GPS Precise Point Positioning Research Articles

The investigation of real-time LEO timing via GPS PPP with different RT products

Low Earth Orbit (LEO) satellites mostly utilize crystal oscillators instead of high-performance atomic clocks mounted on medium to high-orbit satellites. Therefore, keeping high-precision time synchronization between LEO and GNSS satellites is the premise of realizing the high-precision application of LEO satellites. In this contribution, GPS precise point positioning (PPP) technology was employed to release precise timing for LEO satellites with different Real-time (RT) products. GRACE-FO C and GRACE-FO D satellites and five precise RT products from different analysis centers, which are CNES, GFZ, GMV, WHU, and CAS were chosen to achieve precise timing. The results indicated that the overall trend of clock difference fluctuations presented with all real-time products is generally consistent, fluctuating within the range of ± 4 ns. Furthermore, real-time precise products from GMV and GFZ exhibit significant fluctuations during the daily initial time period. Additionally, real-time products from WHU outperform other products and demonstrate greater stability. In terms of frequency stability, the clock stability of various analysis centers is generally consistent, with short-term stability (1280 s) reaching approximately 10−13 and long-term stability (10240 s) reaching around 10−14. WHU's timing stability is notably superior to other real-time products. In the time synchronization experiment, real-time products fluctuate within the range of ± 2 ns, while IGS final products fluctuate within ± 1 ns. In terms of time synchronization stability comparison, short-term stability (1280 s) still fluctuates around 10−13, and long-term stability (10240 s) fluctuates around 10−14. WHU exhibits relatively good overall stability, while GFZ shows comparatively lower overall stability.

The analysis on time transfer of GPS/Galileo /BDS PPP with integer ambiguity resolution

GPS precise point positioning (PPP) approach has been considered for achieving time transfer for a long time. By virtue of GPS/Galileo/BDS FCB products, PPP model has the possibilities for changing phase ambiguities from ‘float’ value to ‘integer’ value. In this study, PPP time/frequency transfer model has been presented and performance of seven links equipped with Hydrogen Masers (H-Masers) and cesium atomic clocks are compared in static and kinematic modes. With partial ambiguity resolution (PAR) enabled, in contrast to GPS, results show that multi-GNSS’s fixing rate is much higher and TTFF(Time To First Fixing) is much shorter. It is verified that the fixing rate and TTFF has nothing to do with the atomic clock type but has strong correlation with the quality of observation. We find that frequency stability of time link is seriously dependent on the type of atomic clock. As far as H-Masers, it has reached the order of 1E-16/1E-15 at the averaging time of 122880 s, respectively. As far as Cesium clock, it has reached the order of 1E-15/1E-14 at the averaging time of 122880 s, respectively. For H-Maser, the long-term frequency stabilities of integer PPP (IPPP) have been improved by roughly 3% at the static mode and 4% at the kinematic mode on average, respectively. For positioning, compared to PPP solutions, the stabilities of the IPPP coordinates are improved after an averaging time of 7680 s in static or kinematic mode.

Reconstructed estimation method of the multi-frequency GNSS inter-frequency clock bias

In consideration of contributions from both carrier phase and pseudorange observations during computation, this study introduces a reconstructed method for estimating the multi-frequency global navigation satellite system (GNSS) inter-frequency clock biases (IFCB). Diverging from conventional approaches that separately calculate the time-varying and constant parts of IFCBs using carrier phase and pseudorange observations, the reconstructed method directly utilizes their combination to estimate satellite IFCBs. To validate the efficacy of the presented approach, 7 d observations from 87 International GNSS Service (IGS) stations are analyzed, with a specific focus on triple-frequency GPS, multi-frequency BDS-3, and Galileo IFCBs, aiming to scrutinize their distinctive characteristics. Furthermore, the performances of satellite IFCB estimation are investigated in both precise point positioning (PPP) and single-point positioning (SPP) using 35 IGS stations over 3 d. The results demonstrate that IFCBs of GPS BLOCK IIIA satellites exhibit centimeter-level variations, distinguishing them from BLOCK IIF counterparts. The Galileo IFCBs vary from millimeter to centimeter level, while those of BDS-3 reach a centimeter level. These variations significantly impact GPS PPP convergence performances but have minimal effects on Galileo and BDS-3 PPP. SPP performances are slightly enhanced when the time-varying IFCB part are taken into account. Additionally, we note disparities in the constant parts of satellite IFCBs computed with differential code bias (DCB) products, reconstructed, and pseudorange observation-based methods, particularly for BDS-3 C2I/C6I-C1P/C5P and C2I/C6I-C1P/C6I combinations. The differences of IFCB estimated with different strategies, SPP and PPP performances show that the reconstructed method is better than others, and the IFCB accuracy decreases when computed with satellite DCB products.

