Two-way Satellite Time Transfer Research Articles

A NavCom Signal Authentication Scheme Based on Twice Two-Way Satellite Time Transfer

Low Earth Orbit (LEO) satellite communication systems typically achieve identity authentication through the encryption and decryption of two-way information, which requires complex key management systems. In contrast, the integration of navigation and communication (NavCom) signals provides novel opportunities for physical observation and authentication solutions due to its measurement functions. This paper introduces a novel signal authentication scheme based on twice two-way satellite time transfer (TWSTT) for LEO satellite systems. It leverages the non-mutated nature of the clock difference to ascertain the legitimacy of the signal by measuring the clock difference of signals at different instances. Unlike traditional authentication methods, this approach directly exploits the temporal and spatial characteristics of the signal, negating the necessity for intricate authorization key systems. Additionally, it adeptly tackles the challenges posed by spoofing interference. The performance analysis indicates that this scheme can achieve a high detection probability for the repeater spoofing signal in the low carrier-to-noise ratio conditions.

Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer

According to general relativity theory (GRT), the clock at a position with lower geopotential ticks slower than an identical one at a position with higher geopotential. Here, we provide a geopotential comparison using a non-transportable hydrogen clock and a transportable hydrogen clock for altitude transmission based on the two-way satellite time and frequency transfer (TWSTFT) technique. First, we set one hydrogen clock on the fifth floor and another hydrogen clock on the ground floor, with their height difference of 22.8 m measured by tape, and compared the time difference between these two clocks by TWSTFT for 13 days. Then, we set both clocks on the ground floor and compared the time difference between the two clocks for seven days for zero-baseline calibration (synchronization). Based on the measured time difference between the two clocks at different floors, we obtained the height difference 28.0 ± 5.4 m, which coincides well with the tape-measured result. This experiment provides a method of height propagation using precise clocks based on the TWSTFT technique.

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.

Improving two-way satellite time and frequency transfer with redundant links for UTC generation

Two-way satellite time and frequency transfer (TWSTFT) is a primary technique for the generation of coordinated universal time (UTC). At present, more than 12 timing laboratories around the world use SAtellite Time and Ranging Equipment (SATRE) modems in TWSTFT operations and contribute data for the realization of UTC. The advantages of TWSTFT are its small calibration uncertainty (⩽1.0 ns if the link is calibrated with a TWSTFT mobile station) and its long-term link stability. However, the precision of SATRE TWSTFT in the operational networks is degraded by a daily variation pattern (diurnal) in the TWSTFT results. The diurnal with varying amplitude appears virtually in all SATRE TWSTFT links. The observed peak-to-peak variation of the diurnals can reach 2.0 ns in some cases. So far, studies on the sources of the diurnal have not provided conclusive understanding of the diurnal’s dominant origin.Therefore, efforts have been made to reduce the impact of the diurnal variation in TWSTFT for UTC computation. The BIPM has been using the combination of SATRE TWSTFT results and GPS carrier-phase precise point positioning solutions (GPSPPP) for UTC computation since 2010. The combination adjusts the GPSPPP results to long-term averages of TWSTFT and is effectively free from the diurnal variations because the GPSPPP results contain almost no diurnal. Lately, the use of software-defined radio receivers (SDR) in TWSTFT has shown one way of how to reduce the diurnal variations by a factor of two to three in most of the inner-continental SATRE TWSTFT links, and furthermore, how the short-term stability for all UTC SDR TWSTFT links can be improved. In addition, there has been research on the full use of the redundancy in the TWSTFT network to improve the TWSTFT link stability. Recent studies on evaluating indirect links revealed that it is possible to apply a simplified procedure to use the redundancy, in a most effective way, to reduce the diurnal variations in the Europe-to-Europe SATRE TWSTFT links by a factor of two to three. Based on these findings, we gained new insights about the diurnals and its dominant origin(s) which are discussed in this paper. The methods of the combination of SATRE TWSTFT and GPSPPP as well as the indirect SATRE TWSTFT links utilize the redundancy in the UTC time transfer network. SDR TWSTFT can largely reduce the diurnal in SATRE TWSTFT, but noticeable residual diurnal remains. In this paper, we provide the analyses of using the combination of SDR TWSTFT and GPSPPP results, as well as using the indirect SDR TWSTFT links. This paper concludes that the use of SDR TWSTFT redundant links can further improve the stabilities of UTC TWSTFT links. In addition, the use of SDR TWSTFT indirect links is a pure TWSTFT solution. The independence of the TWSTFT results to GPS results can improve the robustness of UTC computation.

