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The Carrier-Phase (CP) technique used in the Global Positioning System (GPS) has proved to be a useful spatial tool for remote precise time transfer. Galileo is a Global Navigation Satellite System like GPS. However, currently, given the low number of satellites at any one observation epoch, Galileo's accuracy and continuity of time transfer leave...
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... the number of available Galileo satellites is usually less than four at any observation epoch in many places, which seriously affects the provision of a continuous time transfer service. As shown in Figure 1, the number of available Galileo satellites at every observation epoch during time transfer experiments typically ranges from two to four. Figure 2 presents a typ- ical example of the epoch percentage (65%) of available Galileo satellites (less than four). Thus, the time transfer application based on the Galileo CP technique is hampered by the shortage of available satellites. ...
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... the "Coord" and "T+C" approaches, the station coordinates could also contribute to the slope in time transfer. Since the clock difference series is not fully convergent from epoch 500 onward, the Allan deviation from epoch 500 backward is given in Figure 10 and Table 7, which is at different time intervals for each CP approach for the USN8-NTS1 time link in real-time mode. Note that the approaches with prior constraint information show findings similar to the standard CP at time intervals of 30 s, 60 s, 120 s, 240 s, 480 s and 960 s. ...
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... mode. Figure 11 shows the clock difference for link USN8- NTS1 for the four approaches in post-processed mode. It can be seen that the clock differences determined by the four approaches agree well with one another. ...
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... correlation can be attributed to the accuracy estimation of troposphere zenith delay in post-processed mode. Figure 12 and Table 8 illustrate the Allan deviation values at different time interval for each of the four CP approaches for time link USN8-NTS1 in post-processed mode. It can be seen that the values obtained from any constraint approaches at every time interval have slight improvements compared to the standard Galileo CP. ...
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... five days' statistical results of the short baseline time link (unit: ns). Figure 14. Comparison of the five days' Allan deviations for link USN8-USN9 by four different approaches. ...
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... the short and long baseline links were tested. Figure 13 shows the clock difference of the short baseline time link; the corresponding statistical information after full convergence is given in Table 9, and the Allan devia- tion is shown in Figure 14 and Table 10. With respect to the long baseline time link, the corresponding clock difference is shown in Figure 15 and the Allan deviation is given in Figure 16 and Table 11. ...
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... the short and long baseline links were tested. Figure 13 shows the clock difference of the short baseline time link; the corresponding statistical information after full convergence is given in Table 9, and the Allan devia- tion is shown in Figure 14 and Table 10. With respect to the long baseline time link, the corresponding clock difference is shown in Figure 15 and the Allan deviation is given in Figure 16 and Table 11. ...
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... 13 shows the clock difference of the short baseline time link; the corresponding statistical information after full convergence is given in Table 9, and the Allan devia- tion is shown in Figure 14 and Table 10. With respect to the long baseline time link, the corresponding clock difference is shown in Figure 15 and the Allan deviation is given in Figure 16 and Table 11. It also can be seen that the CP approaches with prior constraint information can improve the time transfer performance. ...
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... 13 shows the clock difference of the short baseline time link; the corresponding statistical information after full convergence is given in Table 9, and the Allan devia- tion is shown in Figure 14 and Table 10. With respect to the long baseline time link, the corresponding clock difference is shown in Figure 15 and the Allan deviation is given in Figure 16 and Table 11. It also can be seen that the CP approaches with prior constraint information can improve the time transfer performance. ...
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... In view of the strong correlation among the station coordinate, ambiguity of the CP, tropospheric delay, and receiver clock parameters in the mathematical model of time and frequency transfer, some extra previous augmented information for those parameters has been used to enhance the solving strength of the observed equation and the performance of time transfer [12][13][14][15][16]. Petit et al [17] directly utilized the integer property of ambiguity to perform precise frequency transfer over durations of up to 95 d, fixed the ambiguity parameter from the float to integer, and allowed frequency comparisons with an accuracy of 1 × 10 −16 over a few days. Zhang et al [18] employed the previous station coordinates and zenith tropospheric delays to augment the Galileo time and frequency transfer. As a result, the performance of time and frequency transfer were improved over 45%; however, the constraints of station coordinates easily caused a certain slope in clock difference [19]. ...
