Atomic Clock Models and Frequency Stability Analyses

This paper describes atomic clock models and frequency stability analyses methods. The time deviation observation model is comprised of the deterministic part (the time deviation, the frequency deviation, the linear frequency drift and the periodical part), the stochastic part which is the clock noise and the observation noise. This paper gives the Allan deviation expressions of these parts. The principle of utilizing Kalman filter to estimate the clock status is not illustrated in some paper clearly. Thus, this paper describes the atomic clock stochastic differential equations and parameters in detail. Then, we propose a method to estimate the clock noises and observation noise levels by means of the Kalman filter estimation results and Allan deviation pictures. Three methods of estimating the linear frequency drift level are proposed and validated by measurements. This paper also proposes the method of estimating the period and level of the periodical part by means of the atomic clock stochastic differential equations, the Kalman filter estimation results and Allan deviation pictures. The real measurements of two domestic hydrogen masers are used to validate these methods. The principles of these methods are distinct. They are practical and easily to be realized. The methods can be used to obtain the estimated Allan deviation values at any observation interval. This research is the basis of a series of successive researches such as time scale algorithms, clock prediction algorithms, steering algorithms.