Foundation and performance evaluation of real-time GNSS high-precision one-way timing system

Global navigation satellite system (GNSS) can realize global time synchronization with tens of nanoseconds precision. For more precise time synchronization applications, two-way satellite time and frequency transfer is commonly used despite its high cost and requiring a geostationary satellite. Considering the high cost, people started to use the GNSS signals to realize high accuracy time transfer, named common-view or all-in-view, which can achieve several nanoseconds according to the analyses and verifications of previous studies. However, time transfer cannot realize real-time timing in a large area as a common GNSS one-way timing receiver does. In such a timing system, a highly stable reference and a matched high-precision timing receiver system are necessary. To solve this problem, we have established a one-way timing system based on a ground-based augmentation system. The system estimates real-time high-precision satellite clocks using the ground-based augmentation network as the time reference. Moreover, the time reference is transferred to the terminal through real-time precise point positioning (PPP). Finally, the timing receiver synchronizes its local clock to the reference by real-time clock adjustment, resulting in high-precision timing. We present the details of this system, including the time reference, the PPP algorithm, and the timing receiver technologies. Finally, we give the precision and stability evaluation of the whole system, especially for one pulse per second (1 PPS) outputs of the terminal. The results show that the stability of the 1 PPS output is better than 1 ns in a day.

Geopotential determination based on a direct clock comparison using two-way satellite time and frequency transfer

Geopotential determination based on a direct clock comparison using two-way satellite time and frequency transfer

Use of software-defined radio receivers in two-way satellite time and frequency transfers for UTC computation

Two-way satellite time and frequency transfer (TWSTFT) is a primary technique for the generation of coordinated universal time (UTC). About 20 timing laboratories around the world continuously operate TWSTFT using satellite time and ranging equipment (SATRE) modems for remote time and frequency comparisons in this context. The precision of the SATRE TWSTFT as observed today is limited by an apparent daily variation pattern (diurnal) in the TWSTFT results. The observed peak-to-peak variation have been found as high as 2 ns in some cases. Investigations into the origins of the diurnals have so far provided no complete understanding about the cause of the diurnals. One major contributor to the diurnals, however, could be related to properties of the receive part in the modem. In 2014 and 2015, it was demonstrated that bypassing the receive part and the use of software-defined radio (SDR) receivers in TWSTFT ground stations (SDR TWSTFT) instead could considerably reduce both the diurnals and the measurement noise.In 2016, the International Bureau of Weights and Measures (BIPM) and the Consultative Committee for Time and Frequency (CCTF) working group (WG) on TWSTFT launched a pilot study on the application of SDR receivers in the TWSTFT network for UTC computation.The first results of the pilot study were reported to the CCTF WG on TWSTFT annual meeting in May 2017, demonstrating that SDR TWSTFT shows superior performance compared to that of SATRE TWSTFT for practically all links between participating stations. In particular, for continental TWSTFT links, in which the strongest diurnals appear, the use of SDR TWSTFT results in a significant suppression of the diurnals by a factor of between two and three. For the very long inter-continental links, e.g. the Europe-to-USA links where the diurnals are less pronounced, SDR TWSTFT achieved a smaller but still significant gain of 30%. These findings are supported by an evaluation of some of the links with an alternate technique based on GPS signals (GPS IPPP) as reported in this paper.Stimulated by these results, the WG on TWSTFT prepared a recommendation for the 21st CCTF meeting, which proposed the introduction of SDR TWSTFT in UTC generation. With CCTF approval of the recommendation, a roadmap was developed for the implementation of SDR TWSTFT in UTC generation. In accordance with the roadmap, most of the stations that participated in the pilot study have updated the SDR TWSTFT settings to facilitate the use of SDR TWSTFT data in UTC generation. In addition, the BIPM conducted a final evaluation to validate the long-term stability of SDR TWSTFT links, made test runs using the BIPM standard software for the calculation of UTC, now including SDR TWSTFT data, and started to calculate SDR TWSTFT time links as backup from October 2017. The use of SDR TWSTFT in UTC generation will begin in 2018.

An Improved Protocol for Performing Two-Way Satellite Time and Frequency Transfer Using a Satellite in an Inclined Geo-Synchronous Orbit.

