Accurate Time Transfer Research Articles

Improving PPP timing and time transfer based on signal distortion biases calibration

Abstract Precise point positioning (PPP) technology has been widely used for more than a decade in timing and time transfer. Pseudorange bias caused by signal distortion will reach up ±3 ns, which cannot be neglected in sub-nanosecond level PPP timing and time transfer. We propose to improve the performance of PPP timing and time transfer by considering signal distortion bias (SDB). In principle, SDB will affect PPP timing and time transfer by influencing the initial clock offset. Then, it is verified by theoretical and experimental analyses. The theoretical results show that the impact of SDB on PPP timing can reach up 1.8 ns in different regions. Also, the impact of SDB on time transfer can reach up 0.8 ns in different regions even if the baseline length and receiver types are the same. For experimental results, the accuracy of PPP timing and time transfer improves with SDB correction. For time transfer, the RMSs are reduced by 54.8%, 61.1% and 17.6% for GPS, BDS3 and Galileo in all links, respectively. The clock frequency consistency obtained from different systems has been improved. And the frequency stability of time link with Hydrogen clocks is improved by 53.0% at 10000s interval with SDB correction.

GNSS carrier phase common-view precision time transfer using the ionospheric-weighted single-differenced model

ABSTRACT High-precision global navigation satellite system (GNSS) time transfer depends on the carrier phase observations, and ionospheric delay affects rapid integer ambiguity resolution. Therefore, this work applies the ionospheric-weighted single-differenced model. Experimental results indicate that for a time-link of 67.9 km, the time transfer accuracy of different single-system is better than 0.03 ns. Compared with single-system, multi-system demonstrates 8% to 14% improvement in accuracy and improvement of no more than 31% in frequency stability. Additionally, compared with the case without ionospheric constraint, imposing ionospheric constraints can improve performance of time transfer, but the gain decreases as the time-link length increases.

Improved Simulated Annealing Algorithm on the Design of Satellite Orbits for Common-View Laser Time Transfer

Laser Time Transfer (LTT) has proven to be able to improve remote time transfer accuracy compared to microwave technology. The impact of satellite clock errors and atmospheric delays during LTT will be further reduced in the common-view mode. The challenge is presented as an optimization problem that is limited by satellite trajectories. This paper introduces an improved simulated annealing algorithm designed to maximize the common-view possibility among various station pairs within regional Satellite Laser Ranging (SLR) networks by optimizing satellite orbit trajectories. The study proposes a system model that integrates LTT principles with satellite visibility considerations. The simulated annealing algorithm is improved with new annealing strategies that incorporate control strategies, and modify the cooling function. Comparative simulation analyses demonstrate the effectiveness of the algorithm, resulting in a significant reduction in computation time by over 10 times. The optimized orbits exhibit common-view windows between 3.337 and 8.955 times longer than existing orbits. Further simulations are conducted to optimize the orbits, and common-view models are established for 45 pairs among 10 stations. The optimizations result in common-view times ranging from 6.183 to 60.633 min in the Asia-Pacific region and from 5.583 to 61.75 min in the Europe-to-Asia region. This can provide valuable references for designing satellite constellations.

An Interstation Undifferenced Real-Time Time Transfer Method with Refined Modeling of Receiver Clock

Due to their advantages of high measurement accuracy and wide coverage, global navigation satellite systems (GNSSs) can carry out long-distance time transfers, among which the precise point positioning (PPP) method is widely used. However, the accuracy and stability of PPP real-time time transfer are restricted by the real-time satellite clock offset products. In addition, the receiver clock offset is usually estimated using the white noise model, which ignores the correlation of the clock offsets between adjacent epochs and the stability of the atomic clock itself. In order to obtain higher performance time transfer results, we propose an interstation undifferenced time transfer method with refined modeling of the receiver clock. This method takes the satellite clock offset as the parameter to be estimated, which can avoid the influence of external satellite clock offset products. In addition, the refined modeling of the receiver clock can improve the strength of the model and the accuracy of time transfer. Based on the ultrarapid satellite orbit products provided by the International GNSS Service (IGS), time transfer experiments are carried out using data from IGS observatories and self-collected data. The results show that sub-nanosecond accuracy can be achieved in real-time time transfer using this method. Compared with the traditional PPP model, the accuracies of the four time links are increased by 88.4%, 92.9%, 88.6%, and 74.5%, respectively, and the stability is increased by approximately 66.4% on average. Moreover, after applying the clock offset constraint model, frequency stability is further improved, in which the short-term stability is improved significantly, with a maximum of 86.9% and an average improvement of approximately 66.8%.

