原子钟频率稳定度评估方法综述

A Compilation of the Theoretical Fundamentals of Atomic Clock Frequency Stability Evaluation Methods

原子钟通过稳定的频标来测量时间,但频标输出信号会受到不同来源噪声的影响,因此原子钟间相位偏差可以看作服从幂律∑hαfα的连续随机过程。该随机过程并非平稳的,一般是通过高阶的差分使得序列平稳化,常用的时域频率稳定度评估方法便是采用此种思路。幂律噪声实际是对白噪声过程进行微分和积分得来,不同幂律的噪声对应不同的随机微分方程,实际上幂律噪声的仿真也是通过白噪声基于此实现的。首先介绍了不同幂律噪声的鉴定方法,并结合文献给出常见幂律噪声对应的微分方程;然后介绍了不同频率稳定度评估方法之间的关系和其相应的传递函数,并简单总结了其置信区间的计算方法。该文的工作有助于构建原子钟随机模型和频率稳定度评估方法。

The atomic clocks measure time by the stable frequency standard,and the output signal of the oscillators is easily affected by noise from different sources which makes the phase deviation between two atomic clocks obeying a continuous power-law random process.Such stochastic process is not stationary and a typical approach by utilizing a high-order backward differencing operator can make the process become stationary,and the commonly used method for assessing the frequency stability in the time domain is based on this idea.This paper focuses on the mathematical fundamentals behind the method for assessing the frequency stability of atomic clocks.The power-law noise is actually derived from the calculus of white noise processes and the different power-law noises correspond to the different stochastic differential equations.In fact,the simulation of the power-law noise is also achieved by some differentiations and integrations operating on the white noise process.This paper first introduces the identification method of different power-law noises and gives the differential equations corresponding to the power-law noises in conjunction with some available literatures.Then,the relationships between the different frequency stability assessment methods and their corresponding transfer functions are presented,and the calculation method of the confidence intervals is briefly summarized.This paper provides some insight into the construction of the stochastic model for atomic clocks and methods for assessing frequency stability in a relatively systematic basis.