Precise Point Positioning Time Transfer Research Articles

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

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

PPP time transfer using an adaptive clock constraint model

ABSTRACT In the processing of Precise Point Positioning (PPP) data, the receiver clock is approached with nearly infinite uncertainty, rendering it difficult to fulfill the requirements of high-precision time frequency applications. Therefore, a receiver clock model is essential. In this study, we first analyze the “over-constraint” problem in the existing clock model and subsequently propose a new clock model, called the Adaptive Clock Constraint (ACC) model, which relies on a sliding window to update covariance and frequency characteristics parameters in real-time. To verify the robustness of the ACC model, three experiments were conducted, and the results show that the ACC model not only is suitable for different types of atomic clock stations but also has superior frequency stability and time transfer precision in contrast to the BIPM PPP, the IGS products and White Noise (WN) model results. Using the optical fiber results as a time reference, the STD of the time difference between the ACC model and optical fiber results is 0.13 ns and the frequency stability is 1.28 × 10−16 on average for one week, representing improvements of more than 10% and 15% compared with the BIPM PPP results.

LEO satellite clock modeling and its benefits for real-time LEO PPP timing

In the kinematic Precise Orbit Determination (POD) process for low earth orbit (LEO) satellites, a significant correlation exists between the orbital and clock parameters. Here, a LEO satellite clock model is proposed to enhance the Precise Point positioning (PPP) timing and time synchronization during the LEO orbit/clock determination. The GRACE-FO satellite was utilized to achieve PPP timing and time transfer for LEO satellites with the real-time (RT) products provided by three analysis centers, namely Centre National d’Etudes Spatiales (CNES), GMV Aerospace and Defense (GMV), and Wuhan Technical University (WHU). For the frequency stability of the PPP timing for LEO satellites, the short-term stability (1280 s) is about 10−13 level, and the long-term stability (10,240 s) is about 10−14 level. Compared with the traditional PPP method (Scheme1), the LEO satellite clock model (Scheme2) is capable of significantly reducing the noise, regardless of whether it is PPP timing or PPP time synchronization. The frequency stability of Scheme 1 shows an improvement in short-term stability (1280 s) by about 8 %-72 % and the max improvement of the long-term stability (10240 s) by approximately 39 %, the result also shows a better improvement in LEO time synchronization.

A new PPP one-way timing approach via BDS-3 PPP-B2b and short-message communication service

In the realm of time-frequency, precise point positioning (PPP) technology has been widely used, the current PPP time transfer or timing necessitates network communication for data transmission, which consequently leads to a reduction in the reliability of PPP timing. Based on the BDS-3 PPP service (PPP-B2b) and the global short message communication (GSMC) service, this study proposes a novel PPP one-way timing method that is not subject to distance limitations or the requirements of network communication. Users can directly obtain the difference with UTC(k). Then, the proposed PPP timing method was validated using four stations equipped with external high-performance atomic clocks, based on a dataset of eight days. According to the findings, the suggested PPP one-way timing technique might reach a timing accuracy of roughly 0.5 ns in environments without a network. In terms of frequency stability, the proposed PPP timing method exhibits a stability of approximately 1.4 × 10−13 at 960 s and a stability of about 3 × 10−14 at 15360 s. Further, even under GSMC communication delays of 1 min, 5 min, and 10 min, the proposed PPP one-way timing accuracy can still achieve better than 0.5 ns.

Modeling and assessment of Galileo PPP one-way timing with RT-product

Precise point positioning (PPP) technology is widely used in positioning, navigation, and timing. In order to meet the needs of users for real-time high-precision time information, a real-time Galileo PPP one-way timing model based on existing real-time (RT) products (CAS, CNES, GMV, and WHU) was established and applied for the timing field. Experiments were designed with 8 GNSS stations with an external H-MASER clock to research Galileo PPP timing with 25 day observations. For the modified Allan deviation (MDEV) of Galileo PPP timing solutions, similar to the timing solutions of GPS, the MDEV of Galileo PPP with CAS and CNES shows worse short-term frequency stability, with 1 to 2 × 10−13 at 960 s stability, and indicates similar long-term frequency stability, with about 5–6 × 10−15 at 61 440 s stability. For Galileo PPP time transfer, the standard deviation values are about 0.01–0.49 ns for all time-links with different products. For the stability of Galileo time transfer, the similar characteristic of Galileo time transfer is comparable to that of GPS. For short-term stability, the MDEV of all time-links from Galileo PPP ranges from 2 × 10−14 to 3 × 10−14 at 960 s. For long-term stability, 1 to 2 × 10−15 levels can be reached at 61 440 s for all time-links, except for that of CNES.

