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The continuously developing Global Navigation Satellite Systems (GNSS), in particular with the latest operational BDS and Galileo, provide good opportunities to enhance the performance of precise positioning. This study evaluates the performance of high-rate precise point positioning (PPP) applied for seismogeodesy with very recent BDS and Galileo. The static experiments with 20-Hz GNSS data show that Galileo and BDS-3/BDS-2 achieve comparable performances, with average 3D RMS values of 0.6–1.3 cm and 0.8–1.2 cm, respectively. In the dynamic experiments, we use a single-axis earthquake simulator of Quanser Shake Table II to simulate seismic waveforms of real earthquakes and collect 20-Hz GNSS data to evaluate the PPP performance. Taking the displacements recorded by the embedded encoder of the shake table as the truth, the accuracies of PPP displacements during the seismic events are 4–8 mm for GPS, 6–9 mm for BDS-2, and 3–6 mm for Galileo and BDS-3/BDS-2. By combining BDS-3 with BDS-2, the positioning accuracy of BDS is improved by 50% with respect to BDS-2 only. Galileo and BDS-3/BDS-2 perform slightly better than GPS, which is likely because the two latest operational systems use the more precise passive hydrogen maser clocks and have lower signal-in-space range error. The multi-GNSS solutions with GPS + Galileo + BDS-3/BDS-2 further improve the accuracy reaching 2–5 mm. We also identify a scale factor in the high-rate PPP displacements, which is probably induced by the dynamic stress error and related to the oscillating frequency. The scale factor reaches the maximum of 1.71 at an oscillating frequency around 2.5 Hz and then descends as the frequency increases. The improved performance of high-rate PPP augmented by the recent BDS-3 and Galileo is helpful to improve the practical level of high-rate GNSS in seismogeodesy and expand its applications to many other high-rate and high-accuracy applications.

We present the results obtained in the course of the development of an optical frequency standard based on cold 87Sr atoms. We describe the parameters of experimental optical schemes developed for the realization of all stages of the consecutive laser cooling and trapping of the 87Sr atoms in the optical lattice. The procedure of clock transition spectroscopy was successfully performed with a spectral transition linewidth of 12 Hz. A measuring complex based on a femtosecond optical frequency synthesizer is developed. This complex enables us to compare the optical frequency standard with a hydrogen maser. The created optical frequency standard on cold 87Sr atoms has been included in the composition of the GET 1-2018 primary standard.

The article presents and summarizes the research results of the UTC-UTC(PL) differences predicting procedure for the Polish Time Scale UTC(PL) developed at the Institute of Metrology, Electronics and Computer Science of the University of Zielona Gora. The research has been conducted in close cooperation with the Time and Frequency Laboratory of Central Office of Measures, responsible for the realization of the UTC(PL). The planned experiment covered a 50-month period, in which the UTC(PL) timescale has been carried out using, as a master clock, atomic clocks with different properties: commercial cesium atomic clock 5071A Opt. 001 (first case) and VCH-1003M hydrogen maser (second and third cases). In case of the developed predicting procedure by means of group method of data handling (GMDH)-type neural network (NN), the transitional period (second case) in which the master clock had been replaced by the new clock, is also very important. For GMDH-type NN, input data as a TS1 and TS2 time series have been prepared, based on the already-known differences of UTC(PL) from UTC and UTC rapid timescales and on determined differences between UTC(PL) and the master clock steering the UTC(PL). The method of preparing TS1 and TS2 time series is an important part of the developed procedure for predicting UTC(PL) differences from UTC, before they will be calculated and published by fr. Bureau International des Poids et Mesures (BIPM). The obtained research results confirmed that the developed predicting procedure by means of GMDH-type NN ensures a proper quality of maintaining the national timescale. The best quality of UTC(PL) predicting has been achieved for the third case, both for data prepared according to the TS1 and TS2 time series. This is confirmed by the calculated values of the prediction quality measures and the Modified Allan deviation. On the other hand, the second case confirmed the possibility of using the proprietary development of the TS2 time series to predict UTC-UTC(k) differences. This time series is a very good alternative for the TS1 time series, when the amount of data in this series is insufficient due to replacement of the clock or its failure.

