Precise Clock Research Articles

Impacts of satellite clock errors on GPS/BDS/Galileo real-time PPP time transfer

By utilizing the real-time precise orbit and clock products provided by International GNSS Service (IGS), it is feasible to calculate real-time PPP (RTPPP) time and frequency transfer. The quality of these real-time precise products has a significant effect on the performance of clock comparisons and time transfer. This paper focuses on real-time clock comparisons with IGS real-time multi-GNSS precise products, which tries to explore the potential of GNSS RTPPP time transfer in time and frequency community. By using real-time precise satellite orbit and clock products from two IGS analysis centers, i.e. CNES and WHU, the clock comparisons and time transfer performance of four time links are comprehensively investigated. It is shown that the statistical uncertainty of real-time clock comparison based on multi-GNSS is within 0.15 ns, and GPS RTPPP provides time transfer results with better performance than BDS-3 and Galileo. In addition, the deviations occur in remote time links results of BDS-3 and Galileo-only between using CNES and WHU, the maximum difference can reach up to 1.10 ns. It is shown that real-time BDS-3 and Galileo satellite products of CNES and WHU are inconsistent, and will affect the time transfer performance. The paper also investigates the receiver clock offset solutions determined by using different available satellites. The results show that there are significant satellite-related biases between different satellites, especially for BDS-3 and Galileo. Thus, the reference time scales determined by using different satellites are inconsistent, and further, the time transfer for long baseline time links will be affected as there are few common view satellites for remote stations.

Assessment Accuracy of Standard Point Positioning Enhanced by Observation and Position Domain Filtering Utilizing a Multi-Epoch Least-Squares Integration Method

To enhance the positioning accuracy of standalone GNSS receivers in environments unable to provide precise ephemeris and clock offset, such as undeveloped forest areas that lack network communication and power supply, this study employed the Time Difference Carrier Phase (TDCP) technology to improve the positioning accuracy of Standard Point Positioning (SPP), where the Least-Squares (LS) and the extended Multi-Epoch Least Squares (MELS) method were applied in the position domain filtering for a single GNSS receiver and compare its performance with the existing observation domain filtering method. Firstly, the simulated data sets with various positioning accuracies were used to verify the effectiveness and convergence of the LS filtering methods. The results indicate that the LS filtering method produces a lower root mean square (RMS) error than the original strategy. Secondly, this study uses two kinematic GNSS data sets to evaluate the performance of the observation and position domain filtering, with an emphasis on the MELS method. The numerical experiment results show that the position domain LS filtering method outperforms the other two methods. The open environment experiments result shows that the positioning domain filtering method achieved positioning accuracies of 0.202 m, 0.843 m, and 2.036 m in the E, N, and U directions, respectively, with improvements of 68.0%, 21.6%, and 24.0%, compared to the original algorithm which achieved positioning accuracies of 0.631 m, 1.076 m, and 2.680 m. It also achieved improvements of 24.0%, 4.0%, and 18.3%, respectively, compared to the observation domain filtering method with positioning accuracies of 0.353 m, 0.886 m, and 2.526 m. The forest scenes experiments result shows that the positioning domain filtering method achieved positioning accuracies of 1.308 m, 1.375 m, and 2.133 m in the E, N, and U directions, respectively, with improvements of 42.4%, 36.2%, and 27.6%, compared to original algorithm which achieved positioning accuracies of 1.863 m, 1.873 m, and 2.722 m, and also achieved improvements of 27.0%, 19.4% and 10.6%, respectively, comparing to observation domain filtering method with positioning accuracies of 1.661 m, 1.642 m and 2.359 m. Moreover, the examination of the LS method results based on different epochs reveals that the filtering accuracy increases as more epochs are incorporated into the position domain integration and the enhancement value reaches a few millimeters.

