Time Transfer Link Research Articles

A 6 month-long real-time time scale steered to NIM-Sr1 optical lattice clock

Abstract NIM-Sr1 optical lattice clock has been operated intermittently for seven consecutive months with an operation uptime around 13.8%, which serves as the reference to steer a hydrogen maser for generating a real-time time scale TS(Sr1). The peak-to-peak time difference of TS(Sr1) compared to UTC is 1.8 ns within 180 days and is less than 0.5 ns within the last month, after correcting the time error induced by a time transfer link abnormality. A dedicated automation system with hardware and software is developed to monitor the operation status of NIM-Sr1, process the measurement data, and periodically predict the hydrogen maser frequency. According to the simulation results, a composite algorithm based on both Kalman filtering (KF) and weighted least squares fitting (WLSF) is utilized for generating TS(Sr1). The KF is utilized when the unavailability of NIM-Sr1 is shorter than one day, and the WLSF with fitting interval T fit=30 d is utilized in other conditions leveraging the long-term predictability of the hydrogen maser. In addition, it is demonstrated by simulation and the post-processing of earlier experimental data that, a time scale with smaller time error can be achieved by shortening the WLSF interval from 30 days to about 5 days under the condition of sufficient measurement data points for reducing the statistical error.

Automatic Detection of Anomalies in Post-Processed Data Applied to UTC Time Transfer Links.

In this article, we present a method for identifying anomalies, particularly time steps, which can affect data. Recognition of these anomalies is essential for understanding the intrinsic nature of problems that may occasionally affect the data, and for guaranteeing system reliability and accuracy. The tool presented, based on the Kalman filter, is optimized to work with post-processed data which means that the dataset is available at the time the algorithm is run. The main aim is to retain as much data as possible, while detecting anomalies, and avoid deleting valuable data. The originality of this tool with respect to the already existing Kalman-filter-based tools for detecting anomalies is substantial, because its objective is not only to enable the system to run but also to avoid unnecessary deletion of valuable data. This tool is designed to accurately determine the date of occurrence and magnitude of these anomalies, focusing on time steps. The tool presented will be applied, by way of example, to the time links used in Coordinated Universal Time (UTC) as calculated by Bureau International des Poids et Measures (BIPM), Paris, France. In addition, the algorithm developed will enable the BIPM's Time Department to be rapidly alerted to unexpected behavior that may compromise UTC performance. To guarantee the reliability and accuracy of UTC, rigorous data validation and rapid problem identification are essential.

A Relativistic Framework to Estimate Clock Rates on the Moon

As humanity aspires to explore the solar system and investigate distant worlds such as the Moon, Mars, and beyond, there is a growing need to estimate and model the rate of clocks on these celestial bodies and compare them with the rate of standard clocks on Earth. According to Einstein’s theory of relativity, the rate of a standard clock is influenced by the gravitational potential at its location and its relative motion. A convenient choice of local reference frames allows for the comparison of local time variations of clocks due to gravitational and kinematic effects. We estimate the rate of clocks on the Moon using a locally freely falling reference frame coincident with the center of mass of the Earth–Moon system. A clock near the Moon’s selenoid ticks faster than one near the Earth’s geoid, accumulating an extra 56.02 μs day−1 over the duration of a lunar orbit. This formalism is then used to compute the clock rates at Earth–Moon Lagrange points. Accurate estimation of the rate differences of coordinate times across celestial bodies and their intercomparisons using clocks on board orbiters at Lagrange points as time transfer links is crucial for establishing reliable communications infrastructure. This understanding also underpins precise navigation in cislunar space and on celestial bodies’ surfaces, thus playing a pivotal role in ensuring the interoperability of various position, navigation, and timing systems spanning from Earth to the Moon and to the farthest regions of the inner solar system.

