ad van tage of the fact that the masers, carefully separated and iso lated from environmental eects, show uncorrelated stochastic behavior. As demonstrated in Fig.2, the in sta bi-lity can then be reduced by averaging over multiple masers. Figure 4 is calculated for an ensemble of =3 . For the measurement distribution in Fig.4(b): =(1.93×10)+(5.93×10)= (1.14 × 1017) (11)is allows a comparison of the optical lattice clock to TAI with an overall uncertainty of ⁄ =(2.0×10)+(1.4×10)+(1.1×10) =(2.7×10) (12)over 35 d . All these contributions are statistical in na-ture, allowing further reduction with repeated comparisons.TAI calibrationsAer seven qualifying measurements reported in Circular T 371 [22], NICT-Sr1 has contributed four mea-surements targeting TAI steering, with results reported in time for the monthly time scale evaluation performed by BIPM. ese were included in Circular T 372-374 and 379. eir results are summarized in Table 1. Based on the measurements of the TAI scale interval reported by all contributing frequency standards, a steering correction of 4×10 was applied to TAI over the period from December 2018 to May 2019.For each of the data sets, all measurements of the maser frequency are collected on a xed 10 s grid. We consider the observed () to represent a linear dri () with overlaid stochastic frequency uc tu a tions () . We choose to coincide with the mid point of the evaluation period and dene and to include any rst order trend of the stochastic behavior.e dead-time induced uncertainty discussed in the pre vious section then represents the error introduced in ex tracting () from the available subset of data. is can be reduced by characterizing and compensating () : e DMTD system continuously provides fre quen cy com-parisons of all local maser frequencies. We select an en-semble of =3 to 5 well-behaved masers to form a reference frequency calculated at 1 ℎ interval. Aer removing any rst order trend, the interpolated dierence of the characterized maser from the ensemble mean provides an approximation () of the stochas tic uctuations. We then calculate a linearized ()()() that is representative of the stability for the entire ensemble. Figure 2 demonstrates the resul ting improvement: Where the original () (aer sub trac ting a linear dri) shows the expected FFN-plateau near 2×10 , the corrected () averages to below 1×10 , consistent with an improve-ment by for an ensemble of =5 masers. Note that as dened, the cor rection has no eect on the extracted and when all of () is available.We determine the statistical uncertainty by tting the logarithm of the Allan variance, followed by extrapola-tion according to () up to the combined mea-sure ment time. For the exemplary data set, we nd =(779853s)=3.9×10. is represents the uncertainty of the mean over all observed data, with bary-center ≠0. We correct for a maser dri with an uncertainty according to the slope un-certainty determined by a linear t. If the mea sure ment intervals are suitably chosen, ≤1 d , for which we nd a typical uncertainty ≤3×10 .We consider an additional uncertainty from the micro-wave link between the maser and the frequency comb: While short-term phase excursions appear in the Allan de vi ation and are automatically included in the stability analy sis, diurnal eects induced by e.g. temperature vari a-tions may aect multiple intermittent measurements in the same way and lead to a persistent frequency error. We in-6TabeT1Steering measurements of the TAI scale interval by NICT-Sr1, reported in Circular T. All values are given in units of 10 . The statistical uncertainty u represents only the optical lattice clock. Uncertainties from maser instability (including dead time induced effects) are included in u . The operational duty cycle, size of the evaluated maser ensemble and the resulting , re-evaluated according to the methods described here, have been added for convenience.DateMJD period ⁄ duty Dec. 2018 58454-584640.84 0.01 0.08 0.05 0.70 0.71 0.490.3% 50.006 Jan. 2019 58479-585090.90 0.04 0.08 0.32 0.23 0.40 0.41.4% 50.134 Feb. 2019 58514-585341.21 0.02 0.07 0.22 0.28 0.37 0.47.2% 40.186 June 2019 58644-586790.68 0.01 0.07 0.21 0.17 0.28 0.423.1% 30.202 96 情報通信研究機構研究報告 Vol. 65 No. 2 （2019）4 原⼦周波数標準
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