The carrier-phase (CP) technique based on the BeiDou global satellite navigation system (BDS-3) has proven to be an important 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, which compromises 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 principle and applied mode are discussed. The algorithm makes full use of both observation of current epoch and practical variation of receiver clock offset, further improving the performance of time and frequency transfer. Five MGEX 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 improved all four time links in terms of noise level, with improvements of 17.0%, 18.3%, 20.3%, and 5.9% for AMC4–PTBB, BRUX–PTBB, OP71–PTBB, and WTZS–PTBB, respectively, when compared with the results from a non-ED model. ED model outputs were better than raw solutions in terms of frequency stability at all time links, particularly for average time intervals (tau) < 1,000 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 1,000 s.
... Currently, research on PPP high-precision time transfer mainly focuses on methods, performance evaluations, and system applications while ignoring the impact of relevant parameters in receiver clock offset calculation. For example, when the receiver clock offset is processed, the correlation between the three-dimensional position of the station and the adjacent epochs of the receiver clock offset affects the solution results [11]. Ge et al. introduced the PPP-B2b service introduced in the Beidou-3 navigation satellite system, and used the new receiver clock model to improve the accuracy of PPP time transfer, especially the improvement effect on BDS-3 and BDS-3/GPS PPP. ...
Satellite 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.
... (cdt s,Q IF,e − cdt s,Q IF,p ) /n (9) where dD AC,Q t is the satellite clock datum of this day, dD AC,Q p is the satellite clock datum of the previous day, cdt s,Q IF,e is the satellite clock corrections at the GPS time 00:00:00 in the precise satellite clock file of this day, cdt s,Q IF,p denotes the predicted ones, and n is the number of satellites. ...
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.
... To achieve high-precision GLObal NAvigation Satellite System (GLONASS)-only PPP-based international time transfer, it is highly recommended to estimate inter-frequency clock bias for each GLONASS satellite [7]. In post-processed mode, the coordinate constraint approach for Galileo time transfer showed a slight improvement compared to the standard PPP technique for both the short baseline and long-baseline time links [8]. Multi-global navigation Satellite system (GNSS) time transfer outperforms single GNSS by increasing the number of available satellites and improving the time dilution of precision [9]. ...
Based on BDS, the QZSS system 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 (IF) 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 PPPAR, and 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 degrees, 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.
... Similar to vertical position parameters, the tropospheric delay also shows a high correlation with receiver clock parameters during PPP convergence (Ouyang et al. 2020). Selecting the IGS final tropospheric products as prior information, Zhang et al. (2018) studied a Galileo PPP time transfer model with tropospheric constraint and improved the type A uncertainty of time transfer results by 51% for the ultra-short baseline. However, there are few studies on tropospheric delay modeling to improve the initial performance of time or frequency transfer in PPP solutions, especially for BDS-3 and multi-GNSS system. ...
Precise point positioning (PPP) can currently achieve time transfer to a precision of one hundred picoseconds. However, the long convergence time is the main drawback of this popular time and frequency transfer method. It is well known that the convergence of position and receiver clock offset parameters in PPP solution is related to the satellite geometry, in which the receiver clock offset is the key parameter in time and frequency transfer and its performance could be reflected by the time dilution of precision (TDOP). This study applies tropospheric augmentation to accelerate PPP initialization and improve PPP frequency transfer performance during the convergence period. With the tropospheric augmentation applied to BDS-3 PPP, the convergence speed of receiver clock offset has been greatly improved when there are few visible satellites. Since GPS and BDS-3/GPS combined PPP, the satellite geometry and TDOP are better than that of BDS-3, the improvement in convergence speed is limited correspondingly. In addition, due to a more stable receiver clock offset estimated with the tropospheric information constraints, the short-term stability of frequency transfer during the convergence period has been greatly improved for GPS, BDS-3 and BDS-3/GPS combined PPP. For the two time links selected in this study, the short-term stability has been improved by more than 60, 45 and 40% in BDS-3, GPS and BDS-3/GPS combined PPP frequency transfer, respectively. However, the contribution of tropospheric augmentation to PPP frequency transfer is no longer significant after convergence.