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

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

A new receiver clock model to enhance BDS-3 real-time PPP time transfer with the PPP-B2b service

A new Precise Point Positioning (PPP) service, called the PPP-B2b service, has been implemented in the BeiDou-3 Navigation Satellite System (BDS-3), which brings new opportunities for time transfer. However, the solution using the traditional PPP method with the PPP-B2b correction still absorbs some unknown errors and needs reconverging when there exist abnormal data. We developed a new receiver clock model to improve PPP time transfer using the PPP-B2b correction. The traditional PPP time transfers using PPP-B2b with BDS-3, Global Positioning System (GPS), and BDS-3/GPS (Scheme1) are compared with the corresponding time transfer with the proposed clock model (Scheme2). The results show that GPS-only PPP is not recommended because of low accuracy of 2 ns. BDS-3 or BDS-3/GPS PPP time transfers in Scheme1 can realize about 0.2 ns accuracy. When the new clock model is applied, the accuracy can be improved by up to 45% and 39.8% for BDS-3 and BDS-3/GPS PPP, respectively. The proposed clock model can significantly improve the short-term frequency stability by 57.4%, but less for the long-term stability.

Time transfer with BDS-3 signals: CV, PPP and IPPP

The third phase of BeiDou navigation satellite system (BDS-3) was officially commissioned on 31 July 2020. In this study, we make a comprehensive evaluation of BDS-3 time transfer with the B1I, B3I, B1C and B2a measurements. The multi-path (MP) errors and noises of different BDS-3 ranging signals are analyzed to illustrate characteristic of the code observations firstly. Then dual-frequency ionosphere-free linear combinations of BDS-3 B1I&B3I and B1C&B2a measurements are used to achieve time transfer. Using Multi-GNSS Experiment station observations, we evaluate the performance of BDS-3 time transfer with common-view (CV), precise point positioning (PPP) and integer ambiguity PPP (IPPP) techniques. Analysis results show that BDS-3 B1C&B2a CV time transfer links show a better performance than GPS L1P&L2P links, whereas BDS-3 B1I&B3I links are worse than GPS links. For the PPP time transfer, GPS links show the best performance, followed by BDS-3 B1C&B2a links and B1I&B3I links. Furthermore, frequency stability of BDS-3 IPPP time transfer is more stable than PPP solutions at the long average interval time. And the long-term frequency stability of BDS-3 IPPP is comparable with GPS IPPP.

Investigation of Precise Single-Frequency Time and Frequency Transfer with Galileo E1/E5a/E5b/E5/E6 Observations

With the rapid upgrade of global navigation satellite system (GNSS) single-frequency (SF) receivers and the increasing market demand for low-cost hardware, SF precise point positioning (PPP) technology has been widely applied in the time and frequency field. The five-frequency signals provided by the whole constellation of Galileo bring more opportunities for the application of SF PPP in time and frequency transfer. In this contribution, using Galileo’s multi-frequency observations, three SF PPP time and frequency transfer models, i.e., the un-combined (UC) model, the ionosphere-free-half (IFH) model, and the ionosphere-weighted constraints (IWCs) model are established. SF PPP time and frequency transfer performance with Galileo E1, E5a, E5b, E5, and E6 multi-frequency observations is evaluated using four links (947.7 km to 1331.6 km) with five external high-precision atomic clocks stations. The results show that the time and frequency transfer performance of SF-UC and SF-IWC is better than that of SF-IFH, and the timing accuracy of SF-UC and SF-IWC is similar. SF PPP time and transfer performance with E5, E5a, E5b, and E6 signals is improved compared with traditional E1 signal. Among them, the frequency stability of E5 improves the most (about 58%), and that of E6 improves the least (about 14%). In addition, the difference in frequency stability between SF and double-frequency (DF) PPP decreases gradually with an increase in average time, and the frequency stability difference between SF and DF PPP can reach 2 × 10−16 in 120,000 s, indicating that SF PPP has the potential to achieve DF PPP frequency stability. Considering the possible frequency data loss during actual observation, the cost of the GNSS SF receiver, and the advantages of Galileo multi-frequency observations, SF PPP can also meet the long-time time and frequency transfer requirements, and the SF-IWC model based on Galileo E5 observations is more recommended.