Studying the Fixing Rate of GPS PPP Ambiguity Resolution Under Different Geomagnetic Storm Intensities

AbstractGlobal Positioning System (GPS) Precise Point Positioning (PPP) with correct fixing ambiguity resolution (AR) can reach cm‐mm level positioning accuracy. However, this accuracy can be degraded by the geomagnetic storm effects. To comprehensively investigate the ambiguity resolved percentage (ARP) of GPS kinematic PPP, referred to as PPP‐ARP, under different intensities of geomagnetic storms, based on the Natural Resources Canada's Canadian Spatial Reference System (CSRS) PPP, this study for the first time gives the correlation between the PPP‐ARP and storm intensity using 67 storms occurred in the past 5 years of 2018–2022. Experimental results indicate that the PPP‐ARP decreases gradually as the increase of geomagnetic storm intensity. Under quiet and low geomagnetic conditions (Dstmin > −50 nT), the PPP‐ARP of global GNSS stations can achieve more than 96%, while these during strong storms (Dstmin ≤ −100 nT) are generally lower than 90.0%, especially for the PPP‐ARP of some stations located at low latitudes which are lower than 40.0%. The mechanism of PPP‐ARP decrease under geomagnetic storms is mainly due to the cycle slips and even loss of lock of GNSS signals caused by the storms induced ionospheric disturbances and scintillations. In addition, different from many previous studies, we found that the CSRS‐PPP with AR can achieve good positioning accuracy (3D RMS <0.2 m) even under strong geomagnetic storms.

Evaluation of Asia-Europe TWSTFT Links Using the Express-80 Satellite

Two-way satellite time and frequency transfer (TWSTFT) is extensively used by the Bureau International des Poids et Mesures (BIPM) in the calculation of coordinated universal time (UTC). The Asia-Europe TWSTFT links using the Express-80 satellite were reestablished in June 2021. This paper uses monthly measurements to evaluate the time comparison performance of the Asia-Europe TWSTFT network. We select TWSTFT data for analysis on the long and short baselines over the same period, respectively. Since the TWSTFT link has not been calibrated, we take the GPS precise point positioning (PPP) link, independent of TWSTFT, as a reference and align the TWSTFT results with it. Then, the results from the TWSTFT and GPS PPP solutions are compared on the different baselines. Finally, the modified Allan deviation (MDEV) and the double clock difference (DCD) between the TWSTFT link and the GPS PPP link are used to evaluate the performance of the TWSTFT results. The results show that the TWSTFT results are consistent with the results of CPS PPP time transfer, and the frequency stability of TWSTFT links on long and short baselines can reach 3E-15 or better with an averaging time of 1 d. The standard deviation of the DCD results is less than 0.4 ns on different baselines, which ensures the accuracy of the TWSTFT link. The Asia-Europe TWSTFT link can be used for UTC time transfer after calibration.

GPS, BDS-3, and Galileo Inter-Frequency Clock Bias Deviation Time-Varying Characteristics and Positioning Performance Analysis