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.

100 Picosecond/Sub-10−17 Level GPS Differential Precise Time and Frequency Transfer

A Global Navigation Satellite System (GNSS) is a high-precision method for comparing clocks and time transfer. The GNSS carrier phase can provide more precise observable information than pseudorange. However, the carrier phase is ambiguous, and only pseudorange can provide the absolute time difference between two clocks. In our study, by taking full advantage of GNSS pseudorange and carrier-phase observables, a differential precise time transfer (DPT) method with a clustering constraint was employed to estimate the time difference between two clocks, aiming to achieve accurate and precise time and frequency transfer. Using this method, several time transfer results were analyzed for different baselines. For the common clock experiment, the time transfer results showed good consistency across different days, with an intra-day accuracy of within 20 ps. Furthermore, we evaluated the self-consistency of DPT using closure among three stations. DPT closure of the three stations had a peak-to-peak value of closure of about 25 ps. The closure did not change over time, indicating the self-consistency of the DPT processing in time transfer. Moreover, our results were compared to station clock solutions provided by the International GNSS Service (IGS), and the standard deviations (STDs) of the four baselines were all less than 100 ps within one month, confirming the time and frequency stability of the DPT method. In addition, we found that the time stability of DPT was less than 20 ps within one week. As for frequency stability, DPT achieved a 10−16 level of modified Allan deviation (MDEV) at an averaging time of about 1 day and a sub-10−17 level at an averaging time of one week.

GNSS/RNSS Integrated PPP Time Transfer: Performance with Almost Fully Deployed Multiple Constellations and a Priori ISB Constraints Considering Satellite Clock Datums

Currently, the space segment of all the five satellite systems capable of providing precise time transfer services, namely BDS (including BDS-3 and BDS-2), GPS, GLONASS, Galileo, and Quasi-Zenith Satellite System (QZSS), has almost been fully deployed, which will definitely benefit the precise time transfer with satellite-based precise point positioning (PPP) technology. This study focuses on the latest performance of the BDS/GPS/GLONASS/Galileo/QZSS five-system combined PPP time transfer. The time transfer accuracy of the five-system integrated PPP was 0.061 ns, and the frequency stability was 1.24 × 10−13, 2.28 × 10−14, and 8.74 × 10−15 at an average time of 102, 103, and 104 s, respectively, which significantly outperforms the single-system cases. We also verified the outstanding time transfer performance of the five-system integrated PPP at locations with limited sky view. In addition, a method is proposed to mitigate the day-boundary jumps of inter-system bias (ISB) estimates by considering the difference in the satellite clock datums between two adjacent days. After applying a priori ISB constraints, the time transfer accuracy of the five-system integrated PPP can be improved by 37.9–51.6%, and the frequency stability can be improved by 14.8–21.6%, 5.3–7.6% and 20.0–29.6% at the three average times, respectively.