Study of high-precision time transfer method enhanced by PPP-AR/PPP-RTK

Abstract With the continuous development and improvement of Global Navigation Satellite Systems (GNSS), the use of GNSS for high-precision time transfer has become increasingly mature. To delve into the contribution of information-enhanced GNSS PPP to time transfer performance, this paper focuses on the comprehensive evaluation and analysis of the time transfer performance of PPP-AR and PPP-RTK. Using GPS as a case study, experimental results demonstrate that the average success fixing rate of PPP integer ambiguity resolution across five stations is 93.57%, with initial fixing times consistently below 20 minutes. The stability of the station clock offset sequence of PPP-AR is better than that of PPP floating solution. Compared with the PPP floating solution, the average improvement of PPP-AR stability is 16.54%. Furthermore, using PPP-AR for time transfer not only enhances the stability of the time transfer link clock offset sequence, but also improves its noise level. The stability is increased by 14.41% on average, and the noise level is improved by 9.11% on average. PPP-RTK also improves the stability and noise level of time transfer even better than PPP-AR. However, as the reference network scale increases, the accuracy of the interpolated atmospheric delay correction decreases, impacting the performance of PPP-RTK.

Transferring time and frequency signal through phase compensated telecommunication fibres

Precise time and frequency signal transfer over White Rabbit Precision Time Protocol (WRPTP) based underground optical fibre link has been experimentally demonstrated for its potential enhancement and better signal integrity. In order to prove its advantages in practical applications, the time synchronization performance of WRPTP-based underground telecommunication optical fibre links have been examined in controlled environment conditions as well as in varying ambient conditions. Under controlled environment conditions, time synchronization has been achieved within ± 100 ps uncertainty but variation in ambient conditions degrades the stability as well accuracy of the time transfer link. The introduction of active phase variation compensation enhances the accuracy by ∼ 66 % of the WRPTP-based underground time transfer link. The link’s instability in terms of Modified Allan deviation reaches to 2.0 E -15 from 7.5 E -15 at 4096 s of integration time which indicate that dynamic phase variation compensation improves the stability of WRPTP-based time transfer link under varying ambient conditions.

Time Transfer Link fusion algorithm based on wavelet multi-resolution analysis

To raise the precision and stability of time transfer links, a wavelet-based multi-resolution data fusion technique is offered. This approach fixes the “Day-Boundary discontinuities” in global positioning system (GPS) precise point positioning (PPP) link and lessens the diurnal in Two-way satellite time and frequency transfer (TWSTFT) link by integrating the model-based dynamic system analysis method with the statistically based multi-scale signal transformation method. It can also handle data from GPS PPP links and TWSTFT links at different sampling rates. More specifically, after applying wavelet transformation to the raw data and Kalman filtering estimation on various scales, this method uses the Mallat fast reconstruction algorithm of wavelet transform to achieve the fused results. The National Time Service Center (NTSC) and the Physikalisch-Technische Bundesanstalt (PTB) handle time transfer results using this method. Experiments show that this strategy greatly improves the link's short-term stability and can manage atypical interruptions while also boosting the link's robustness and reliability, which has a wide range of possible applications.

Improved performance of BDS-3 time and frequency transfer based on an epoch differenced model with receiver clock estimation

The carrier phase (CP) technique based on the BeiDou Global Satellite Navigation System (BDS-3) has proven to be a crucial spatial tool for remote time and frequency transfer. The current CP technique models the receiver clock offset as a white noise stochastic process and easily absorbs some unmodeled errors, thus compromising the time and frequency transfer performance. To further improve the performance of time and frequency transfer, a new BDS-3 receiver clock estimation algorithm based on the epoch difference (ED) model is presented, and the mathematical principles and applied modes are discussed. The algorithm makes full use of both observations of the current epoch and practical variations of the receiver clock offset, further improving the performance of time and frequency transfer. Five Multi-Global Navigation Satellite System Experiment network stations equipped with various types of receivers and antennas with dual-frequency BDS-3 signals were used to establish four time transfer links (i.e., AMC4–PTBB, BRUX–PTBB, OP71–PTBB, and WTZS–PTBB) to evaluate their effectiveness. The ED model improves all the four time links in terms of noise level, with improvements of 17.0%, 18.3%, 20.3%, and 5.9%, respectively, when compared with the results from a non-ED model. The ED model outputs were better than the raw solutions in terms of frequency stability at all time links, particularly for average time intervals (tau) < 1000 s. The mean improvement was 8.1% for AMC4–PTBB, 16.1% for BRUX–PTBB, 10.0% for OP71–PTBB, and 18.6% for WTZS–PTBB when the average time (tau) was less than 1000 s.

