Application of Three-Cornered Hats for Frequency Stability Analysis of Atomic Clock

Abstract

Three-Cornered Hats is a classical method to obtain the frequency stability of one single atomic clock without more stable frequency standards available. In this paper, the measurement data of three hydrogen masers in a ground station is used to analyze the frequency stability of one single atomic clock. The analysis steps and problems in application of this method are introduced. The negative values of the calculated Allan variance of one clock with averaging time larger than 4000s occur. It probably implies that the hypothesis of uncorrelated clocks is not acceptable, which will be analyzed further.

Improving Global Monthly and Daily Precipitation Estimation by Fusing Gauge Observations, Remote Sensing, and Reanalysis Data Sets

“…The covariance matrix of D is regarded as the Allan covariance when TCH was initially proposed to evaluate the instability of clocks, which requires a filtering operation on the original time series before differencing. However, the covariance of D, that is, the R matrix, does not necessarily have to be the Allan covariance but can be the common sample variance, as used in some studies (Liu et al, 2013;Rieckh & Anthes, 2018). Equation 5 can be reformatted as…”

“…The covariance matrix of D is regarded as the Allan covariance when TCH was initially proposed to evaluate the instability of clocks, which requires a filtering operation on the original time series before differencing. However, the covariance of D , that is, the R matrix, does not necessarily have to be the Allan covariance but can be the common sample variance, as used in some studies (Liu et al, 2013; Rieckh & Anthes, 2018). Equation can be reformatted as where is the ( N − 1) × ( N − 1) matrix and r is the ( N − 1) vector [ r 1 N r 2 N ⋯ r N − 1, N ] grouping covariance estimates with the N th time series and r NN denotes the variance of N th time series.…”

“…Recently, there are some validation researches that are not dependent on gauge stations (Gruber et al, 2016; Liu et al, 2013; McColl et al, 2014; Rieckh & Anthes, 2018). The three‐cornered hat (TCH) method and the triple collocation (TC) method are two commonly used ways to evaluate the uncertainty of remote sensing or hydrological products without using ground gauges (Ferreira et al, 2016; Long et al, 2014; Massari et al, 2017).…”