We present quad-constellation (namely, GPS, GLONASS, BeiDou and Galileo) time group delay (TGD) and differential code bias (DCB) correction models to fully exploit the code observations of all the four global navigation satellite systems (GNSSs) for navigation and positioning. The relationship between TGDs and DCBs for multi-GNSS is clearly figured out, and the equivalence of TGD and DCB correction models combining theory with practice is demonstrated. Meanwhile, the TGD/DCB correction models have been extended to various standard point positioning (SPP) and precise point positioning (PPP) scenarios in a multi-GNSS and multi-frequency context. To evaluate the effectiveness and practicability of broadcast TGDs in the navigation message and DCBs provided by the Multi-GNSS Experiment (MGEX), both single-frequency GNSS ionosphere-corrected SPP and dual-frequency GNSS ionosphere-free SPP/PPP tests are carried out with quad-constellation signals. Furthermore, the author investigates the influence of differential code biases on GNSS positioning estimates. The experiments show that multi-constellation combination SPP performs better after DCB/TGD correction, for example, for GPS-only b1-based SPP, the positioning accuracies can be improved by 25.0%, 30.6% and 26.7%, respectively, in the N, E, and U components, after the differential code biases correction, while GPS/GLONASS/BDS b1-based SPP can be improved by 16.1%, 26.1% and 9.9%. For GPS/BDS/Galileo the 3rd frequency based SPP, the positioning accuracies are improved by 2.0%, 2.0% and 0.4%, respectively, in the N, E, and U components, after Galileo satellites DCB correction. The accuracy of Galileo-only b1-based SPP are improved about 48.6%, 34.7% and 40.6% with DCB correction, respectively, in the N, E, and U components. The estimates of multi-constellation PPP are subject to different degrees of influence. For multi-constellation combination SPP, the accuracy of single-frequency is slightly better than that of dual-frequency combinations. Dual-frequency combinations are more sensitive to the differential code biases, especially for the 2nd and 3rd frequency combination, such as for GPS/BDS SPP, accuracy improvements of 60.9%, 26.5% and 58.8% in the three coordinate components is achieved after DCB parameters correction. For multi-constellation PPP, the convergence time can be reduced significantly with differential code biases correction. And the accuracy of positioning is slightly better with TGD/DCB correction.

Code multipath is an unmanaged error source in precise global navigation satellite system (GNSS) observation processing that limits GNSS positioning accuracy. A new technique for mitigating multipath by installing a wave-absorbing shield is presented in this paper. The wave-absorbing shield was designed according to a GNSS requirement of received signals and collected measurements to achieve good performance. The wave-absorbing shield was installed at the KUN1 and SHA1 sites of the international GNSS Monitoring and Assessment System (iGMAS). Code and carrier phase measurements of three constellations were collected on the dates of the respective installations plus and minus one week. Experiments were performed in which the multipath of the measurements obtained at different elevations was mitigated to different extents after applying the wave-absorbing shield. The results of an analysis and comparison show that the multipath was mitigated by approximately 17%–36% on all available frequencies of BeiDou Navigation Satellite System (BDS), Global Positioning System (GPS), and Global Navigation Satellite System (GLONASS) satellites. The three-dimensional accuracies of BDS, GPS, and GLONASS single-point positioning (SPP) were, respectively, improved by 1.07, 0.63 and 0.49 m for the KUN1 site, and by 0.72, 0.79 and 0.73 m for the SHA1 site. Results indicate that the multipath of the original observations was mitigated by using the wave-absorbing shield.

