With the launch of BDS-3 and Galileo new satellites, the BeiDou navigation satellite system (BDS) has developed from the regional to global system, and the Galileo constellation will consist of 26 satellites in space. Thus, BDS, GPS, GLONASS, and Galileo all have the capability of global positioning services. It is meaningful to evaluate the ability of global precise point positioning (PPP) of the GPS, BDS, GLONASS, and Galileo. This paper mainly contributes to the assessment of BDS-2, BDS-2/BDS-3, GPS, GLONASS, and Galileo PPP with the observations that were provided by the international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS). The Position Dilution of Precision (PDOP) value was utilized to research the global coverage of GPS, BDS-2, BDS-2/BDS-3, GLONASS, and Galileo. In particular, GPS-only, BDS-2-only, BDS-2/BDS-3, GLONASS-only, Galileo-only, and multi-GNSS combined PPP solutions were analyzed to verify the capacity of the PPP performances in terms of positioning accuracy, convergence time, and zenith troposphere delay (ZTD) accuracy. In view of PDOP, the current BDS and Galileo are capable of global coverage. The BDS-2/BDS-3 and Galileo PDOP values are fairly evenly distributed around the world similar to GPS and GLONASS. The root mean square (RMS) of positioning errors for static BDS-2/BDS-3 PPP and Galileo-only PPP are 10.7, 19.5, 20.4 mm, and 6.9, 18.6, 19.6 mm, respectively, in the geographic area of the selected station, which is the same level as GPS and GLONASS. It is worth mentioning that, by adding BDS-3 observations, the positioning accuracy of static BDS PPP is improved by 17.05%, 24.42%, and 35.65%, and the convergence time is reduced by 27.15%, 27.87%, and 35.76% in three coordinate components, respectively. Similar to the static positioning, GPS, BDS-2/BDS-3, GLONASS, and Galileo have the basically same kinematic positioning accuracy. Multi-GNSS PPP significantly improves the positioning performances in both static and kinematic positioning. In terms of ZTD accuracy, the difference between GPS, BDS-2/BDS-3, GLONASS, and Galileo is less than 1 mm, and the BDS-2/BDS-3 improves ZTD accuracy by 20.48% over the BDS-2. The assessment of GPS, BDS-2, BDS-2/BDS-3, GLONASS, Galileo, and multi-GNSS global PPP performance are shown to make comments for the development of multi-GNSS integration, global precise positioning, and the construction of iGMAS.

The third-generation BeiDou navigation satellite system (BDS-3) began providing a global positioning, navigation and timing (PNT) service on 27 December 2018. After completion of the construction of BDS-3, BDS-2 will continue to provide PNT services for the next few years. Hence, the technology of BDS-2/BDS-3 joint precise point positioning (PPP) has become very important. BDS-2 and BDS-3 are two generations of navigation systems, so a time delay bias may exist between them. To investigate the influence of time delay bias on BDS-2/BDS-3 joint PPP performance, four kinds of time delay bias processing strategies are performed, i.e. no operation, random constant, random walk process, and white noise process, with the datasets provided by the multi-GNSS experiment and the international GNSS monitoring and assessment system. The results demonstrate that the JAVAD TRE_3, CETC-54-GMR-4016 and GNSS_GGR receivers have obvious time delay bias between BDS-2 and BDS-3, whereas the UB4B0-13478 receiver has no obvious time delay bias. The positioning performances of the receivers with time delay bias in terms of positioning accuracy and convergence time can be improved when estimating the time delay bias parameters. It is recommended that the time delay bias is estimated as a random constant as it is the most effective of the four strategies. The positioning accuracy of BDS-2/BDS-3 PPP with time delay bias estimated as a random constant is improved by 2.38%, 9.71% and 6.74%, and the convergence time is reduced by 2.39%, 10.21% and 6.28%, respectively, compared with the no operation strategy in three coordinate components.