GNSS positioning relies on orbit and clock information, which is predicted on ground and transmitted by the individual satellites as part of their broadcast navigation message. The predictions are typically refreshed at least once per day and partitioned into short-arc ephemeris data sets covering a representative validity period of 0.5-4 h. For an increased autonomy of either the space or user segment, the capability to predict a GNSS satellite orbit over extended periods of up to two weeks is studied. A tailored force model for numerical orbit propagation is proposed that offers high accuracy but can still be used in real-time environments. Aside from Earth-orientation parameters, six state vector components and three empirical solar radiation pressure parameters are employed for each satellite and adjusted to past orbits. Using the Galileo constellation with its high-grade hydrogen maser clocks as an example, global average signal-in-space range errors of less than 25 m RMS and 3D position errors of less than about 50 m are demonstrated after two week predictions in 95% of all test cases over a half-year period. The autonomous orbit prediction model thus enables adequate quality for a rapid first fix or contingency navigation in case of lacking ground segment updates.

The large volume and weak environmental adaptability of fiber optical frequency combs (OFCs) have become the main obstacles for their applications in various fields. To address these issues, in this study, we present a compact, low-cost f-to-2f interferometer and fiber actuator with a large tuning range and a high control bandwidth for a 200-MHz OFC that is based on a 1.5-μm all-polarization-maintaining fiber mode-locked laser. By employing customized fiber-coupled gradient index lenses, our f-to-2f interferometer is encapsulated in a miniature tube with a diameter of only 4 mm and a length of 40 mm, which substantially reduces the optical section size of the frequency comb as compared to conventional devices. The carrier envelope offset beat with a signal-to-noise ratio of 40 dB is detected in a resolution bandwidth of 360 kHz. In addition, a laboratory-made piezoelectric transducer-driven mechanical actuator for repetition rate regulation exhibited a large tuning range of 106 kHz (corresponding to an effective temperature drift of 53 °C) and a high control bandwidth of approximately 1 kHz. This resulted in a robust repetition rate locking with an Allan deviation of 330 μHz at a gate time of 1 s and a residual integrated timing jitter of 418 fs [3 Hz to 1 MHz] when referenced to a hydrogen maser. Along with reducing the size and improving the environmental adaptability of the OFC, our design can also decrease the power consumption of the system significantly. Our findings provide a new direction to the development of OFCs for various applications.

We characterize a 1.14 μm ultrastable semiconductor laser system for precision spectroscopy of Tm inner-shell clock transition using a frequency comb. We stabilize both the repetition and the carrierenvelope offset frequencies of a commercial Ti : sapphire femtosecond laser to a passive hydrogen maser using a home-built f-2f interferometer. By measuring the absolute frequency of the 1.14 μm laser stabilized to a high-finesse ULE cavity, we determine the zero-expansion temperature point of the cavity and the rate of linear drift of the the cavity resonance frequency due to “aging” of the ULE glass. We achieve less than 10 Hz frequency instability of the laser within 1,000 s after the linear drift compensation. We also measured the absolute frequency of the 1.14 μm transition in Tm to be 262 954 938 269 213(30) Hz.

The Ka-band dual one-way measurements from Inter-Satellite Link (ISL) devices equipped on the third-generation Beidou Navigation Satellite System (BDS3) follow a time division multiple access (TDMA) structure and can calculate inter-satellite and satellite-ground clock offsets. L-band two-way satellite time and frequency transfer (TWSTFT) is also applied for time synchronization between satellites and ground master. We focus on a full-ISL clock offset estimation and prediction algorithm that estimates all satellite clock parameters simultaneously utilizing ISL clock observations and also synchronizes the constellation to the system time in Beidou Time (BDT) using Ka-band satellite-ground clock observations. We discuss the applications of this algorithm by assessing the clock performance of all BDS3 satellites equipped with a passive hydrogen maser (PHM) or rubidium atomic clock. After investigating the proper prediction model for each satellite, we use the full-ISL algorithm for 24-h clock predictions. The constant hardware delays in the ISL measurements are calibrated by comparing the derived clock parameters with TWSTFT measurements; the full-ISL clock products show high accuracy and continuity. The BDS3 PHMs and rubidium clocks both have a small clock rate drift of 10–20 s/s2. The frequency stability of the BDS3 PHMs and some rubidium clocks is approximately 6–9 × 10–15 at 1-day intervals. A linear model is suitable for these small-drift clocks, while a quadratic model is essential for the other rubidium clocks. Applying the full-ISL clock prediction method improves the RMS of the 24 h prediction error from 0.88 to 0.75 ns for PHMs and from 2.62 to 1.64 ns for rubidium clocks. The estimated ISL hardware delay STDs are less than 0.2 ns, and the prediction errors evaluated with TWSTFT clock observations are similar to those evaluated with Ka-band clock observations.