... The potential of using Galileo E5 observation for time transfer has been well investigated using a single frequency or by forming dual-frequency observation with E1 (1575.42 MHz) measurements (Martínez-Belda et al. 2011Zhang et al. 2019). ...
... at the end of 2018. Figure 1 presents the ground tracks of Galileo satellites available for time transfer on February 1, 2019. Although a huge potential exists for Galileo time and frequency transfer, particularly because of its superior E5 frequency, studies in recent years have focused only on dual-frequency observations and not on multi-frequency observations (Martínez-Belda et al. 2011Zhang et al. 2019). With Galileo's superior E5 signal and its sub-carriers (E5a and E5b) and E1 observations, additional combination options are available, and the redundancy of observations is significantly increased compared to that of current dualfrequency Galileo time transfer. ...
The global positioning system (GPS) carrier-phase (CP) technique is a widely used spatial tool for remote precise time and frequency transfer. However, the performance of traditional GPS time and frequency transfer has been limeted because the ambiguity paramter is still the float solution. This study focuses on the performance of GPS precise time and frequency transfer with integer ambiguity resolution and discusses the corresponding mathematical model. Fractional-cycle bias (FCB) products were estimated by using an ionosphere-free combination. The results show that the satellite wide-lane (WL) FCB products are stable, with a standard deviation (STD) of 0.006 cycles. The narrow-lane (NL) FCB products were estimated over 15 min with the STD of 0.020 cycles. More than 98% of the WL and NL residuals are smaller than 0.25 cycles, which helps to fix the ambiguity into integers during the time and frequency transfer. Subsequently, the performances of the time transfers with integer ambiguity resolution at two time links between international laboratories were assessed in real-time and post-processing modes and compared. The results show that fixing the ambiguity into an integer in the real-time mode significantly decreases the convergence time compared with the traditional float approach. The improvement is ~49.5%. The frequency stability of the fixed solution is notably better than that of the float solution. Improvements of 48.15% and 27.9% were determined for the IENG–USN8 and WAB2–USN8 time links, respectively.
... Thereafter, the all-in-view (AV) approach was proposed to overcome the limitations of the common-view satellite condition and pseudorange measurements in the CV approach [4]. Considering that GPS carrier phase observations are two orders of magnitude more precise than that of the pseudorange measurement, a GPS carrier-phase (CP) approach was proposed for precise time and frequency transfer [5][6][7], which exhibited better performance when compared to the CV and AV approaches. Therefore, the GPS CP approach became a primary means in time laboratories worldwide. ...
The modernized GPS, Galileo, and BeiDou global navigation satellite system (BDS3) offers new potential for time transfer using overlap-frequency (L1/E1/B1, L5/E5a/B2a) observations. To assess the performance of time and frequency transfer with overlap-frequency observations for GPS, Galileo, and BDS3, the mathematical models of single- and dual-frequency using the carrier-phase (CP) technique are discussed and presented. For the single-frequency CP model, the three-day average RMS values of the L5/E5a/B2a clock difference series were 0.218 ns for Galileo and 0.263 ns for BDS3, of which the improvements were 36.2% for Galileo and 43.9% for BDS3 when compared with the L1/E1/B1 solution at BRUX–PTBB. For the hydrogen–cesium time link BRUX–KIRU, the RMS values of the L5/E5a/B2a solution were 0.490 ns for Galileo and 0.608 ns for BDS3, improving Galileo by 6.4% and BDS3 by 12.5% when compared with the L1/E1/B1 solution. For the dual-frequency CP model, the average stability values of the L5/E5a/B2a solution at the BRUX–PTBB time link were 3.54∙× 10−12 for GPS, 2.20 × 10−12 for Galileo, and 2.69 × 10−12 for BDS3, of which the improvements were 21.0%, 45.1%, and 52.3%, respectively, when compared with the L1/E1/B1 solution. For the BRUX–KIRU time link, the improvements were 4.2%, 30.5%, and 36.1%, respectively.
... Time and frequency transfer is one of the crucial issues for the comparison of remote time and frequency references. Currently, various methods exist for implementing remote time and frequency transfers, such as the two-way satellite time and frequency transfer (TWSTFT) technology technique based on mobile stations, the optical fibre technique, and the Global Navigation Satellite System (GNSS) technique [1,2]. The TWSTFT technique is limited in use because of the necessity of a mobile ground station (MS) and a common satellite transponder, along with the high transportation costs. ...