Development and Test of a 48-optical Ports High Precision Clock Distributor Board

Development and Test of a 48-optical Ports High Precision Clock Distributor Board

BDS-3/BDS-2 Combined Precise Clock Estimation and Time Transfer Using Ultrarapid Products

BDS-3/BDS-2 Combined Precise Clock Estimation and Time Transfer Using Ultrarapid Products

Clock synchronizing radio access networks to picosecond precision using optical clock distribution and clock phase caching

Performing positioning of future mobile devices using trilateration through radio access networks would provide a robust alternative to currently used global navigation satellite systems. However, the positioning accuracy is strongly dependent on the time synchronization accuracy of the antennas used as location reference points. Consequently, achieving sub-30 cm positioning accuracies requires the synchronization of radio access network antennas to sub-nanosecond accuracy. Here we show a clock phase synchronization and optical clock signal distribution approach to clock synchronization in radio access networks that achieves 0.98-ps root-mean-square precision clock synchronization, in a real-time field-trial demonstration on 37.6-km dark fiber, with optical clock frequency synchronization and clock phase caching operating using 25.6-Gb/s commercial transceivers. We quantify the clock synchronization performance of our approach using standard metrics, including time deviation (TDEV) and mean time interval error (MTIE). Furthermore, we estimate the impact of varying the phase update rate used in clock phase caching on the clock synchronization performance of our approach. Through our two combined approaches, we explore a route towards achieving sub-nanosecond clock synchronization in radio access networks.

USER IMPLEMENTATION AND ASSESSMENT OF BDS-3 PRECISE POINT POSITIONING AUGMENTATION SERVICE WITH NO ECONOMIC COST

Abstract. The satellite-based precise point positioning (PPP) service enables users with high accuracy positions without Internet connections. Currently, two types of satellite-based PPP services are available. One type is commercial service, such as Trimble CenterPoint RTX service. The second type is non-commercial and cost-free service, including the BDS-3 satellite-based PPP service based on PPP-B2b signals. This service is currently open access to all receiver manufacturers. This contribution firstly presents a detailed instruction on how to apply PPP-B2b signals into positioning. Afterwards, the performance of BDS-3 PPP service is validated with both static and kinematic experiments carried out in Wuhan, China, during day of year 168 and 172, 2022. Results indicate that PPP-B2b signals mainly improve BDS-3 clock precision and GPS orbit accuracy. With BDS-3 PPP-B2b augmentation messages, the static satellite-based PPP shows 3.9/6.9/10.3 mm daily solution repeatability in E/N/U directions, respectively. An average of 13.9 min convergence time and 3.42/2.16/6.65 cm E/N/U positioning accuracy are achieved in the simulated kinematic mode. During a 28-min stepper motor driven movement test, 3.48/14.88 cm 2D/3D kinematic positioning accuracy is obtained using the BDS-3 PPP service.

Fundamental Accuracy-Resolution Trade-Off for Timekeeping Devices.

From a thermodynamic point of view, all clocks are driven by irreversible processes. Additionally, one can use oscillatory systems to temporally modulate the thermodynamic flux towards equilibrium. Focusing on the most elementary thermalization events, this modulation can be thought of as a temporal probability concentration for these events. There are two fundamental factors limiting the performance of clocks: On the one level, the inevitable drifts of the oscillatory system, which are addressed by finding stable atomic or nuclear transitions that lead to astounding precision of today's clocks. On the other level, there is the intrinsically stochastic nature of the irreversible events upon which the clock's operation is based. This becomes relevant when seeking to maximize a clock's resolution at high accuracy, which is ultimately limited by the number of such stochastic events per reference time unit. We address this essential trade-off between clock accuracy and resolution, proving a universal bound for all clocks whose elementary thermalization events are memoryless.

