We present a robust, transportable ${\mathrm{Ca}}^{+}$ optical clock, with a systematic uncertainty of $1.3\times {10}^{-17}$ limited by the black-body radiation (BBR) field evaluation and an uptime rate of $>75\%$ over a 20-day period. The clock is then installed in an air-conditioned car trailer, making it more convenient for applications. Referenced to a stationary laboratory clock, geopotential measurements are made with the transportable clock with a total uncertainty of 0.33 m (statistically 0.25 m and systematically 0.22 m) and agree with the spirit level measurement. After being moved $>1200$ km, the absolute frequency of the ${\mathrm{Ca}}^{+}$ optical clock transition is measured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of $5.6\times {10}^{-16}$, which is about one order of magnitude smaller than our previous measurement. The transportable built can be used for sub-meter-level elevation measurements, comparing intercontinental optical clocks, verifying basic physical theories, etc.

We report on the absolute frequency measurement of the 6 s ^{2 1} S ₀ –6 s 6 p ³ P ₀ transition in ¹⁷¹ Yb with a fractional uncertainty of 7.3 × 10 ^–16 . A global positioning system carrier phase frequency transfer was established between National Institute of Metrology of China and East China Normal University, which linked the optical frequency of the ECNU Yb1 clock to the second in the International System of Units (SI) through international atomic time. Frequency measurements were carried out in 15 separate days with a total time over 3.8 × 10 ⁵ s. The absolute frequency was determined to be 518 295 836 590 863.30(38) Hz. Our result is in good agreement with the recommended value in neutral Yb as a secondary representation of the SI second endorsed by the International Committee for Weights and Measures.

A road map for the implementation of the BeiDou Navigation Satellite System (BDS) time transfer in coordinated universal time (UTC) has been drawn up, including a pilot experiment to evaluate BDS time transfer on multiple baselines. In the pilot experiment, several laboratories contributing to UTC have been equipped or are planned to be equipped with BDS time and frequency transfer receivers made by the National Institute of Metrology (NIM, Beijing). In the first phase, concentrating on the evaluation for the global capacity of BDS time transfer, the experiments have been implemented on multiple inter-continental baselines, involving NIM, Bureau International des Poids et Mesures (BIPM, Sevres), other institutes in China and the Czech Republic, and stations from the International Global Navigation Satellite System (GNSS) Service (IGS) network. The satellite signal coverages at various sites were characterized for satellite number, satellite elevation and satellite azimuth. Stability and accuracy of time transfer by BDS have been evaluated, based on common clock difference and multiple inter-continental baselines experiments, concluding agreement between BDS time transfer and GPS time transfer and a time stability of less than 1 ns at some thousand seconds averaging time at the present satellite coverage of BDS.

Frequency measurements for complex single-tone signals under additive Gaussian noise cover extensive engineering fields. Existing direct discrete Fourier transform (DFT) interpolation methods suffer both degraded accuracies under noisy conditions and biased estimation performances for a restricted number of samples. To address these problems, this paper proposes a fast and accurate frequency estimation scheme using two-sample DFT interpolation. Firstly, this work introduces a frequency deviation detector that can exactly recognize the interpolation direction. Additionally, to correct the estimation biases of existing direct estimators, this paper further develops an unbiased and extremely accurate estimator for an arbitrary number of samples. Finally, a fast and accurate frequency estimation scheme is proposed based on the developed detector and estimator. Results of tests indicate that the proposed scheme exhibits good noise tolerance and can provide exact bias corrections for small and medium numbers of samples. The proposed strategy can provide superior precision and serve as an efficient frequency estimation scheme in various engineering fields.

Relative to single Global Navigation Satellite System (GNSS) measurements, i.e., the measurements from a single GNSS system, a single GNSS code, and a single GNSS receiver, multi-GNSS measurements for time transfer could improve reliability and provide better short-term stability. Previous studies applied equal weighting to different GNSS systems or different GNSS time transfer receivers, which, to some extent, revealed the improvement in the additional short-term stability from the combination of two or more kinds of GNSS measurements. In this study, the effects of the different weight allocation for multi-measurements of GNSS time transfer were analyzed, and a federated Kalman filter was designed and applied to fuse multi-GNSS measurements combined with the standard-deviation-allocated weight. Tests with real data showed that the proposed approach can reduce the noise level to well below about 250 ps for short averaging times.

One credible method for performance evaluation of network timing service was proposed, based on one kind of disciplined time standard with GNSS time transfer, NIMDO. The performance of the NTP timing service were characterized over multiple baselines on both the Internet and the Intranet, and the network delay and the timing offset were analyzed in detail. The results show that on the Internet the averaged timing offsets via the NTP servers are roughly hundreds of μs to several ms level, and on the Intranet the averaged timing offsets via the NTP servers are at about 20 μs level. NTP timing service was mainly affected by white phase noise, and flicker phase noise at the different sites. The maximum change of the timing offset was one-half of the maximum change of RT_Delay. The uncertainties have been separately evaluated as less than 30 ms on the Internet and less than 60 μs on the Intranet for NTP timing service.