Multi-frequency observations are now available from GNSSs, thereby bringing new opportunities for precise point positioning (PPP). However, they also introduce new challenges, such as inter-frequency clock bias (IFCB) between the new frequencies and the original dual-frequency observations due to triple-frequency observations, which severely impact the PPP. In this paper, we studied the estimation and correction methods of uncombined inter-frequency clock bias of GPS, BDS-3, and Galileo, analyzed the time-varying characteristics and short-term stability of IFCB, and analyzed the influence of IFCB on the positioning of the GPS, BDS-3, and Galileo, based on a triple-frequency un-differential non-combined PPP model. The obtained results show that the amplitude of Block IIF satellites of the GPS can reach up to 10–20 cm, and the IFCB in BDS-3, Galileo, and GPS Block III satellites can be neglected. After correction by IFCB, the 3D positioning accuracy of the GPS triple-frequency PPP was 1.73 cm and 4.75 cm in the static and kinematic modes, respectively, while the convergence time was 21.64 min and 39.61 min. Compared with the triple-frequency GPS PPP without any correction with IFCB, the static and kinematic 3D positioning accuracy in this work was improved by 27.39% and 17.34%, and the corresponding convergence time was improved by 10.55% and 15.22%, respectively. Furthermore, the delayed IFCB was also used for positioning processing, and it was found that a positioning performance comparable to that of the same day can be obtained. The standard deviation of IFCB for a single satellite was found to be no more than 1 cm, when the IFCB value of a neighboring day was subtracted from the IFCB value of same day, which proves the short-term stability of IFCB.

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.

Küresel BeiDou Sistemi (BDS-3) için hassas nokta konumlama performansının değerlendirilmesi

The main objective of this study is to evaluate the positioning performance of the global BeiDou system (BDS-3) in terms of Precise Point Positioning (PPP). The PPP performance of BDS-3 was compared with both GPS and the regional BeiDou system (BDS-2). In addition, the contribution of BDS-3 to the PPP performance was analyzed through multi-GNSS combinations of these three systems. For this purpose, seven processing scenarios in total were composed, and the observation dataset collected at 15 International GNSS Service (IGS) stations over the period of November 21 and 30, 2021 were processed under these scenarios. The results showed that positioning accuracies of 0.0152, 0.0605, and 0.0203 m could be acquired from the GPS, BDS-2, and BDS-3 PPP solutions, respectively. Also, average convergence times obtained from these solutions were respectively computed as 60.94, 261.71, and 63.06 minutes. While results of the BDS-2 PPP solution remained substantially behind the GPS results, comparable results with the GPS PPP were acquired from the BDS-3 PPP solution. Besides, the obtained results revealed that the positioning performance could be improved significantly when double and triple combinations of these navigation systems were employed. The positioning accuracy and convergence time obtained from the PPP solution where GPS, BDS-2, and BDS-3 systems were used in common were 0.0136 m and 26.45 minutes. In this study, tropospheric delay estimations were also evaluated to analyze the PPP performance comprehensively. The results demonstrated that the BDS-3 solution could provide close results to the GPS PPP solution in terms of tropospheric delay estimation and the best troposphere estimation performance could similarly be acquired from the multi-GNSS solution where three systems were employed in common.

Signal-in-Space and Positioning Performance of BDS Open Augmentation Service

As a typical augmentation satellite system for centimeter-level positioning, PPP (Precise Point Positioning) service based on PPP-B2b signal of China’s new generation BeiDou system (BDS-3) was released for Asia-Pacific area on July, 2020. This paper first introduces the recovery theory of PPP-B2b SSR (State Space Representation) messages and then implements a real-time PPP-B2b precise positioning terminal to decode and obtain the PPP-B2b SSR orbit, clock, and biases. On those bases, the coverage, signal-in-space, and positioning performance of PPP-B2b SSR are evaluated. The results show that PPP-B2b SSR of BDS-3 can cover the most area of 50°E-180°E, 30°S-70°N and improve signal-in-space accuracy significantly. The improvement rate on BDS clock offset can reach 77%, which far exceeds average 40% improvement on BDS orbit, while it is opposite for GPS with 80% improvement rate on orbit and 61% on clock offset. Average SISRE (signal-in-space range error) of PPP-B2b SSR is better than 10 cm. The 95% positioning results show that centimeter- to decimeter-level positioning can be achieved after a few minutes of convergence based on PPP-B2b SSR, which satisfies the BDS open service performance standard. Comparing to BDS PPP based on PPP-B2b SSR, BDS + GPS PPP can promote convergence significantly with average 40% improvement rate for 95% epochs and can further improve positioning accuracy with 30%-35% improvement rate in horizontal and 10%–15% in vertical direction.