Characterizing the fault performance of real-time precise satellite orbit and clock correction products

The a priori fault probability of the real-time precise satellite orbit and clock correction products is the critical parameter for integrity monitoring of precise point positioning (PPP). The traditional fault probability evaluation methods use the worst-case instantaneous user ranging error (IURE) as the conservative test statistic. However, the systematic biases of IURE contained in the worst-case IURE barely affect the PPP accuracy, which will undermine the statistical distribution of test statistic and reduce the sensitivity of fault detection. The fault probability will be estimated over-conservatively for the traditional methods. By clarifying the sources of the systematic biases, a new test statistic is constructed by deliberately removing the systematic biases of IURE originated from satellite orbit and clock errors. One-year Global Positioning System correction products evaluation results have demonstrated that the constructed test statistic follows the Gaussian distribution with the decreased uncertainty and the improved fault detection sensitivity. The real-world data experiments have shown that the a priori probabilities of the satellite fault and the constellation fault are at the order of 10−4 and 10−5 levels, respectively.

Research on the Real-Time Ambiguity Resolution Algorithm of GPS/Galileo/BDS Based on CNES Real-Time Products

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR.

Remote Residual Instability Evaluation of Comb-Based Precise Frequency Transmission for Optical Clock

Optical clocks can be used as the absolute frequency reference due to their high accuracy and stability. In a precise optical clock transmission system, the instability loss of the link is usually evaluated by beating the remote optical signal with the reference clock, which is not suitable for real frequency distribution applications. Therefore, it is necessary to assess the performance directly at the remote site for the optical frequency transfer, because the two sites of the link are usually not co-located. In this paper, we proposed a comb-based remote residual instability evaluation scheme. Two coherent optical combs with different wavelengths were extracted from a frequency stable comb and transmitted after multiplexing. The residual instability was evaluated directly at the remote site by measuring the phase fluctuation difference between the two combs. We achieved 8.61 × 10−19 at 40,000 s over a 10 km fiber link, reaching the instability of optical clocks. These results revealed that our scheme can evaluate optical clock frequency transmission directly at the remote site, which made the method truly practical.

Advances in satellite atomic clock technologies for the GNSS

Abstract High-precision time frequency lays a foundation for the normal operation and accurate service of the global navigation satellite system (GNSS). The satellite clock, a payload vital to GNSS operation, has become a hot topic in GNSS technology research. This paper gives a systematic introduction to the operation features and principles of satellite clock, and an overview of its research status and current development. On this basis, several techniques that deserve attention of the satellite clocks are categorized in terms of precise orbit determination and clock estimation, performance assessment and characteristic analysis, and clock offset prediction. On this basis, a comprehensive description and analysis is given separately. In the end, this paper gives some prospects over the development trend of techniques of the satellite clock based on the current research achievements and development of the GNSS.

Performance evaluation of BDS-3 new B1C/B2a and legacy B1I/B3I signals: Observational quality, POD and PPP

In addition to the BeiDou regional navigation satellite system (BDS-2) backward compatible B1I and B3I signals, the BeiDou global navigation satellite system (BDS-3) also broadcast the B1C and B2a signals for compatibility with other Global Navigation Satellite System (GNSS), and providing satellite-based augmentation service for the International Civil Aviation Organization. Considering that the majority of the existing researches on the BDS-3 precise orbit determination (POD) and precise point positioning (PPP) are based on the B1I/B3I signals, the special attention that systematically comparing the data quality, POD accuracy and PPP performance through B1I/B3I and B1C/B2a signals is aroused in this paper. Signal characteristics of different receivers and antennas for the aforesaid four various signals were analyzed in terms of the carrier-to-noise density ratio (C/N0), pseudorange multipath and observation noise. The B1C signal exhibits the minimum C/N0 values, and the B3I and B2a signals have the smaller pseudorange multipath errors. The smallest pseudorange noise can be observed form the B2a signal, while the root mean squares (RMSs) for carrier phase noise show tiny differences among the four signals. The BDS-3 POD results indicate that the orbit overlapping arc error in three-dimensional (3D) direction is 0.069 and 0.076 m for the B1C/B2a and B1I/B3I, and the standard deviation of the satellite laser ranging validation is 0.041 m for both the two schemes. The clock offset products were evaluated with respect to the precise clock products from Deutsches GeoForschungsZentrum (GFZ), and the standard deviations (STDs) are 0.166 and 0.176 ns for the B1C/B2a and B1I/B3I. Finally, there is no apparent difference in the RMSs for B1C/B2a and B1I/B3I static PPP, while the convergence time that shortened by 31.4 % can be achieved for B1C/B2a. For kinematic PPP, the 3D RMS is 0.043 m and the convergence time is 31.1 min for the B1C/B2a, which is reduced by 14.0 % and 35.2 %, respectively, compared to B1I/B3I.

