Galleani Lorenzo, Sesia Ilaria
IEEE Trans Ultrason Ferroelectr Freq Control. 2019 Oct;66(10):1667-1683. doi: 10.1109/TUFFC.2019.2927424. Epub 2019 Jul 8.
Atomic clocks are essential elements in a variety of applications, such as global navigation satellite systems. Consequently, monitoring their performances is fundamental. The Allan variance is the key statistical tool for the performance characterization of atomic clocks. This paper proves that the Allan variance computed from frequency measurements with missing data is affected by a bias, which can make it dramatically different from the expected behavior in the full data case. Furthermore, it shows how to eliminate (or largely reduce) this bias by correcting the Allan variance. The corrected Allan variance is obtained for some of the most common atomic clock noise components, and it is validated through numerical simulations.
原子钟是全球导航卫星系统等多种应用中的关键元件。因此，监测其性能至关重要。阿仑方差是表征原子钟性能的关键统计工具。本文证明，由缺失数据的频率测量计算得到的阿仑方差会受到偏差影响，这可能使其与完整数据情况下的预期行为有显著差异。此外，本文还展示了如何通过修正阿仑方差来消除（或大幅降低）这种偏差。针对一些最常见的原子钟噪声成分，得到了修正后的阿仑方差，并通过数值模拟进行了验证。