Galileo E3 Total Time Delay Calibration in NTSC Time and Frequency Comparison

In order to improve the reliability of the time transfer link, Bureau International des Poids et Mesures (BIPM) has offcially taken the Galileo time comparison as the backup link for UTC calculation since 2020. Therefore, Galileo calibration of receiver is a necessary work for all timekeeping labs around the world to participate in the UTC link. Taking the GPS link calibrated by Physikalisch-Technische Bundesanstalt (PTB) and the National Time Service Center (NTSC) as reference, this paper sets PT09 as reference station to calibrate and verify the Galileo E3 (E1&E5a) total delay of NT02 and NT05 receivers from NTSC. The results show that the Galileo E3 total delay of NT02 and NT05 are 74.6 ns and 46.5 ns, respectively, the calibration uncertainty is 3.5 ns, and the calibration delay is relatively stable. After calibration, GPS P3 and Galileo E3 Common View results between NT02/NT05 and calibrated receivers of other timekeeping labs are basically consistent. Taking the GPS P3 links comparison results as reference between NTP3 and receivers from other labs, the average deviation is less than 1.5 ns, which is within the calibration uncertainty range.

Undifferenced precise time transfer with information‐constraints

AbstractSatellite navigation systems enable long‐distance and high‐precision time transfers. The authors proposed an undifferenced precise time transfer method with information constraints in this study. A more accurate receiver clock offset can be obtained by constraining the station coordinate parameters and receiver clock offset parameters to achieve a precise time transfer. In this example, the research object is the time transfer link established by the Global Positioning System observation station using a caesium clock, rubidium clock, and hydrogen clock. The clock difference sequence of the time‐transfer link was calculated by combining the observation data and precise products. Following analysis of the examples, the following conclusions were reached. The undifferenced precise time transfer method based on information constraints can effectively be used to smooth the clock difference sequence of the receiver and the clock difference sequence of the time transfer link. To some extent, this method can also be used to reflect the performance of atomic clocks at Global Positioning System stations and is better suited for the precise time transfer of the equal‐clock long‐baseline time transfer link. Simultaneously, the frequency stability of this method is improved significantly in the short term compared to the traditional scheme without any constraints. The improvement of frequency stability is helpful to improve the accuracy of time transfer.

Time transfer with BDS-3 signals: CV, PPP and IPPP

The third phase of BeiDou navigation satellite system (BDS-3) was officially commissioned on 31 July 2020. In this study, we make a comprehensive evaluation of BDS-3 time transfer with the B1I, B3I, B1C and B2a measurements. The multi-path (MP) errors and noises of different BDS-3 ranging signals are analyzed to illustrate characteristic of the code observations firstly. Then dual-frequency ionosphere-free linear combinations of BDS-3 B1I&B3I and B1C&B2a measurements are used to achieve time transfer. Using Multi-GNSS Experiment station observations, we evaluate the performance of BDS-3 time transfer with common-view (CV), precise point positioning (PPP) and integer ambiguity PPP (IPPP) techniques. Analysis results show that BDS-3 B1C&B2a CV time transfer links show a better performance than GPS L1P&L2P links, whereas BDS-3 B1I&B3I links are worse than GPS links. For the PPP time transfer, GPS links show the best performance, followed by BDS-3 B1C&B2a links and B1I&B3I links. Furthermore, frequency stability of BDS-3 IPPP time transfer is more stable than PPP solutions at the long average interval time. And the long-term frequency stability of BDS-3 IPPP is comparable with GPS IPPP.