BDS/QZSS integrated PPPAR time–frequency transfer

Based on BeiDou navigation satellite system (BDS), the Quasi-Zenith satellite system (QZSS) was added to assist in studying the precise point positioning (PPP) time and frequency transfer effect. Ambiguity resolution (AR) is the key to the rapid conversion of the PPP method. Therefore, this paper also used the ionospheric-free combination and the observable-specific signal bias (OSB) product of Wuhan University to test the time–frequency transfer effect of BDS ambiguity-fixed. In this way, BDS PPP, BDS + QZSS PPP, BDS PPP-AR, and global positioning system (GPS) PPP methods were formed. Six stations located in Japan and Australia were selected for experiments. Conclusion: BDS can reach the same level as GPS; when the cut-off angle is greater than 15°, adding QZSS could improve the success rate, accuracy, and frequency stability of the solution of time links effectively; the ambiguity fixed strategy can improve the time transfer accuracy but not the short-term frequency stability.

BDS-3 RDSS two-way time transfer with asymmetric delay compensation model

In the BeiDou navigation satellite system-3 (BDS-3) radio determination satellite service (RDSS), there exists a natural two-way link between the center station and the user site that can be used to achieve time transfer. Traditionally, RDSS two-way time transfer is realized by analogy with the two-way satellite time and frequency transfer (TWSTFT) technique. However, unlike TWSTFT, the signal propagation delays are not completely symmetrical in the RDSS two-way link because of the differences in signal emission time. In this study, a model of two-way time transfer with BDS-3 RDSS is presented. An asymmetric delay compensation method is introduced to solve the asymmetry of RDSS signals and improve the accuracy of two-way time transfer. In addition, BDS-3 RDSS common clock difference experiments are designed to test the performance of two-way time transfer with an asymmetric delay compensation model. Based on analyses of the experimental results, three conclusions can be drawn. First, the accuracy of RDSS two-way time transfer is improved when the asymmetric delay compensation model is applied. Second, BDS-3 RDSS two-way time transfers in different in-station beams and subbands do not show many discrepancies on the whole, and the standard deviation values of the BDS-3 RDSS time transfer results range from 1.7 ns to 2.6 ns for the test signals. Third, the two-way time transfer results are not generally affected by receiver coordinate errors.

Comprehensive Analysis of PPP-B2b Service and Its Impact on BDS-3/GPS Real-Time PPP Time Transfer

2020 saw the official completion of the BDS-3 and the start of the PPP-B2b signal-based real-time precise point positioning (PPP) service to users in China and the neighboring areas. In this work, the quality of PPP-B2b products is first evaluated and compared with real-time products from the CNES and the differential code bias (DCB) from the Chinese Academy of Science (CAS). Then, a detailed performance evaluation of the PPP time transfer based on the PPP-B2b service (B2b-RTPPP) is conducted. Three solutions, namely, GPS-only (G), BDS-3-only (C), and GPS + BDS-3 (GC) B2b-RTPPP solutions, are compared and assessed. The results suggest that for the PPP-B2b products, BDS-3 satellites have better orbit and clock offset quality than GPS satellites, while the opposite is true for CNES products. The quality of the PPP-B2b orbit and clock offset is poorer than those of the CNES. The PPP-B2b DCB shows excellent agreement with the CAS DCB. The accuracy of the B2b-RTPPP solutions is sub-nanosecond level. The accuracy of B2b-RTPPP time transfer with DCB correction is approximately improved by 64% compared with that without DCB correction. The GC B2b-RTPPP solution has the greatest frequency stability, while G B2b-RTPPP solution has the poorest. Considering that the receiver may be blocked, the B2b-RTPPP time transfer performance is also evaluated at different cut-off elevation angles. As the angle increases, the B2b-RTPPP time transfer performance decreases. Additionally, the short-term frequency stability remains constant at different cut-off elevation angles, but deteriorates in the long term, especially when the angle is 40°.