Analysis and Comparison for Fusion Algorithms of Time Transfer

In order to improve the reliability of precise time comparison, this paper takes advantage of long-term stability of TWSTFT (Two-Way Satellite Time and Frequency Transfer) and short-term stability of PPP (GPS Precise Point Positioning). Stability weighting, Vondrák-Čepek combined filtering, and Kalman filtering methods are applied to fuse the TWSTFT and GPS PPP time comparison between the NTSC (National Time Service Center) and PTB (Physikalisch-Technische Bundesanstalt). The results show that the three fusion methods all improve the diurnal variations in TWSTFT and the discontinuities in GPS PPP solution, and the absolute value of the DCD (Double Clock Difference) between fusion results and PPP solution is kept within the link calibration uncertainty. The 1d time and frequency stability of the three methods can reach the order of sub-nanosecond and 10−15, respectively. The Vondrák-Čepek fusion method has the highest stability within 1d, which is suitable for the fusion of time comparison links with requirements for short stability. Stability weighting and Kalman filtering fusion have better fidelity, which are suitable for the fusion of time comparison links that require high accuracy.

Analyzing the contributions of multi-GNSS and INS to the PPP-AR outage re-fixing

GNSS observation outage occurs inevitably in various situations, e.g., automobile driving in urban environments. Although the ambiguity resolution (AR) significantly shortens the initialization time of precise point positioning (PPP), frequent re-initialization of PPP AR may be needed due to outages. The inertial navigation system (INS) can be used for acquiring highly accurate position information during GNSS outages. In the previous studies, the GPS PPP/INS with the ambiguity resolution model is proposed, and the experimental results confirm that the INS could facilitate the re-fixing of the interrupted GNSS ambiguity. Multiple GNSS can also be used to shorten the PPP convergence time. We compare the contribution of multi-GNSS and the INS to the ambiguity re-fixing during GNSS outage. Results show that the multi-GNSS, e.g., Galileo, GLONASS and BDS, without ambiguity resolution has little contribution to the re-fixing of GPS ambiguity in PPP/INS, while INS can provide highly accurate positioning results during the GNSS outages. The higher the accuracy of the predicted INS positioning, the lower the contribution of multi-GNSS to the re-fixing of the ambiguity in the PPP/INS. The finding is verified by a theoretical analysis, carborne experiment and shipborne experiment. Experiment results show that the re-fixing time is 43 s for GPS PPP and MEMS-grade INS coupled system in GNSS outage of 1 s. The re-fixing time of GPS is slightly changed when adding the multi-GNSS, e.g., Galileo, GLONASS and BDS, without the ambiguity resolution. However, by performing ambiguity resolution to the added GNSS system, the re-fixing time of PPP/INS is significantly reduced from 43 to 4 s. The reason is that, although the multi-GNSS provides little improvement on the accuracy of the ambiguity, it enlarges the number of the ambiguity parameter. The possibility of ambiguity resolution is increased due to the large candidate set of the ambiguity, which reduces re-fixing time.

Impact of Geomagnetic Storms on Ionosphere Variability and Precise Point Positioning Application in High Latitudes of the Northern Hemisphere

Based on the ionospheric scintillation data of the Canadian High Arctic Ionospheric Network (CHAIN), the variation characteristics of ionospheric Total Electric Content (TEC), phase scintillation and Rate of TEC Index (ROTI) were analyzed during the 26 August 2018 geomagnetic storm period. Results show that the TEC anomalies reach 20 TECU on global scale and 6 TECU over Canadian regions, respectively. The occurrence of phase scintillations is about 12.6% during the selected stormy day, which is only around 1% during geomagnetic quiet period. The occurrence of ROTI exhibits high correlation with that of phase scintillations during stormy geomagnetic conditions. The impact of ionospheric scintillations on positioning performance was analyzed by means of GPS Precise Point Positioning (PPP). It is proved that the 3D positioning root mean square errors are within 0.4 m for all test stations during the quiet geomagnetic condition. When it comes to the high geomagnetic condition, the magnitude of positioning errors significantly increase, which reaches 0.9 and 1.7 m in horizontal and vertical directions, respectively.