Advancing Precise Orbit Determination and Precise Point Positioning of BDS-3 Satellites from B1IB3I to B1CB2a: Comparison and Analysis

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time.

Sensitivity of phase difference between short-range acoustic multipaths to changes in sound speed and source depth

Ocean acoustic tomography often relies on precise clocks and knowledge of the range between acoustic instruments to estimate ocean-driven sound speed changes. In this study, we explore an alternative method utilizing the difference in the carrier phase between two broadband pulse arrivals to estimate small-scale changes in source depth and sound speed. By leveraging acoustic multipathing, this phase difference approach obviates the need to know the acoustic propagation's precise range and absolute travel time. Observations from a mid-frequency (1–10 kHz) acoustic experiment at short ranges (2–3 km) demonstrate the sensitivity of the difference in the 4 kHz carrier phase between two arrivals to changes in both source depth and sound speed. The difference in the arrival phase is modeled using measurements of the time-varying source depth and sound speed. The comparison between the modeled and observed arrival phase differences reveals a significant agreement, supporting the potential of using phase difference as a reliable estimator for perturbations in either source depth or sound speed for short-range acoustic propagation.

Effect of Measurement Backaction on Quantum Clock Precision Studied with a Superconducting Circuit

Effect of Measurement Backaction on Quantum Clock Precision Studied with a Superconducting Circuit

Quantum-enhanced sensing on optical transitions through finite-range interactions.

The control over quantum states in atomic systems has led to the most precise optical atomic clocks so far1-3. Their sensitivity is bounded at present by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can-nevertheless-be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real-world sensors is extremely challenging. Here we illustrate a pathway for harnessing large-scale entanglement in an optical transition using 1D chains of up to 51 ions with interactions that decay as a power-law function of the ion separation. We show that our sensor can emulate many features of the one-axis-twisting (OAT) model, an iconic, fully connected model known to generate scalable squeezing4 and Greenberger-Horne-Zeilinger-like states5-8. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of the structure factor, that is, spin-wave excitations (SWE), at finite momenta, the generation of spin squeezing comparable with OAT (a Wineland parameter9,10 of -3.9 ± 0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of multi-headed cat states in the Q-distribution. We demonstrate the metrological utility of the states in a Ramsey-type interferometer, in which we reduce the measurement uncertainty by -3.2 ± 0.5 dB below the standard quantum limit for N = 51 ions.

Measuring the gravity potential between two remote sites with CVSTT technique using two hydrogen clocks

ABSTRACT According to General Relativity Theory (GRT), by comparing the frequencies between two precise clocks at two different stations, the gravity potential (geopotential) difference between the two stations can be determined due to the gravity frequency shift effect. Here, we conduct a clock-transportation experiment for measuring geopotential differences based on frequency comparisons via satellite links between two remote hydrogen atomic clocks. Based on the net frequency shift between the two clocks in two different periods, the geopotential difference between stations of the Beijing 203 Institute Laboratory (BIL) and Luojiashan Time-frequency Station (LTS) is determined. Comparisons show that the experimental result deviated from the reference of Earth gravity model EGM2008 result by (38.545.9) m in Orthometric Height (OH). The results are consistent with the frequency stabilities of the hydrogen clocks (at the level of ) used in the experiment. With the rapid development of time and frequency science and technology, the approach discussed in this study for measuring the geopotential is prospective and thus, could have broad applications.