Two-way satellite time and frequency transfer (TWSTFT) using satellites in inclined geo-synchronous orbit (IGSO) is fundamentally more difficult than using satellites in geostationary orbit (GEO), due to the fact that IGSO satellites are constantly moving relative to a ground station, which brings in large residual effects. In this paper, we designed a protocol and an algorithm to correct several factors that affect the precision of TWSTFT using IGSO satellites. We used two ground stations, each equipped with sending and receiving channels, to conduct real-time measurements of the distance and the speed of an IGSO satellite, and data collected were used to make appropriate corrections. We tested this concept by conducting TWSTFT experiments using an IGSO satellite (BEIDOU I1-S), and compared the results with that obtained using a GEO satellite (CHINASAT 12). Indeed, the individual components that contribute to the residual effects of TWSTFT measurements using the IGSO satellite were several orders of magnitude greater than that of the GEO satellite. By using our modified protocol, TWSTFT results with an IGSO satellite were well accorded with that of using a GEO satellite; the standard deviation of residuals was less than 0.4 ns, well within the limit for the measurement uncertainty of TWSTFT. Therefore, we have expanded the use of IGSO satellites for TWSTFT. In principle, it should also be applicable to medium earth orbit and other satellites.

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system

A two-way satellite time and frequency transfer (TWSTFT) device equipped in the BeiDou navigation satellite system (BDS) can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination (MPOD) method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service (IGS) analysis centers (ACs) show that the reference time difference between BeiDou time (BDT) and golbal positoning system (GPS) time (GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10−12, which is similar to the GPS IIR.

Orbit determination and time synchronization for new-generation Beidou satellites: Preliminary results

Five new-generation Beidou Satellite Navigation System (BDS) satellites, including two satellites in the Inclined Geostationary Orbit (IGSO) and three satellites in the Medium Orbit (MEO), have completed deployment on 1st February 2016. The mission of the five new-generation satellites is to validate the new system designs and the new technologies that will successfully expand BDS’s Positioning, Navigation and Timing (PNT) services from regional to global. Responsible to keep time and frequency standards that are used to generate navigation signals, atomic clocks are important payloads onboard BDS satellites. Using data from BDS’ two-way satellite time and frequency transfer system, this paper evaluates performance of those new generation atomic clocks (Hydrogen Maser and Rubidium). Compared to the regional operational satellites onboard atomic clocks, the prediction accuracy of the new-generation onboard atomic clocks is improved. The short-term prediction error of IGSO satellites drops from 0.65 to 0.30 ns, the short-term prediction error of MEO satellites drops from 0.78 to 0.32 ns, and the media-term prediction error of IGSO and MEO satellites drops from 2.50 to 1.50 ns. Inter-Satellite Links (ISL) with measurement and data communication capabilities is one of the most important ingredient for global BDS system design. With ISL data collected for the five new-generation satellites, this paper compares differences in space signal accuracy, or orbits and clocks in broadcast navigation messages, with or without ISL contribution. Our finding confirms ISL contributes a great deal to the space signal accuracy, in particular when the satellites are not tracked by a regional network. With ISL measurements, the prediction error of MEO broadcast satellite clock parameters drops from 3 ns to within 1 ns when the MEO satellites go into the visual field once more. When ISL measurements join orbit determination as additional observation to L Band code and phase measurements, the orbit determination and prediction accuracy is greatly improved: the radial orbit overlap difference is better than 0.1 m, three-dimensional overlap difference better than 0.5 m and 24 h prediction radial orbit overlap difference is better than 0.2 m, three-dimensional overlap difference better than 1.0 m. Furthermore, with clock measurements obtained with ISL, clock estimates may be decoupled from orbital estimates during orbit determination process for better solutions. A new strategy is proposed in this paper, in which the variation of the satellite clock offsets is constrained and kept as known in orbit determination. With the new strategy, the 4 h prediction UERE drops from 1.04 to 0.82 m.