Performance Evaluation of Precise Point Positioning Using Dual Frequency Multi-GNSS Observations

Abstract In addition to GPS and GLONASS constellation, the number of (Global Navigation Satellite System) GNSS satellites are increasing, it is now possible to evaluate and analyze the position accuracy with multi GNSS constellation. In this paper, statistical assessment of static Precise Point Positioning (PPP) using GPS, GLONASS, dual system GPS/GLONASS, three system GPS/GLONASS/Galileo, GPS/GLONASS/BeiDou and multi system GPS/GLONASS/Galileo/BeiDou PPP combinations is evaluated. Observation data of seven whole days from seven IGS multi GNSS experiment (MGEX) stations is used for analysis. Position accuracy and convergence time is analyzed. Results show that the GPS/GLONASS positioning accuracy increases over GPS PPP. Standard deviations (STDs) of position errors for GPS PPP are 4.63, 3.00 and 6.96 cm in east, north and up components while STDs for GPS/GLONASS PPP are 4.10, 3.42 and 6.50 cm respectively. Root mean square for three dimension (RMS3D) for GPS/GLONASS PPP solution is 8.96 cm. With the addition of Galileo and BeiDou to the combined GPS/GLONASS further enhances the positioning accuracy. Root mean square for horizontal component reach to 5.35 cm of GPS/GLONASS/Galileo/BeiDou PPP solutions. Results analysis of GPS/GLONASS/Galileo PPP solutions show an improvement of convergence time by only 3.81% to achieve accuracy level of 3.0 cm over GPS/GLONASS/BeiDou PPP mode. Results also demonstrate that position accuracy improvement after adding BeiDou observations to the GPS/GLONASS PPP mode is not significant.

Evaluation of the Effect of Higher-Order Ionospheric Delay on GPS Precise Point Positioning Time Transfer

In high-precision GPS precise point positioning (PPP) time transfer, errors caused by the effect of ionosphere delay have to be corrected. Usually the ionosphere-free combinations of the pseudo code and the carrier phase is used in GPS PPP data processing, and it effectively eliminates the effect of the first-order ionospheric delay. This study quantitatively analyzes the errors caused by higher-order ionospheric (Ion2+) delays in precise PPP time transfer. Data of two 7-day test periods, including low and moderate ionospheric conditions, from 20 stations located in middle- and low-latitude, were analyzed. The difference in clock solution with and without the Ion2+ correction, including the receiver clock solution and time-link clock solution, was deeply analyzed and discussed. The difference sequence shows a constant bias plus some variations with a diurnal variation. For the difference of the receiver clock solutions, the mean standard deviation of the variations is 3.92 ps in low-latitude, which is much larger than that of 2.59 ps in mid-latitude due to the influence of the larger ionospheric electron density on the low-latitude. The maximum constant bias reached more than 15 ps and was negative at most stations in the northern hemisphere, while it was positive at most stations located in the southern hemisphere. The difference in the time-link solutions correlates not only with time and region, but also with the length of the time-links. The largest difference in the long time-link SYDN-PTBB, BJNM-SYDN, AMC2-SYDN, etc., reaches more than 25 ps, while that of the short time-link IENG-PTBB, BRUX-PTBB, etc., is less than 3.5 ps. Therefore, the Ion2+ correction is necessary for high-precision PPP time transfer over long time-links, especially time-links made by one station located in the northern hemisphere and another located in the south hemisphere; however, it could be ignored for short time-links.

GPS\u2009+\u2009Galileo\u2009+\u2009BeiDou precise point positioning with triple-frequency ambiguity resolution

Along with the rapid development of GNSS, not only BeiDou, but also Galileo, and the newly launched GPS satellites can provide signals on three frequencies at present. To fully take advantage of the multi-frequency multi-system GNSS observations on precise point positioning (PPP) technology, this study aims to implement the triple-frequency ambiguity resolution (AR) for GPS, Galileo, and BeiDou-2 combined PPP using the raw observation model. The processing of inter-frequency clock bias (IFCB) estimation and correction in the context of triple-frequency PPP AR has been addressed, with which the triple-frequency uncalibrated phase delay (UPD) estimation is realized for real GPS observations for the first time. In addition, the GPS extra-wide-line UPD quality is significantly improved with the IFCB correction. Because of not being contaminated by the IFCB, the raw UPD estimation method is directly employed for Galileo which currently has 24 satellites in operation. An interesting phenomenon is found that all Galileo satellites except E24 have a zero extra-wide-lane UPD value. With the multi-GNSS observations provided by MGEX covering 15 days, the positioning solutions of GPS + Galileo + BeiDou triple-frequency PPP AR have been conducted and analyzed. The triple-frequency kinematic GNSS PPP AR can achieve an averaged 3D positioning error of 2.2 cm, and an averaged convergence time of 10.8 min. The average convergence time can be reduced by triple-frequency GNSS PPP AR by 15.6% compared with dual-frequency GNSS PPP AR, respectively. However, the additional third frequency has only a marginal contribution to positioning accuracy after convergence.