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

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

Modelling and Assessment of BDS-3 Real-time Precise Point Positioning Time Transfer Based on PPP-B2b Service

In 2020, users in and around China had access to a new real-time precise point positioning (RTPPP) service with the BeiDou global navigation satellite system (BDS-3) B2b (PPP-B2b) signal. In this study, the quality of PPP-B2b products is first assessed and compared with the CNAV1 broadcast ephemeris. Then a mode of BDS-3 PPP time transfer with PPP-B2b (B2b-RTPPP) is developed and evaluated in static and kinematic modes. The results demonstrate that the discontinuity of orbit is improved by applying the PPP-B2b, and its root mean square errors (RMSEs) are 0.081 m, 0.165 m, and 0.107 m in the radial, along-track, and cross-track components, respectively. The standard deviation (STD) of the PPP-B2b clock offset is 0.08 ns, greatly better than that of the broadcast clock offset. For time transfer, the type A uncertainty of the B2b-RTPPP solution is approximately 0.1 ns in static mode, and approximately 0.3 ns in kinematic mode. The B1I/B3I B2b-RTPPP time transfer solution performs better than the B1C/B2a solution. For frequency stability, the modified Allan deviation (MDEV) of the B2b-RTPPP solution is comparable to that of the post-processing solution. The B1C/B2a combination has better short-term frequency stability than B1I/B3I, while the long-term frequency stability of B1C/B2a is worse. In addition, the contribution of the differential code bias (DCB) to B2b-RTPPP time transfer is also investigated. The type A uncertainty of the B2b-RTPPP solution without DCB correction is worse than that of the B2b-RTPPP solution with DCB correction. The B1C/B2a B2b-RTPPP solution without DCB correction has better frequency stability than the B1I/B3I B2b-RTPPP solution.

Performance Evaluation of Near Real-time GNSS PPP Time Transfer with IGS Products

The GNSS time transfer technology is the high precision time transfer method based on the navigation satellite system and has been widely applied in time and frequency. Benefiting from the development of GNSS time transfer technology and the expansion of user needs for real-time time service applications, real-time time transfer technology has become an important research direction. GNSS Precise Point Positioning (PPP) is one of the most commonly used methods of GNSS time transfer technology. With the development of the many facilities, the application of the real-time GNSS PPP has become wider and wider. In this paper, we demonstrate and evaluate the performance of the international GNSS service (IGS) products in the near real-time PPP time transfer technology. A set of the PPP solutions were computed from the observed data from the timekeeping laboratories, and three types of products provided by IGS, including Ultra-Rapid (IGU), Rapid (IGR), and Final (IGS final) orbit and clock offset products. IGS final and IGR products have extremely high accuracy and stability and are used as a reference for the time transfer with IGU product. The near real time clock offset and the comparison link performed with the IGU product can provide a time comparison service with an accuracy of 0. 5ns for near real time applications.

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.

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.

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

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

Performance of BDS-2/3, GPS, and Galileo Time Transfer with Real-Time Single-Frequency Precise Point Positioning

Single-frequency (SF) receivers are much cheaper than that of dual-frequency (DF). Even though DF precise point positioning (PPP) is nowadays applied in the time community, the cost of equipment is one of the key considerations for time users. Furthermore, the hardware delay calibration of single-frequency devices is simpler than that of dual-frequency devices. In addition, there is no literature to study real-time SF PPP time transfer. In this contribution, the possibility of time transfer using SF PPP was studied. The Un-combined SF PPP was employed for time transfer with ionospheric-constraint using real-time precise products. In this case, 18 multi-GNSS experiment (MGEX) stations and one time lab station were used to study real-time SF PPP time transfer using GPS, Galileo and BDS-2/3 satellites with 20-day. The results suggested that real-time single-frequency PPP can meet time transfer. the standard deviation (STD) of the clock difference obtained from GPS-only, Galileo-only and BDS-2/3 single-frequency PPP are about (0.51, 0.54, 0.91) ns, respectively. The frequency stability of real-time single-frequency PPP can achieve (1E-12, 1E-13, 1E-13) level at short-term and (1E-13, 1E-13, 1E-14) level at long-term, respectively, for BDS-2/3, Galileo-only and GPS-only based.