8th Symposium on Frequency Standards and Metrology 2015

8th Symposium on Frequency Standards and Metrology 2015

Stability improvement of an operational two-way satellite time and frequency transfer system

To keep national time accurately coherent with coordinated universal time, many national metrology institutes (NMIs) use two-way satellite time and frequency transfer (TWSTFT) to continuously measure the time difference with other NMIs over an international baseline. Some NMIs have ultra-stable clocks with stability better than 10−16. However, current operational TWSTFT can only provide frequency uncertainty of 10−15 and time uncertainty of 1 ns, which is inadequate. The uncertainty is dominated by the short-term stability and the diurnals, i.e. the measurement variation with a period of one day. The aim of this work is to improve the stability of operational TWSTFT systems without additional transmission, bandwidth or increase in signal power. A software-defined receiver (SDR) comprising a high-resolution correlator and successive interference cancellation associated with open-loop configuration as the TWSTFT receiver reduces the time deviation from 140 ps to 73 ps at averaging time of 1 h, and occasionally suppresses diurnals. To study the source of the diurnals, TWSTFT is performed using a 2 × 2 earth station (ES) array. Consequently, some ESs sensitive to temperature variation are identified, and the diurnals are significantly reduced by employing insensitive ESs. Hence, the operational TWSTFT using the proposed SDR with insensitive ESs achieves time deviation to 41 ps at 1 h, and 80 ps for averaging times from 1 h to 20 h.

The method and experiment analysis of two-way common-view satellite time transfer for compass system

Time synchronization between ground and satellites is a key technology for satellite navigation system. With dual-channel satellite, a method called Two-Way Common-View (TWCV) satellite time transfer for Compass system is proposed, which combines both characteristics of satellite common-view and two-way satellite-ground time transfer. By satellite-ground two-way pseudo-range differencing and two stations common-view differencing, this TWCV method can completely eliminate the influence of common errors, such as satellite clock offset, ephemeris errors, troposphere delay and station coordinates errors. At the same time, ionosphere delay related to signal frequency is also weakened significantly. So the precision of time transfer is improved much more greatly than before. In this paper, the basic principle is introduced in detail, the effect of major errors is analyzed and the practical calculation model in the Earth-fixed coordinate system for this new method is provided. Finally, experiment analysis is conducted with actual Compass observing data. The results show that the deviation and the stability of the satellite dual channel can be better than 0.1 ns, and the accuracy of the two-way common-view satellite time transfer can achieve 0.4 ns. All these results have verified the correctness of this TWCV method and model. In addition, we compare this TWCV satellite time transfer with the independent C-band TWSTFT (Two-Way Satellite Time and Frequency Transfer). It shows that the result of the TWCV satellite time transfer is in accordance with the C-band TWSTFT result, which further suggests that the TWCV method is a remote high precision time transfer technique. The research results in this paper are very important references for the development and application of Compass satellite navigation system.

Study of optical frequency transfer via fiber

Optical clocks are considered as promising candidates for redefining the second in the International System of Units. Compared with microwave clocks, optical clocks are powerful tools for the fundamental research such as the constancy of the fundamental constants, the validity of Einstein’s theory of general relativity, and the predictions of quantum electrodynamics. Recently two research groups have demonstrated the optical clocks with an unprecedented precision level of 10-18, which is two orders better than the present primary frequency standard. Using two Sr optical clocks and three Cs fountain clocks, SYRTE group has demonstrated the definition of second with optical clocks.#br#For redefining the second with optical clocks in the future, the optical clocks from the remote laboratories should have a high precision and the frequency of the optical clocks need to be transferred over a long distance, with extremely high precision. Unfortunately the conventional means of frequency transfer such as two-way satellite time and frequency transfer can reach a 10-16 level in one day which is far below the requirement for an optical clocks. Various methods have been developed to transfer optical frequency signal via optical fibers. Especially a research group from Germany has achieved a frequency transfer stability of 10-19 level in hundreds of seconds with a fiber length of 1840 km.#br#We demonstrate the recent development of optical frequency transfer over a 70-km fiber spool at National Time Service Center. The measurement shows that the compensation for the fiber noise is close to the limitation induced by the fiber delay for the Fourier frequency from 1 Hz to 250 Hz. The transfer stability (Allan deviation) of the fiber link is 1.2×10-15 in 1 s averaging time, and 1.4×10-18 in 10000 s. A preliminary test of the optical frequency transfer over a 100-km spooled fiber is achieved with a stability of roughly one order worse than the 71 km result, 5×10-15 in 1 s.#br#We demonstrate a new scheme of remote compensation for optical frequency transfer via fibers against conventional local compensation method. This new scheme has the advantage of great simplification of the local site, which can find applications in massive extension of star network. The key feature is that we transfer the mixture of the round-trip signal and local reference to the remote user’s end via an auxiliary fiber. At remote site, the fiber noise is measured and compensated by AOM2 accordingly.#br#Transfer stabilities of 13×10-15 in 1 s averaging time and 4.8×10-18 in 10000 s are achieved with the remote fiber noise compensation via a 25 km fiber spool. The demonstrated transfer stability is comparable to that obtained by the local fiber noise compensation method.#br#The future star fiber network of optical frequency transfer can benefit from this method, because the simpler local setup is required and even can be shared in the central site for multitudinous remote users.