An analysis of PPP-GPS-based decentralized train multi-sensor navigation system

GPS precise point positioning (PPP) is increasingly being used in many precise positioning applications to achieve sub-meter level accuracy using a stand-alone user receiver. To achieve the full-scale navigation parameters of position, velocity and attitude, GPS is often combined with the inertial navigation system (INS) to deliver navigation solutions in high update rate. However, GPS signals cannot always be tracked in difficult areas, which leads to an integration performance degradation because of INS sensor errors. Therefore, the authors propose a PPP-GPS/INS/odometer/map-matching integrated navigation system. The positioning performance based on the different International GNSS Service (IGS) products for train kinematic positioning applications is investigated. A field test was conducted on a specific low-density line to evaluate the proposed system. The test results confirm that the proposed multi-sensor navigation system can provide seamless navigation in both GPS available and unavailable situations with the accuracy of decimeter. Different IGS satellite orbits and clock offset products were used to generate the PPP results, and it was concluded that the IGS final products provide the best performance, with a distance root mean square (DRMS) of 0.138 m, and the IGS ultra-rapid product can also generate acceptable positioning solutions with a DRMS of 0.222 m.

Performance of ionospheric-free PPP time transfer models with BDS-3 quad-frequency observations

The BeiDou Navigation Satellite System (BDS) has as achieved the status of a global navigation satellite system. Compared to BDS-2 satellites, BDS-3 satellites transmit B1C, B2a, and B2b signals but not B1I and B3I signals. In this study, for the four open-services of BDS-3 satellites, four ionospheric-free combinations, namely (B1I/B3I), (B1I/B2a), (B1C/B2a) and (B1C/B3I) were first proposed. Then, the performance of the BDS-3 carrier-phase time transfer was assessed and investigated. For comparison and evaluation purposes, precise point positioning (PPP) time transfer with BDS-2, GPS, and Galileo was also assessed. Analogous to the BDS-3 signal structure, the performance of BDS-2 based on the B1I/B2I- and B1I/B3I- combined PPP solutions was first validated. Then, with respect to the GPS and Galileo PPP time transfer, the BDS-3 B1I/B3I, B1I/B2a, B1C/B2a, and B1C/B3I; BDS-2 B1I/B2I; and BDS-2 + BDS-3 B1I/B3I PPP time transfers were assessed and analysed. The experimental results demonstrated that the BDS-3 B1I/B3I performance was slightly better than the BDS-3 B1I/B2a, B1C/B3I and B1C/B2a performances due to the differential code bias (DCB) accuracy. Furthermore, the BDS-2 B1I/B3I PPP was worse than the other PPP solutions, while BDS-2 + BDS-3 B1I/B3I PPP outperformed the other PPP solutions. Compared with the BDS-2 B1I/B3I PPP, the mean reductions in the standard deviation (STD) values were approximately (77.2, 21.3, 1.8, 1.3, 13.1) % from (0.241, 0.687, 0.547, 0.218, 0.585) ns to (0.136, 0.566, 0.537, 0.215, 0.517) ns calculated from BDS-3 and (97.5, 23.5, 4.9, 4.8, 16.7)% from (0.241, 0.687, 0.547, 0.218, 0.585) ns to (0.122, 0.556, 0.521, 0.208, 0.501) ns calculated and BDS-2 + BDS-3, respectively. For the frequency stability, BDS-3 demonstrated better results, while BDS-2 + BDS-3 presented significant improvements with respect to BDS-2. The maximum improvement in BDS-2 + BDS-3 reached up to 56.1% from 3.3973E-14 to 1.49E-14. Additionally, the modified Allan deviation (MDEV) of BDS-2 + BDS-3 was analogous to that of GPS and Galileo.

