差分析中使用。该量的形式被广泛用于检测信号中的噪声模式和稳定性指示。然而，这个数量的属性是不知道的，通常发生的过程，其协方差结构是非平稳的，在这些情况下，一个错误的解释的AV可能会导致误导性的结论。本文将AV的理论形式推广到某些非平稳过程，同时对弱平稳过程也是有效的。一些模拟的例子表明，这种新的形式可以帮助理解的AV是能够区分这些固定的情况下，从而允许在应用的情况下，这个数量的更好的解释过程。
英文摘要：
The Allan Variance (AV) is a widely used quantity in areas focusing on error measurement as well as in the general analysis of variance for autocorrelated processes in domains such as engineering and, more specifically, metrology. The form of this quantity is widely used to detect noise patterns and indications of stability within signals. However, the properties of this quantity are not known for commonly occurring processes whose covariance structure is non-stationary and, in these cases, an erroneous interpretation of the AV could lead to misleading conclusions. This paper generalizes the theoretical form of the AV to some non-stationary processes while at the same time being valid also for weakly stationary processes. Some simulation examples show how this new form can help to understand the processes for which the AV is able to distinguish these from the stationary cases and hence allow for a better interpretation of this quantity in applied cases.
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