Global navigation satellite system (GNSS) precise point positioning (PPP) has been widely used for high-precision time and frequency transfer. However, the day-boundary discontinuities at the boundary epochs of adjacent days or batches are the most significant obstacle preventing PPP from continuous time transfer. The day-boundary discontinuities in station estimates and time comparisons are mainly caused by the code-pseudorange noise during the analysis of observation data in daily batches, where the absolute clock offset is determined by the average code measurements. However, some discontinuities with amplitudes even more than 0.15 ns may still appear in station clock estimates and time comparisons, although several methods had been proposed to remove such discontinuities. The residual small amplitude of the day-boundary discontinuities in some PPP station clock estimates and time comparisons through new GNSSs like Galileo seems larger, especially using precise clock products with large discontinuities. To further understand the origin of the day-boundary discontinuities, the influence of GNSS precise products on the day-boundary discontinuities in PPP station clock estimates and time comparisons is investigated in this paper. Ten whole days of Multi-GNSS Experiment (MGEX) from modified Julian date (MJD) 59028 to 59037 are used as the observation data. For a comparative analysis, the station clock estimates are compared with global positioning system (GPS) and Galileo observations through PPP and network solutions, separately. The experimental results show that the daily discontinuities in current combined GPS final and rapid clock products are less than 0.1 ns, and their influence on the origin of day-boundary discontinuities in PPP station clock estimates and time comparison are statistically negligible. However, the daily discontinuities in individual Analysis Centers (ACs) GPS products are more extensive, and their influence on the origin of the day-boundary discontinuities in GPS PPP station clock estimates cannot be ignored. The day-boundary discontinuities demonstrate random walk noise characteristics and deteriorate the station clocks’ long-term frequency stability, especially at an average time of more than one day. Although Galileo clock daily discontinuities are different from those of GPS, their influence on the day-boundary discontinuities in station clock estimates is nearly similar to the GPS PPP. The influence of daily discontinuities of Galileo clocks on PPP time comparison is similar to GPS and is not particularly critical to time comparison. However, combined and weighted MGEX products should be developed or Galileo IPPP should be used for remote comparison of high-stability clocks.

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.

The BeiDou-3 system (BDS-3) broadcasts PPP-B2b signals to provide real-time PPP service. Compared with the traditional PPP technique, the PPP-B2b service broadcasts corrections through satellite links, covers a wide area, and is independent of the internet. With the PPP-B2b service, users can obtain high-precision positioning information through the real-time PPP. Many studies have been conducted to evaluate the positioning performance of PPP-B2b. In theory, high-precision timing information could also be obtained through PPP-B2b. With the development of science and technology, the need for highly accurate time measurement, even at the sub-nanosecond level, is experiencing significant growth. However, the GNSS standard timing service can hardly meet these requirements. This contribution analyzes the timing performance of the PPP-B2b service and proposes a sub-nanosecond precise timing method of Coordinated Universal Time (UTC) based on the PPP-B2b service. BDS-3 and GPS observations from nine tracking stations and real-time collected PPP-B2b corrections over 516 days were used to analyze the performance of the proposed timing method. The results show that: (1) The difference between the PPP-B2b-restored UTC, which was realized by one-way timing with the UTC offsets in broadcast ephemeris, and UTC (NTSC), fluctuates within a few ns. (2) The timing uncertainty of the zero baseline based on the proposed method is better than 0.2 ns. (3) Compared with the post-processed PPP time transfer, the UTC dissemination uncertainty of the short and long baseline with the proposed method is better than 0.7 ns. The experiment results verified the feasibility of the proposed sub-nanosecond level precise UTC dissemination method based on the PPP-B2b service.

Water vapor is one of the most important greenhouse gases in the world. There are many techniques that can measure water vapor directly or remotely. In this work, we first study the Global Positioning System (GPS)- and the Global Navigation Satellite System (GLONASS)-derived Zenith Wet Delay (ZWD) time series based on 11 years of the second reprocessing campaign of International Global Navigation Satellite Systems (GNSS) Service (IGS) using 320 globally distributed stations. The amount of measurement, the local environment, and the antenna radome are shown to be the main factors that affect the GNSS ZWDs and the corresponding a posteriori formal errors. Furthermore, antenna radome is able to effectively reduce the systematic bias of ZWDs and a posteriori formal errors between the GPS- and GLONASS-based solutions. With the development of the GLONASS, the ZWD differences between the GPS- and the GLONASS-based solutions have gradually decreased to sub-mm-level after GLONASS was fully operated. As the GPS-based Precipitable Water Vapor (PWV) is usually used as the reference to evaluate the other PWV products, the PWV consistency among several common techniques is evaluated, including GNSSs, spaceborne sensors, and numerical products from the European Center for Medium-Range Weather Forecasts (ECMWF). As an example of the results from a detailed comparison analysis, the long-term global analysis shows that the PWV obtained from the GNSS and the ECMWF have great intra-agreements. Based on the global distribution of the magnitude of the PWV and the PWV drift, most of the techniques showed superior agreement and proved their ability to do climate research. With a detailed study performed for the ZWDs and PWV on a long-term global scale, this contribution provides a useful supplement for future research on the GNSS ZWD and PWV.