Abstract In this study, a real‐time and dynamic time transfer method based on double‐differenced (DD) real‐time kinematic (RTK) mode is proposed. First, the method forms the DD observations of Global Navigation Satellite System (GNSS) to fix the DD ambiguity, and then, all of the fixed single‐differenced (SD) ambiguities are recovered while defining the SD ambiguity datum; finally, the method uses the SD observations to realise the time transfer by using the fixed SD ambiguities. Five different baseline links were used for the validations. The results demonstrated that the DD‐RTK method can be used for both kinematic positioning and precise time transfers, and it provides for much better accuracy and stability than the un‐differenced precise point positioning method because it is operated by the broadcast ephemeris, which is more convenient for real‐time applications.
... However, especially over intercontinental distances, optical fibre links and quantum techniques create challenges. GNSS-based time and frequency transfer are dependent on strict modelling of both code and carrier phase measurements, which can lead to precise measurements at subnanoseconds without being restricted by distance or weather conditions [3][4][5][6][7]; therefore, GNSS transfer is still the optimal method for use by high-demand time/frequency users. ...
Satellite timing is an effective and convenient method that has been widely accepted in the time community. The key to satellite timing is obtaining a clean receiver clock offset. In this paper, instead of regarding the receiver clock offset as white noise, a two-state stochastic clock model involving three kinds of noise was conceived and used in PPP filter estimation. The influence of clock type and sampling time on satellite timing performance was first analysed. In addition, the kinematic scheme and static scheme were both investigated for meeting the demands of multi-occasional users. The values show that the model works well for both the kinematic scheme and static scheme; in contrast to that of the white noise model, the timing stability is enhanced at all the sampling times. For the six stations, especially when the averaging time is less than 1000 s, the average stability improvement values of the kinematic scheme are 75.53, 43.24, 75.00, 69.05, 40.57, and 25.45%, and the average improvement values of the static scheme are 65.49, 77.94, 56.71, 60.78, 64.41, and 39.41%. Furthermore, the enhancement magnitude is related to clock type. For a high-stability clock, the improvement of the kinematic scheme is greater than that of the static scheme, whereas for a low-stability clock, the improvement of the kinematic scheme is less than that of the static scheme.
... The potential of using Galileo E5 observation for time transfer has been well investigated using a single frequency or by forming dual-frequency observation with E1 (1575.42 MHz) measurements (Martínez-Belda et al. 2011Zhang et al. 2019). ...
... at the end of 2018. Figure 1 presents the ground tracks of Galileo satellites available for time transfer on February 1, 2019. Although a huge potential exists for Galileo time and frequency transfer, particularly because of its superior E5 frequency, studies in recent years have focused only on dual-frequency observations and not on multi-frequency observations (Martínez-Belda et al. 2011Zhang et al. 2019). With Galileo's superior E5 signal and its sub-carriers Content courtesy of Springer Nature, terms of use apply. ...
GNSSs, such as Galileo and modernized GPS, BeiDou and GLONASS systems, offer new potential and challenges in precise time and frequency transfer using multi-frequency observations. We focus on the performance of Galileo time and frequency transfer using the E1, E5a, E5b and E5 observations. Dual-frequency, triple-frequency and quad-frequency models for precise time and frequency transfer with different Galileo observations are proposed. Four time and transfer links between international time laboratories are used to assess the performances of different models in terms of time link noise level and frequency stability indicators. The average RMS values of the smoothed residuals of the clock difference series are 0.033 ns, 0.033 ns and 0.034 ns for the dual-frequency, triple-frequency and quad-frequency models with four time links, respectively. With respect to frequency stability, the average stability values at 15,360 s are 9.51 × 10−15, 9.46 × 10−15 and 9.37 × 10−15 for the dual-frequency, triple-frequency and quad-frequency models with four time links, respectively. Moreover, although biases among different models and receiver the inter-frequency exist, their characteristics are relatively stable. Generally, the dual-/triple-/quad-frequency models show similar performance for those time links, and the quad-frequency models can provide significant potential for switching among and unifying the three multi-frequency solutions, as well as further enhancing the redundancy and reliability compared to the current dual-frequency time transfer method.