An improved method for real-time PPP timing and time transfer with broadcast ephemerides

Due to the problem of network communication, it is difficult to ensure the reliability of real-time precise point positioning (PPP) timing/time transfer with real-time precise products. With the continued reduction in the signal-in-space range error, the performance and feasibility of GPS and Galileo PPP timing/time transfer with broadcast ephemeris were analyzed for the first time in real time. Then, we present a smoothing method and time-series decomposition method to reduce the noise and the interpolation error for GPS and Galileo PPP timing\ ime transfer with broadcast ephemeris in real time. The results show that GPS or Galileo PPP timing with broadcast ephemeris can achieve a 4 × 1 × 10−14 level at 15 360 s in the current state. The accuracy is about (0.46–0.81) ns and (0.44–0.61) ns for GPS and Galileo PPP time transfer. The frequency stability is at about 7.0 × 1 × 10−14 and 5.0 × 1 × 10−14 levels at 15 360 s for GPS and Galileo PPP. It is important to note that by applying our approach, the maximum improvement in frequency stability for GPS and Galileo PPP timing/time transfer is up to 99%. Furthermore, the average accuracy of GPS or Galileo PPP time transfer can achieve approximately 0.3 ns, which is an improvement of up to 67.3% compared to the traditional method.

A High-Precision Transfer of Time and RF Frequency via the Fiber-Optic Link Based on Secure Encryption

This paper presents a high-precision transfer system of time and RF frequency via the fiber optic link based on secure encryption. On the basis of the two-way time transfer of optical fiber, a security strategy composed of an SM2 encryption algorithm is introduced, which can resist the security risk of time information being tampered with. The experimental results show that the developed picosecond-precision fiber-optic time transfer equipment can ensure high stability while realizing the encryption function. Time synchronization stability in terms of time deviation (TDEV) of 1 PPS can reach around 10.7 ps at 1 s and 7.1 ps at 10 s averaging time. The stability of the 10 MHz frequency can reach around 4.7 × 10−12 at 1 s and 1.1 × 10−12 at 10 s averaging time. There is no significant difference in time transfer accuracy, compared with unencrypted conditions. Furthermore, this paper realizes a ring time transfer network via a 150 km fiber-optic link with three nodes using three devices. The TDEV of 1PPS can reach around 20.8 ps at 1s averaging time. This paper provides a reference to establish a high-precision, safe, and stable time synchronization fiber network in the future.

Galileo Time Transfer with Five-Frequency Uncombined PPP: A Posteriori Weighting, Inter-Frequency Bias, Precise Products and Multi-Frequency Contribution

Galileo satellites can broadcast signals on five frequencies, namely E1, E5A, E5B, E5 (A+B), and E6. The multi-frequency integration has become an emerging trend in Global Navigation Satellite System (GNSS) data processing. This study focused on the precise time transfer based on Galileo five-frequency uncombined precise point positioning (PPP), including the performance comparison of PPP time transfer with a priori and a posteriori weighting strategies, with different inter-frequency bias (IFB) dynamic models, and with the precise satellite products from different analysis centers, as well as the contribution of multi-frequency observations for time transfer. Compared with the a priori weighting strategy, the short-term frequency stability of time transfer adopting the Helmert variance component estimation method can be improved by 28.9–37.6% when the average time is shorter than 100 s. The effect of IFB dynamic models on Galileo five-frequency PPP time transfer is not obvious. When employing the post-processed precise satellite products from seven analysis centers, the accuracy of time transfer can be better than 0.1 ns, while an accuracy of 0.253 ns can be obtained in the real-time mode. At an average time of approximately 10,000 s, the post-processed time transfer with Galileo five-frequency PPP can provide a frequency stability of 3.283 × 10−14 to 3.459 × 10−14, while that in real-time mode can be 3.541 × 10−14. Compared with dual-frequency PPP results, the contribution of multi-frequency combination to the accuracy and frequency stability of time transfer is not significant, but multi-frequency PPP can achieve more reliable time transfer results when the signal quality is poor.

GNSS Timing Performance Assessment and Results Analysis.