A three-cornered hat analysis of instabilities in two-way and GPS carrier phase time transfer systems

A three-cornered hat analysis has been performed on three independent time transfer systems between the United States Naval Observatory (USNO) and the National Institute of Standards and Technology (NIST). These include (1) a direct Two-Way Satellite Time and Frequency Transfer (TWSTFT) link provided by the USNO, (2) an indirect TWSTFT link, and (3) GPS carrier phase (GPSCP) links. Time transfer instabilities for individual links, as quantified with the time deviation and TOTAL time deviation, have been measured for the first time for averaging periods between 2 h and 85 days. Time transfer instabilities beyond one day are roughly flicker phase in nature and generally range between 40 ps and 120 ps. Frequency transfer instabilities, as quantified by the modified Allan deviation, are observed to be as low as 1 × 10−16 for a 20 day comparison and into the mid 10−17 range at longer comparison times.

Performance of Multi-GNSS Real-Time UTC(NTSC) Time and Frequency Transfer Service Using Carrier Phase Observations

The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and clock determinations has enabled GNSS time and frequency transfer using the CP technique to be performed in real-time mode, without any issues associated with latency. In this contribution, we preliminarily built the prototype system of real-time multi-GNSS time and frequency transfer service in National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS), which undertakes the task to generate, maintains and transmits the national standard of time and frequency UTC(NTSC). The comprehensive assessment of the availability and quality of the service system were provided. First, we assessed the multi-GNSS state space representation (SSR) correction generated in real-time multi-GNSS prototype system by combining broadcast ephemeris through a comparison with the GeoForschungsZentrum (GFZ) final products. The statistical results showed that the orbit precision in three directions was smaller than 6 cm for global positioning system (GPS) and smaller than approximately 10 cm for BeiDou satellite system (BDS). The root mean square (RMS) values of clock differences for GPS were approximately 2.74 and 6.74 ns for the GEO constellation of BDS, 3.24 ns for IGSO, and 1.39 ns for MEO. The addition, the GLObal NAvigation Satellite System (GLONASS) and Galileo satellite navigation system (Galileo) were 4.34 and 1.32 ns, respectively. In order to assess the performance of real-time multi-GNSS time and frequency transfer in a prototype system, the four real-time time transfer links, which used UTC(NTSC) as the reference, were employed to evaluate the performance by comparing with the solution determined using the GFZ final products. The RMS could reach sub-nanosecond accuracy in the two solutions, either in the SSR or GFZ solution, or in GPS, BDS, GLONASS, and Galileo. The frequency stability within 10,000 s was 3.52 × 10−12 for SSR and 3.47 × 10−12 for GFZ and GPS, 3.63 × 10−12 for SSR and 3.53 × 10−12 for GFZ for BDS, 3.57 × 10−12 for SSR and 3.52 × 10−12 for GFZ for GLONASS, and 3.56 × 10−12 for SSR and 3.48 × 10−12 for GFZ for Galileo.

Studies on Temperature Sensitivity of a White Rabbit Network-Based Time Transfer Link

Studies on Temperature Sensitivity of a White Rabbit Network-Based Time Transfer Link

Optimization of time and frequency fiber-optic links exploiting bi-directional amplifiers, based on real-time performance measurement

Long-distance fiber-optic time and frequency transfer links exploit bi-directional optical amplifiers whose gains need to be optimized to limit the noise propagating along with the desirable signals. Unlike the usual optimization of such links that are based on simulations or on a trial and error approach, we propose here a technique where the link is initially set-up with a pre-set algorithm, using optical powers measured in the amplifiers installed along the link. After that the final optimization is performed based on jitters measured in the end terminals of the link with a dedicated hardware. All the required parameters (i.e. the optical powers and jitters) are measured in a real-time in a live link. Various methods of assessment of the link performance, using the jitter measurements performed either in one or both end terminals, as well as various optimization criteria (like minimax, square root of sum of RMS jitters or analysis of a single-end jitter measurements), are investigated. The developed procedures were tested experimentally in the laboratory and also during a field trial in a real fiber telecom infrastructure. Obtained results (55% jitter reduction, 7 dB SNR improvement, comparing to the link state after its initial set-up) suggest that the proposed solutions allow optimizing effectively the link performance and may be used to supplement or replace simulation methods, particularly on initial start-up or when reconfiguring the link (e.g. due to a link route modification or after a fiber break).