Data from single orbital periods of the two Galileo satellites E14 (GSAT 202) and E18 (GSAT 201) in highly eccentric orbits on 4 separate days during portions of 2018–2021 have been used to test a possible violation of Einstein's General Relativity (GR). Precise Galileo E14 and E18 orbit/clock solutions of 5 Analysis Centers (AC), participating in the Multi-GNSS Experiment (MGEX), have been used in the GR validity (scale) tests. Using the AC clock solutions without any orbit corrections, possible single-orbit GR scale variations were detected at the 1 × 10−4 level with the weighted mean of all single-orbit GR scale solutions of (4.1 ± 1.9) × 10−5. In order to correct for possible orbit errors affecting the AC clock solutions, the 5 AC E14 and E18 orbit/clock solutions have been combined for 3 separate days during 2020–21, approximating the Final GPS orbit/clock combination method routinely performed by the International GNSS Service (IGS). All 5 AC E14 and E18 orbit solutions agreed at the 1–2 cm level and most AC clock solutions agreed within 20–60 ps, which is approaching the precision and consistency of the well matured IGS AC GPS orbit/clock solutions. When the combined E14 and E18 AC clock solutions, corrected for the radial orbital errors obtained from the above orbit combinations, were used in the GR tests, the solution of (3.5 ± 3.3) × 10−5 (implying no GR violation) was obtained, based on 5 orbital periods of E14 and E18, during 2020–2021. These GR tests critically rely on well-behaving and stable Passive Hydrogen Maser (PHM) clocks. The E14 PHM clocks behaved well and within the Galileo PHM specifications during the period of 2018–2021, analyzed here. However, up to about mid-2020, the E18 PHM clock behaved poorly, outside the specifications, and could not be used before mid-2020.

The Passive Hydrogen Maser (PHM) has excellent mid-long term frequency stability. What’s more, it’s small and light. So it is suitable for global navigation satellite system (GNSS). The Galileo is the first GNSS that equips with PHMs on satellites. The BeiDou Navigation Satellite System deploys PHMs in its third generation (BDS-3) too. The full completion of the BDS-3 constellation deployment has accomplished for almost 1 year. How do the PHMs in Beidou-3 running? The telemetries of PHMs onboard will be analyzed to indicate their running status. They are the typical state parameters, including voltage of Oven Controlled Crystal Oscillator (OCXO), voltage of cavity, amplitude of second harmonic and light intensity of ionization source. By checking, filtering, smoothing and modeling the data, the situations of PHMs and their components is clear. Further, they have been extrapolated to see their status in future. It is verified that the PHMs all work well in orbit, and can work for more than 10 years.

A single-state selection system based on the adiabatic rapid passage technique has been designed for active hydrogen masers to improve the frequency stability. This system eliminates more than 96% of undesirable atoms from the beam. State selection effectiveness was determined by measuring generation power as a function of atomic line quality and by the double resonance method for measurement of the population difference of hyperfine sublevels. Frequency stability caused by microwave cavity thermal noises has been improved by a factor of 1.5. Frequency stability of two active hydrogen masers with single- state selection systems was measured. Long-term frequency stability better than 1•10−16 at averaging time 105 s has been achieved in the experiment.

We report the GPS satellite clock estimation using 20 globally distributed receivers with an external hydrogen maser atomic clock. By applying corrections for the Sagnac effect, the relativistic effect due to orbit eccentricity, tropospheric and ionospheric delays, satellite and receiver antenna phase center offsets and variations, solid earth tides, ocean tide loading, phase wind-up effect, and P1-C1 bias, our satellite clock results matches the IGS final clock product within ± 1.4 ns with comparable frequency stability for an averaging time of less than 1000 sec and a 10–30% worse frequency stability for an averaging time of greater than 1000 sec, on MJD 58244. This small atomic clock network results in a fast computation that becomes increasingly appealing when the real-time satellite orbit and clock estimation is needed and as the GNSS constellations and the GNSS signals expand.

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8x10$^{-13}$/$\sqrt{\tau}$ for times less than 100 s and a flicker noise floor of 1x10$^{-14}$ out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the AC Stark shift. The retrace was measured to 5.7x10$^{-13}$ after 30 hours of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the SI meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser., Comment: 5 pages, 5 figures

Active hydrogen maser is the main frequency standard for establishing and maintaining the time scale. It has the characteristics of high short-term stability and low phase noise. At present, it plays an increasingly important role in the international atomic time (TAI) and various local time scales. Firstly, in combination with the internal state parameters of an active hydrogen maser, the correlation between the internal state parameters and the comparison data of a hydrogen maser is analyzed, and a method for the performance monitoring of a hydrogen maser is proposed. Secondly, according to the characteristics of hydrogen maser performance, a method for evaluating the performance of a hydrogen maser is given. The hydrogen maser performance includes mainly two aspects, namely the frequency stability and predictability. The performances of two types of active hydrogen masers (CH1-75 and MHM-2010) are evaluated by this method. The correlation analysis of the atomic clock state parameters and comparison data shows that the state parameter monitoring can effectively predict the variation of the hydrogen maser performance. The evaluation results of atomic clock frequency stability and predictability show that the atomic clock with a higher medium-and-long term frequency stability has a better predictability. There are two methods for the predictability evaluation, one is based on the data published by BIPM (Bureau International des Poids et Measures), and another one is based on the quadratic model. Both methods are consistent with the weights published by BIPM. Therefore, the two methods can be used as a quantitative method to evaluate the predictability of a hydrogen maser.