Multi-constellation GNSS precise point positioning with multi-frequency raw observations and dual-frequency observations of ionospheric-free linear combination

Precise point positioning (PPP) is famous for its capability of high-precision positioning with just one station as long as the receiver can receive global navigation satellite system (GNSS) signals. With the rapid development of BDS and Galileo, the number of available satellites for positioning has increased significantly. In addition, GPS III, GLONASS-K, BDS, and Galileo satellites can transmit triple-frequency signals. The potentials of multi-constellation GNSS PPP requires further analysis on a global scale. Therefore, we selected 96 multi-GNSS experiment (MGEX) stations with a global distribution and used 1 week’s data to assess the PPP performance. The results show that the PPP based on multi-frequency raw observations with spatial and temporal constraints has better performance than PPP using dual-frequency ionospheric-free observations. The main contribution of multi-constellation GNSS PPP is to shorten the convergence time. The convergence time for GPS PPP is approximately 40 min, which can be shortened to less than 20 min in multi-GNSS PPP. After convergence, the positioning accuracy of multi-GNSS PPP is improved by 0.5 to 1.0 cm compared with GPS or GLONASS PPP. The positioning accuracy of multi-GNSS could be further improved in the future with the BDS and Galileo precise products of orbits, clock and phase center offset/variation.

Performance Analysis of Two-Way Time Comparison of Eurasian Satellites Based on 1 Mcps/s Code

The bandwidth leased on Earth satellites directly affects the operation cost of TWSTFT (Two-Way Satellite Time and Frequency Transfer). Until May 2017, the Ku-band TWSTFT between Asian-European laboratories involved in UTC (Coordinated Universal Time) computing had been using the 2.5 Mcps/s pseudo-random codes with a bandwidth of 2.5 MHz. In order to reduce the cost without affecting the performance of time and frequency, a pseudo-random code with 1 Mcps/s and bandwidth of 1.7 MHz is first attempted to transmit time bidirectionally between Eurasian and Asian satellites in China. An indirect calibration for the bidirectional links by using the calibrated GPS PPP (Global Position System Precise Point Positioning) links reduces the link uncertainty. The TWSTFT link data of December 2018 are selected to analyze the link performance. It is found that the daily frequency stability and time stability of TWSTFT link constructed with 1 Mcps/s code rate reach 10−15 and 0.3 ns respectively through the ABS-2A satellite. The results show that it is feasible to use 1 Mcps/s code rate for ultra-long distance TWSTFT. Compared with the traditional methods, the system has a low cost, and the time transfer performance can meet the needs of international atomic time calculation.

Analysis on the Impacts of Slant Tropospheric Delays on Precise Point Positioning

Tropospheric delay is one main factor affecting the accuracy of precise point positioning (PPP) ambiguity-float and fixed solutions. Investigations mainly focused on evaluating the contributions of tropospheric corrections to the accuracy and reliability of PPP solutions. The tropospheric corrections generally contained the zenith tropospheric delay (ZTD) and the horizontal gradients estimated from relative positioning or PPP. However, the estimated tropospheric delays can be partly absorbed by the carrier phase residuals if the stochastic model is not well-defined. Therefore, along with the ZTD and horizontal gradients, the carrier phase residuals from PPP backward filter are considered to reconstruct slant tropospheric delay (STD). Based on the proposed STD model, its marginal effects on GPS PPP were investigated. Results indicated that the consideration of carrier phase residuals for STD modeling can improve the three-dimensional accuracy to 0.5 cm/1 cm/1.2 cm in the South/North/Up (N/E/U) components. Then, the effects of internal and external STD corrections on PPP float and fixed solutions were analyzed. Compared to the ZTD + gradients augmentation, STD corrections from the same station could improve the PPP accuracy by 51%/51%/60%; the large improvements were because the multipath error and observation noise were eliminated. In comparison, the improvement was 14%/28%/31% using external STD corrections, which indicated the effects of unmodeled tropospheric errors in the phase residuals. The ambiguity-fixing results indicated that the fixing rate of PPP ambiguity was increased by 30% with STD augmentation. As the BeiDou System (BDS) suffered longer convergence than that of GPS, the benefits of STD modeling to the BDS observations were also validated. Overall, the results validated the performance of STD-augmented PPP, which demonstrated the potential application of high-accuracy troposphere products.