High-precision dual-wavelength time transfer via1085-km telecommunication fiber link

To reduce the influence of fiber dispersion on accuracy of fiber-based time synchronization, a method of dispersion-error corrected dual-wavelength time synchronization is proposed in this paper. Specificlly, the method is to measure the dispersion coefficient of the fiber link, and then input it to each remote terminal, the time delay error caused by the fiber dispersion is eliminated through the delay phase controller. With the self-developed engineering prototypes, the experimental verifications are subsequently made both in laboratory and real field. Before the test, 16 devices of time synchronization are connected in series for calibration. The time synchronization system is able to keep delay difference within ± 15 ps after being calibrated. In the laboratory, the experimental setup is built by cascading 16 rolls of 50km-long fiber coils, and the total length of the fiber link is 800 km. The experimental results show that the dispersion coefficient of 800 km fiber link is 13.36 ps/(km·nm), and the delay error caused by dispersion is maintained within 10 ps after correction. The stability of the time transfer is 5.7 ps in standard deviation and the time deviation is 1.12 ps at an averaging time of 100000 s. In the real field test, a 1085-km-long field fiber link is utilized, along which 16 self-developed time-frequency transceiversare set at the cascaded fiber-optic stations. After being corrected with a dispersion coefficient of 16.67 ps/(km·nm) for 1085 km urban fiber link, the time transfer is demonstrated to have a dispersion-caused delay error of 60 ps. The experimental results show that the time standard deviation is 18 ps and the time transfer instability is 9.2 ps at an averaging time of 1 s and 5.4 ps at an averaging time of 40000 s. Finally, the time uncertainty of 800-km-long laboratory optical fiber link and 1085-km-long urban optical fiber link are evaluated, and the time uncertainty is 18.4 ps and 63.5 ps, respectively. This work paves the way for constructing the time synchronization fiber network in China. To further reduce the delay error caused by dispersion in a long-distance time transfer link, the more accurate thermal control of the lasers should be adopted to reduce the shifts of forward and backward wavelengths.

Performance Optimization Method of Two-Way Satellite Time and Frequency Transfer Link based on Conditional Adjustment

Two-Way Satellite Time and Frequency Transfer (TWSTFT) is one of the time transfer methods with the highest accuracy at present, and it is also the main method to compare the atomic time scale among the time-keeping laboratories participated in the international atomic time calculation. Improving the short-term stability of TWSTFT links and reducing the influence of Diurnal on the link time transfer result have practical significance for optimizing the performance of TAI (International Atomic Time). In this paper, a method of TWSTFT link performance optimization based on conditional adjustment is proposed. Firstly, the optimized network of TWSTFT link performance (hereinafter briefly called as optimized network) is established according to the noise level and spectrum analysis result of TWSTFT link measurements, and then the weight coefficient matrix is set according to the analysis result of measurement noises of all the links in the optimized network to establish the conditional adjustment model. The Two-Way Satellite Time and Frequency Transfer link between the National Institute of Metrology (NIM) and the National Time Service Center (NTSC) of Chinese Academy of Sciences in the Asia-Pacific region is selected as the link to be optimized, and the TWSTFT links among NTSC, NIM, and Physikalisch-Technische Bundesanstalt (PTB) are used to compose the optimized network. The networking method and conditional adjustment model are verified by experiments. The results show that the short-term stability of the link to be optimized after adjustment is improved, and the influence of Diurnal is reduced about 24.6%. Using this method, the time transfer performance of the link to be optimized can be improved effectively.