In the past decade, the research on optical frequency comb and its applications has achieved rapid development, bringing revolutionary progress to the metrology field. Frequency stabilization and absolute frequency measurement of the CW laser through optical frequency combs is very important for establishing new length standards. A tunable near-infrared CW laser is phase locked to a commercial optical frequency comb referring to a Rubidium atomic clock for frequency stabilization. A home-made comb is phase locked to a hydrogen maser for measuring the absolute frequency of the frequency stabilized CW laser obtained. The procedure of frequency stabilization and absolute frequency measurement based on optical frequency combs is demonstrated and the uncertainty and stability of the frequency stabilized CW laser are estimated.

The optical lattice clock NICT-Sr1 [1] regularly reports calibration data for the international atomic time TAI, obtained by intermittent measurements of a flywheel hydrogen maser. Continuous frequency measurements of this maser against the local UTC(NICT) and a GNSS satellite link then provide a traceable chain to UTC, which differs from TAI by the number of accumulated leap seconds, but shares its frequency. By using data publicly available from the International Bureau of Weights and Measures (BIPM), we extend the chain to eight individual primary frequency standards that reported calibration data for suitably similar intervals. For 63 such directly traced comparisons, we individually determine nine uncertainty contributions, including clock statistical and systematic uncertainties, the satellite link instability, and operating interval extrapolations that address measurement deadtime and mismatched evaluation periods. A covariance matrix constructed from these contributions addresses correlated and uncorrelated uncertainties. A suitable distribution of weights is found by a least-squares approach based on the Gauss-Markov theorem. Direct tracing to individual primary standards allows a flexible choice of evaluation intervals and provides results in terms of the nominal SI second even when the BIPM calculation of the TAI scale interval error includes contributions of secondary standards. From 776 hours of strontium clock data acquired over four years, we thus find the absolute frequency of the 87Sr clock transition to be f(Sr) = 429 228 004 229 873.08(8) Hz [2], with a fractional uncertainty of less than 1.8e-16, approaching the systematic limits of the best realizations of the SI second. The evaluation shows no statistical anomalies or significant variation over time. Our result is consistent with a recent measurement performed at PTB [3] against local primary standards, which determined the 87Sr clock transition frequency as f(Sr@PTB) = 429 228 004 229 873.00(7) Hz. A loop closure over the absolute frequencies of 87Sr, 171Yb [4,5] and direct optical measurements of their ratio [6] also finds excellent consistency. If this level of agreement between independent measurements is reflected in a revision of the recommended frequencies provided by the International Committee of Weights and Measures (CIPM), it will support optical lattice clocks operating as frequency standards with absolute uncertainties of 2e-16 or below, outperforming all but the best cesium clocks even before a redefinition of the SI second. References: [1] H. Hachisu et al. “SI-traceable measurement of an optical frequency at the low 10?16 level without a local primary standard“, Opt. Express 25 8511–23 (2017) DOI: 10.1364/OE.25.008511 [2] N. Nemitz et al. “Absolute frequency of 87Sr at 1.8 × 10?16 uncertainty by reference to remote primary frequency standards”, submitted to Metrologia arXiv:2008.00723 (2020); [3] R. Schwarz et al. “Long term measurement of the 87Sr clock frequency at the limit of primary Cs clocks”, Phys. Rev. Res. 2, 033242 (2020) DOI: 10.1103/PhysRevResearch.2.033242 [4] W. F. McGrew et al. “Towards the optical second: verifying optical clocks at the SI limit”, Optica 6 448-454 (2019) DOI: 10.1364/OPTICA.6.000448 [5] M. Pizzocaro et al. “Absolute frequency measurement of the 1S0–3P0 transition of 171Yb with a link to international atomic time”, Metrologia 57 035007 (2020) DOI: 10.1088/1681-7575/ab50e8 [6] Boulder Atomic Clock Optical Network, “Frequency ratio measurements with 18-digit accuracy using a network of optical clocks“ arXiv: 2005.14694 (2020)