The analysis on BDS-3 carrier phase time transfer under the mode of basic navigation mode

The BeiDou navigation satellite system 3rd generation (BDS-3) has been operating officially since the middle of 2020 which can provide service for the global users. The precise point positioning (PPP) time transfer is the crucial application for the global navigation satellite system. Besides the number of visible satellites, the performance of precise time transfer also strongly depends on the quality of satellite orbit and clock products. The contribution of this work is to comprehensively evaluate the precision of BDS-3 satellite orbit and clock of four post-processed products (GBM, IAC, WUM and SHA) as well as one real-time product (CNT) and analyze the performance of PPP time transfer using these products. The std of clock differences of IAC and WUM showed better agreement respect to GBM, followed by SHA and CNT. The statistics of four links show, of all the averaging time intervals, BDS-3 results estimated by the GBM, IAC and WUM scenarios are comparable, and they are more stable than those of CNT and SHA in the smooth time link in terms of frequency stability. Whereas, the discrepancy on the scenarios can be neglected in the noisy time link. For global position system (GPS) and Galileo PPP time transfer with different products, BDS-3 and Galileo has similar performance which are slightly worse than GPS.

Research on Evaluation Method of Time Transfer Performance Between Ground Stations in Two-Way Satellite Comparison Network

High-precision time synchronization between ground stations is essential for the precise measurement and determination of satellite orbits. Among the numerous time synchronization methods available, two-way satellite time and frequency transfer (TWSTFT) technology is widely used because of the approximate symmetry of its signal transmission path, such that most of the error terms can be offset to obtain subnanosecond time transmission accuracy. A C-band two-way satellite comparison network has been constructed at National Time Service Center (NTSC), Chinese Academy of Sciences for orbit determination and to compare the times between ground stations. The gradual increase in the number of ground stations has created a problem in need of urgent resolution: the facile and rapid evaluation of the time transfer performance between ground stations by a two-way satellite comparison network without the use of additional equipment. We solve this problem by applying the TWSTFT triangle closure method and the precise point positioning time transfer method to the NTSC two-way satellite comparison network and conduct joint observations between terrestrial stations to evaluate the network time transfer performance. We select the Xi'an, Kashi and Sanya stations of the NTSC two-way satellite comparison network to carry out verification tests. The results show that the NTSC two-way satellite comparison network can achieve subnanosecond time synchronization accuracy. The accuracy of time synchronization between stations can be checked conveniently and quickly without the use of additional equipment. This study presents the most recent developments for the NTSC two-way satellite comparison network and serves as a reference for evaluating the time transfer performance of similar networks.

Analysis on the time transfer performance of BDS-3 signals

The BeiDou global navigation satellite system (BDS-3) was formally commissioned to provide positioning, velocity, and timing services to global users on 31 July 2020. We analyzed its pseudorange measurement noise, the precision of conventional common view (CV) and all-in-view (AV) time comparison, and the instability of the precise point positioning (PPP) time transfer to assess the time transfer performance of BDS-3. We found that the elevation-dependent biases found in BDS-2 code measurements are mitigated in BDS-3. The time transfer performance of the BDS-3 satellites is over 50% higher than that of the BDS-2 satellites. In terms of the CV time comparison, the standard deviations of the zero-baseline common clock time comparison of the new BDS-3 signal combination of B1C and B2a reach 0.36 ns, which are the same levels for Galileo E1 and E5a and the global positioning system (GPS) L1 and L2. In the long baseline AV comparison links over 7000 km, the standard deviation of the time comparison of the B1C and B2a combination also reaches 0.8 ns, and the improved gain is 55% relative to that of the BDS-2 B1I and B2I. We also tested the PPP time transfer performance with BDS-2 and BDS-3 satellites and found that the time transfer performance of BDS B1I and B3I is comparable to that of GPS L1 and L2.

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.