Global Navigation Satellite System (GNSS) timing is a main service function. Each GNSS has its own time performance specification. However, a uniform timing performance assessment methodology and its outcomes do not exist. Firstly, the timing performance specifications of each GNSS are analyzed. Then, time transfer accuracy is considered as the key GNSS timing performance indicator. Secondly, an assessment method for the Coordinated Universal Time (UTC) published by the Bureau International des Poids et Mesures (BIPM) and UTC kept by the National Time Service Center of China (UTC(NTSC)) is proposed. Thirdly, the uncertainty budget of the assessment method is given. The timing performances of BDS, GPS, GLONASS, and Galileo are assessed and compared. The results show that the time transfer accuracy of BDS, GPS, GLONASS, and Galileo was 13.8 ns, 4.5 ns, 16.8 ns, and 4.2 ns, respectively, in 2021, meeting their performance requirements specified by GNSS (30 ns or 40 ns). Meanwhile, the assessment results of GPS and Galileo are much better than requirements, while the assessment results of BDS and GLONASS show fixed time offset and can still be improved further. If the local reference time of GNSS users can be connected with UTC, this assessment method can be used.

Open-loop polarization mode dispersion mitigation for fibre-optic time and frequency transfer.

The non-reciprocal and dynamic nature of polarization mode dispersion (PMD) in optical fibers can be a problem for accurate time and frequency transfer. Here, a simple, passive solution is put forward that is based on transmitting optical pulses with alternating orthogonal polarization. The fast and deterministic polarization modulation means that the PMD noise is pushed far away from the frequencies of interest. Furthermore, upon reflection from a Faraday mirror at the receiver, the pulses have a well-defined polarization when they return to the transmitter, which facilitates stable optical phase detection and fibre phase compensation. In an open-loop test setup that uses a mode-locked laser and a simple pulse interleaver, the polarization mode dispersion is shown to be reduced by more than two orders of magnitude.

High precision time transfer based on laser wavelength tracking

In a high-precision optical fiber time transfer system, in order to solve the scientific problem of time transfer dispersion deviation caused by the inconsistency of the two-way laser wavelengths, a high-precision time transfer method based on laser wavelength tracking is proposed in this paper. In the two-way time comparison, the laser emitted by the local site is used as a reference, and other lasers in the system track the reference, and the difference between the two-way laser wavelengths is small enough and stable for a long time, thereby greatly reducing the time transfer deviation caused by the inconsistency of the two-way laser wavelengths. In order to verify the performance of laser wavelength tracking, a double-layer temperature controlled externally modulated laser is designed, an experimental device for automatic laser wavelength tracking is designed, and laser wavelength tracking experimental modules are developed. The results show that the standard deviation of wavelength jitter is 55 fm, and the long-term relative stability of laser wavelength tracking is better than 5 fm@1×10<sup>4</sup> s, which ensures that the two laser wavelengths can remain relatively stable for a long time. In the case of long-distance fiber time transfer, by optimizing the setting value of the wavelength difference between each laser and the reference light on the link, the dispersion deviation of time transfer can be further reduced. In order to verify the feasibility of the high-precision optical fiber time transfer method based on laser wavelength tracking, a long-distance multi-station optical fiber time transfer experimental setup is built in our laboratory. The experiment is carried out in the laboratory by using 0.005, 250, 500, 750 km optical fiber links. The experimental results obtained on 750 km link show that the time transfer deviation is better than 5 ps, the stability is 4.7 ps@1 s, 0.4 ps@4×10<sup>4</sup> s, and the uncertainty is 8.4 ps. In the engineering application of optical fiber time transfer, by optimizing the working sequence of the system, the holding time length of the remote site clock can be reduced, and the accuracy of optical fiber time transfer can be further improved, which lays a foundation for realizing high-precision long-haul optical fiber time transfer.

Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite

Two-way Laser Time Transfer (TLTT) using the Ajisai satellite has been considered as a more accurate and stable time transfer technique than existing methods; TLTT requires the kHz laser pulses to decrease the systematic restrictions for TLTT realization. However, because of the low energy of the kHz laser pulses as well as the low cross section due to the small size of the Ajisai reflecting mirror, the link budget is an important issue to establish the TLTT link between two ground stations. In this study, the TLTT link budget is investigated to find the optimal laser pulse energy via analysis of geometric effects using 30 days of orbital data of the Ajisai satellite from 29 March 2021 within a ground network consisting of four stations located in three countries. The geometric configuration reduces the TLTT link budget by three orders of magnitude due to free space loss, atmospheric transmission, and effective cross section; then, the pulse energy is required to be much higher than laser ranging to the Ajisai satellite. It is shown from the simulation that a few tens of mJ level of pulse energy at the transmitting station is quite enough for TLTT realization.

Relativistic Modelling for Accurate Time Transfer via Optical Inter-Satellite Links

The DLR Institute for Communication and Navigation is currently working on a new GNSS architecture that enables accurate autonomous inter-satellite synchronization at picosecond-level. Synchronization is achieved via time transfer techniques enabled by optical inter-satellite links (OISLs), paving the way for a system in which space (orbits) and time (synchronization) can be effectively separated, leading to a high level of synchronization throughout the constellation, which in turn greatly improves accurate orbit determination. This is possible provided that relativistic effects are adequately taken into account. This work focuses on a two-way time transfer scheme based on the exchange of time stamps via optical signals, which allows the synchronization of a GNSS satellite system with respect to a defined coordinate time with picosecond-level accuracy. We analyse the impact of relativistic effects in clock offset estimation between optically linked clocks: results show that to achieve synchronization at this level of accuracy it is necessary to account for terrestrial geopotential harmonics up to the third order while the gravitational influence of additional celestial bodies can be neglected. Relativistic delays in the propagation of electromagnetic waves through spacetime are also evaluated. It is shown that for a two-way synchronization method, the Euclidean expression for the propagation of light is sufficient to achieve picosecond synchronization, provided m-level orbit determination of both satellites is available, and the hardware delays are well calibrated to the targeted accuracy. Also, we show how to practically achieve autonomous synchronization via a sequence of pair-wise synchronizations across all satellites of the constellation.

Monitoring and Analysis of SMPTE ST 2059-2 PTP Networks and Media Devices

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">As All-IP studios leveraging the SMPTE ST 2110 document suite gain traction, one of the fundamental pillars upon which such systems rely is an accurate and reliable time transfer protocol. SMPTE ST 2059 standardized such a model based on the IEEE 1588 Precision Time Protocol (PTP). Every element, whether it be network or media devices, impacts the overall time transfer accuracy. This impacts the timing of the ST 2110 media streams that are generated or received by the media nodes. While PTP does provide fault tolerance capabilities, performance degradation of time transfer is not always well understood. This can significantly impact operations in live networks, it being due to a sudden event or a degradation over time. Therefore, an overarching view of the end-to-end timing system including backup, standby, and network devices is required. Monitoring of such capabilities should be common to all devices, whenever possible, including different means to verify in-band and out-of-band measurements as to how devices are performing, with respect to time transfer. Combined with historical archiving of the monitored data, this provides the framework for tracking and correlating possible events. This paper describes the different monitoring capabilities, their advantages and weaknesses, and the value they provide to the monitored datasets. It further focuses on the means to make the process uniform across all monitored devices to ensure consistency in the collected data. Finally, we discuss the ongoing efforts in SMPTE and other standardization bodies around PTP monitoring, the common trends, expected outcomes, and how these will contribute to streamlining time transfer monitoring, supervision, and analysis</i> .

Photometric space object classification via deep learning algorithms

Accurate time transfer by time of flight measurements via diffuse reflections on passive orbiting space debris targets requires a selection of suitable objects out of a large catalogue of debris items. In this paper, we report on our development of an automatic classification system of space objects based on photometric observations of sun illuminated satellite and debris items from the Mini–Mega TORTORA (MMT) system observation data base by a deep learning algorithm. A deep neural network model based on a convolutional long short-term memory network has been designed to identify four different object categories with a test accuracy of over 85%. The method is also suitable for an automated analysis of the temporal evolution of the orbit motion of specific space objects.