Effect of atmospheric turbulence on timing instability for partially reciprocal two-way optical time transfer links

In this paper we analyze the limits of optical time transfer through atmospheric turbulence and relate those predictions to timing uncertainty analysis using the Allan timing variance (TVAR). The power spectrum of timing uncertainty due to atmospheric turbulence is expressed with the help of Taylor's frozen flow hypothesis, identifying a ${f}^{\ensuremath{-}8/3}$ and ${f}^{\ensuremath{-}2/3}$ power-law behavior for uncorrelated and partially correlated turbulence, respectively. The scaling of each power law is related to the geometry of the link and the turbulence profile. The power-law slopes are used to calculate two TVAR scaling coefficients relevant to turbulence timing noise, ${c}_{5/3}$ and ${c}_{\ensuremath{-}1/3}$, which can be applied to time-transfer analysis of timing data affected by turbulent fluctuations. Examples of a 2-km horizontal partially overlapping two-way link estimate the atmospheric contribution to timing fluctuations to be below $10\phantom{\rule{4pt}{0ex}}\mathrm{fs}$, while a two-way link to a medium-Earth-orbit satellite experiences timing fluctuations on the order of $2\phantom{\rule{4pt}{0ex}}\mathrm{fs}$. Comparison of turbulence theory to a recent two-way optical time transfer experiment shows good agreement with the expected power-law behavior and scaling factors.

Multi-GNSS time transfer based on the CGGTTS

This paper studies the use of multiple GNSS constellations for time transfer. The performances of each constellation are compared to one another. We show that, with its current constellation, Galileo already provides time transfer results with the same or better performances than GPS, for which some time links are affected by a diurnal variation. The paper also investigates different ways of combining the constellations into one global time transfer solution. We show that in a global AV solution, only one constellation should be calibrated, due to the inherent inter-system biases in the multi-GNSS clock products. Our results show that the best combination is to use the Galileo solution as a reference, and to combine the observations applying one bias (with respect to Galileo) per satellite of the other constellations. This allows reducing the impact of diurnal variations present in some GPS clock solutions. Combining Galileo and GPS satellites in this way improves the time transfer link with respect to the GPS-only or Galileo-only solutions. Adding moreover BeiDou-2 and GLONASS satellites gives, depending on the link, a solution similar or worse than the solution obtained from GPS and Galileo.

Study of the GPS inter-frequency calibration of timing receivers

When calibrating Global Positioning System (GPS) stations dedicated to timing, the hardware delays of P1 and P2, the P(Y)-codes on frequencies L1 and L2, are determined separately. In the international atomic time (TAI) network the GPS stations of the time laboratories are calibrated relatively against reference stations. This paper aims at determining the consistency between the P1 and P2 hardware delays (called dP1 and dP2) of these reference stations, and to look at the stability of the inter-signal hardware delays dP1–dP2 of all the stations in the network. The method consists of determining the dP1–dP2 directly from the GPS pseudorange measurements corrected for the frequency-dependent antenna phase center and the frequency-dependent ionosphere corrections, and then to compare these computed dP1–dP2 to the calibrated values.Our results show that the differences between the computed and calibrated dP1–dP2 are well inside the expected combined uncertainty of the two quantities. Furthermore, the consistency between the calibrated time transfer solution obtained from either single-frequency P1 or dual-frequency P3 for reference laboratories is shown to be about 1.0 ns, well inside the 2.1 ns uB uncertainty of a time transfer link based on GPS P3 or Precise Point Positioning. This demonstrates the good consistency between the P1 and P2 hardware delays of the reference stations used for calibration in the TAI network.The long-term stability of the inter-signal hardware delays is also analysed from the computed dP1–dP2. It is shown that only variations larger than 2 ns can be detected for a particular station, while variations of 200 ps can be detected when differentiating the results between two stations. Finally, we also show that in the differential calibration process as used in the TAI network, using the same antenna phase center or using different positions for L1 and L2 signals gives maximum differences of 200 ps on the hardware delays of the separate codes P1 and P2; however, the final impact on the P3 combination is less than 10 ps.

Large-dynamic-range time pre-compensation scheme for fiber optic time transfer

In this paper we experimentally demonstrate a transmission delay compensation scheme for precise fiber-optic time transfer. The scheme is based on a clock counter and an electronic variable delay line, which theoretically can provide unlimited compensation range. We perform successive tests in three optical fiber links of different lengths in which both continuous drifts and abrupt hop of the transmission delay are effectively compensated. The total transmission delay variation induced in the experiments is much larger than most of the reported cases. This large-dynamic compensation scheme is quite suitable for time transfer links whose transmission delay varies a lot.