Comparison of Two-Way and BeiDou Common View Time Transfer between NTSC and BEIJ Station

The data obtained by the two-way satellite time and frequency transfer (TWSTFT) and the BeiDou common view (BDCV) experiments between the National Time Service Center (NTSC) and Beijing station (BEIJ) will be compared in this paper. Results with high agreement between the two techniques will be described. Data analysis results demonstrated that the two-way satellite time and frequency transfer (TWSTFT) and the BeiDou common view (BDCV) can back up each other.

Direct comparison of optical lattice clocks with an intercontinental baseline of 9000 km.

We have demonstrated a direct frequency comparison between two ⁸⁷Sr lattice clocks operated in intercontinentally separated laboratories in real time. Two-way satellite time and frequency transfer technique, based on the carrier-phase, was employed for a direct comparison, with a baseline of 9000 km between Japan and Germany. A frequency comparison was achieved for 83,640 s, resulting in a fractional difference of (1.1±1.6)×10⁻¹⁵, where the statistical part is the largest contributor to the uncertainty. This measurement directly confirms the agreement of the two optical frequency standards on an intercontinental scale.

Improved two-way satellite time and frequency transfer with Multi-GEO in BeiDou navigation system

Due to the limitation of Geostationary Earth Orbit (GEO) satellite resources, only very few TWSTFT links with parallel counterpart operating via different GEO satellites between two ground stations are available. There are 5 GEO satellites in BeiDou Navigation System, which enables an improved TWSTFT with Multi-GEO. Two algorithms are put forward to take the advantage of Multi-GEO links to improve the performance of time and frequency transfer respectively. The dynamic weight average algorithm based on a newly proposed dynamic time variance aiming at improving the performance of time transfer is shown to be able to reduce the dynamic time deviation of the two-way measurement result to 1/\(\sqrt N \) dynamic time deviation of the single link using N-GEO links, if each link has similar level of link noises. The algorithm of cancelling out the link noise Allan variances with 2-GEO links is expected to obtain the Allan variance of clock difference between two ground stations. The experiment results using 2-GEO links in BeiDou Navigation System show that the dynamic weight average algorithm can improve the dynamic time deviation of the two-way measurement to around 0.6 of that of the single link in an average concept. And the estimated Allan deviation of the clock difference using the algorithm for cancelling the noise Allan variances of both links can reach 7×10−12(τ −0.65) for the averaging time 1–105 s which is within the same order of magnitude as the estimated Allan deviation based on carrier Doppler measurement for the averaging time 10 s–104 s, despite the noisy links with the Allan deviation follows 3 × 10−10(τ −1).

A New Method of Data Pre-Processing to Two-Way Satellite Time and Frequency Transfer Experiments

Based on the basic theory of two-way satellite time and frequency transfer (TWSTFT), the mathematical model on real errors of observations is established in this paper. However, the model is rank-deficient. In order to solve this problem effectively, the paper introduces the algorithm of combining parameters, and applies Quasi-Accurate Detection of Gross Errors (QUAD) proposed in reference [ to data pre-processing. The method programs opportune algorithms and resolves the problem of detecting gross errors. In the end, the method has been verified to be successful by calculating and analysing simulated data and practical measured data.

Carrier-phase-based two-way satellite time and frequency transfer

We performed measurements of carrier-phase-based two-way satellite time and frequency transfer (TWST-FT) with an A/D sampler and conventional TWSTFT system. We found that an instability resulting from a local signal at the satellite transponder was negligible. The short-term stability of 4 × 10(-13) at 1 s was achieved in a short-baseline measurement. The results showed good agreement with the GPS carrier phase.

Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network

In this work, we demonstrate for the first time that it is possible to transfer simultaneously an ultra-stable optical frequency and precise and accurate timing over 540 km using a public telecommunication optical fiber network with Internet data. The optical phase is used to carry both the frequency information and the timestamps by modulating a very narrow optical carrier at 1.55 μm with spread spectrum signals using two-way satellite time transfer modems. The results in terms of absolute time accuracy (250 ps) and long-term timing stability (20 ps) well outperform the conventional Global Navigation Satellite System or geostationary transfer methods.