A Method for Measuring Gravitational Potential of Satellite’s Orbit Using Frequency Signal Transfer Technique between Satellites

We introduce an approach for the direct measurement of the gravitational potential (GP) along the trajectory of a satellite, with a specific focus on Low-Earth Orbit (LEO) satellites. A LEO satellite communicates with several Geosynchronous Equatorial Orbit (GEO) satellites via frequency signal links. The GP difference can be measured in real-time using the gravitational frequency shift approach by equipping both LEO and GEO satellites with precise atomic clocks. Since the GP at the high orbits of the GEO satellites can be precisely determined by the present gravitational field model EGM2008, the GP along the LEO satellite’s trajectory can be determined. In this study, simulation experiments were conducted, featuring a GRACE-type satellite as the LEO satellite in communication with three equidistant GEO satellites. The results indicated that the accuracy of the GP measurements along the LEO satellite’s trajectory primarily depends on the precision of the onboard atomic clocks. Supposing optical atomic clocks attain an instability level of 1×10−17τ−1/2 (τ in seconds), we determined the GP distribution covered by the LEO satellite’s trajectories with 30-day observations. Then, we determined a gravitational field at the centimeter level based on the GP distribution. The GP data derived from the trajectory of a LEO satellite can be utilized to establish temporal gravitational fields, which have broad applications in different disciplines.

Multi-GNSS precise point positioning with predicted orbits and clocks

Global Navigation Satellite Systems (GNSS) Real-time Precise Point Positioning (RT-PPP) strongly relies on the precise satellite orbits and clocks, especially the latter requires high update rate, e.g., five seconds, due to its limited prediction accuracy. Such a high-rate update frequency is a burden to both the data analysis and communicating, and interruption in communicating is almost unavoidable. For the new constellations such as Galileo and BDS-3 with high-stability hydrogen clocks onboard, it is possible to predict satellite clocks to a longer arc. Moreover, recent developments in multi-GNSS ultra-rapid precise orbit determination enables the half-hourly update, ensuring the availability with a prediction arc of 30–60 min. We investigate multi-GNSS RT-PPP using half-hourly predicted products and demonstrate that a 3-D accuracy of 2.9 and 11.3 cm can be achieved for static and simulated kinematic solutions, respectively. We present the different clock prediction accuracies of different types of satellites and propose a satellite-specific weighting strategy in PPP, which exploits the benefits of the satellites of good performance. The method is based on the prediction accuracy of both, satellites and clocks, and shows an improvement of 15 to 60% compared to those without satellite-specific weighting or with simplified weighting strategies. We also demonstrate that Galileo satellites contribute the most in the quad-constellation solution, thanks to the highly stable satellite clocks.

Asynchronous Hyperbolic UWB Source-Localization and Self-Localization for Indoor Tracking and Navigation

Hyperbolic localization measures the time difference of arrivals (TDOAs) of signals to determine the location of a wireless source or receiver. Traditional methods depend on precise clock synchronization between nodes so that time measurements from independent devices can be meaningfully compared. Imperfect synchronization is often the dominant source of error. We propose two new message based TDOA equations for hyperbolic localization which require no synchronization and meet or exceed state-of-the-art accuracy. Our approaches leverage anchor nodes that observe each other’s packet arrival times and a novel reformulation of the TDOA equation to reduce the effect of clock drift error. Closed-form equations are derived for computing TDOA in both self-localization and source-localization modes of operation along with bounds on maximum clock drift error. Three experiments are performed including a clock drift simulation, a non-line-of-sight (NLOS) simulation, and an indoor validation experiment on custom ultra wideband (UWB) hardware all of which involved eight anchor nodes and one localizing node in a 128m3 capture volume. Our source-localization approach achieved unprecedented accuracy with lower cost equipment and trivial setup. Our self-localization matched state-of-the art accuracy but with infinite scalability and high privacy. These results could enable economical and infinite density indoor navigation and dramatically reduce the economic cost and increase the accuracy of implementing industrial and commercial tracking applications.