The development of a global navigation satellite system (GNSS) brings the benefit of positioning, navigation and timing (PNT) services with three or even more available frequency signals. This paper developed five-system multi-frequency precise point positioning (PPP) models based on mathematical and stochastic models. Static positioning performances were evaluated and analyzed with multi-GNSS experiment (MGEX) network datasets and a vehicle-borne kinematic experiment was conducted to verify the kinematic PPP performances. In addition, the receiver clock, zenith tropospheric delay (ZTD), inter-frequency bias (IFB) and differential code bias (DCB) estimates were discussed. Results show that the triple-frequency PPP performances perform slightly better than the dual-frequency solutions, apart from the GPS-related PPP models based on a single ionosphere-free (IF) combined measurement. By introducing the external ionospheric products, the mean convergence time is reduced. For instance, the mean convergence time of ionosphere-constrained (IC) multi-frequency PPP is reduced by 7.4% from 35.7 to 33.1 min and by 19.0% from 7.8 to 6.3 min, for Galileo-only and five-constellation solutions, respectively, compared with dual-frequency IF PPP models. Similarly, the kinematic PPP can also achieve improved performances with more frequency signals and multi-GNSS observations.

For the global ordinary users, the broadcast ephemeris plays important roles in positioning, navigation and timing (PNT) services. With the construction of a new generation of the BeiDou navigation satellite system (BDS), the development of BDS has entered the era of globalization. It is meaningful for global users to analyze and assess the BDS-2 and BDS-3 broadcast ephemeris. Therefore, the satellite orbits and clock offsets calculated by broadcast ephemeris are compared with the precise orbit and clock offset products provided by three analysis centers (i.e., Helmholtz Centre Potsdam German Research Center for Geosciences (GFZ), Wuhan University (WHU) and Shanghai Astronomical Observatory (SHA)), and the corresponding signal-in-space range error (SISRE) and the orbit-only SISRE are analyzed to assess the accuracy of BDS broadcast ephemeris. Due to the upgrade of BDS-3 satellite hardware technology and inter-satellite links payload and the development of satellite orbit determination algorithm, the accuracy of broadcast orbit and clock offsets has been greatly improved. The root mean square (RMS) of BDS-3 broadcast orbit errors is improved by 86.30%, 89.47% and 76.86%, and the standard deviation (STD) is improved by 79.41%, 77.00% and 76.78% compared with BDS-2 in the radial, along-track and cross-track directions. The corresponding RMS and STD of all BDS-3 satellite clock offsets are improved by 40.34% and 52.49% than that of BDS-2, respectively. Meanwhile, the mean RMS and STD are 1.78 m and 0.40 m for BDS-2 SISRE, 1.72 m and 0.34 m for BDS-2 orbit-only SISRE, 0.50 m and 0.14 m for BDS-3 SISRE, and 0.17 m and 0.04 m for BDS-3 orbit-only SISRE. It is noteworthy that the average broadcast-minus-precise (BMP) clock values of BDS-2 and BDS-3 are inconsistent, which can indirectly prove that the datum of broadcast clock offsets for BDS-2 and BDS-3 are inconsistent. The inconsistency of the datum of satellite clock offsets and receiver hardware delay bias between BDS-2 and BDS-3 will result in the inter-system bias (ISB) on the receiver segment. For JAVAD TRE_3 receivers, the ISB is relatively small and thus can be ignored. However, for the TRIMBLE ALLOY, SEPT POLARX5, CETC-54-GMR-4016, CETC-54-GMR-4011, GNSS-GGR and UB4B0-13478 receivers, estimating ISB can improve the positioning accuracy of single point positioning (SPP) by 20.15%, 19.81% and 12.76% in north, east and up directions, respectively.

BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for the BDS-2 and BDS-3 default civil service signals (B1I/B3I) and the increase of new signals (B1C/B2a) for BDS-3, a systemically bias exists in the receiver-end when receiving and processing BDS-2 and BDS-3 signals, which leads to the inter-system bias (ISB) between BDS-2 and BDS-3 on the receiver side. To fully utilize BDS, the BDS-2 and BDS-3 combined precise time and frequency transfer are investigated considering the effect of the ISB. Four kinds of ISB stochastic models are presented, which are ignoring ISB (ISB_NO), estimating ISB as random constant (ISB_CV), random walk process (ISB_RW), and white noise process (ISB_WN). The results demonstrate that the datum of receiver clock offsets can be unified and the ISB deduced datum confusion can be avoided by estimating the ISB. The ISB_CV and ISB_RW models are superior to ISB_WN. For the BDS-2 and BDS-3 combined precise time and frequency transfer using ISB_NO, ISB_CV, ISB_RW, and ISB_WN, the stability of clock differences of old signals can be enhanced by 20.18%, 23.89%, 23.96%, and 11.46% over BDS-2-only, respectively. For new signals, the enhancements are −50.77%, 20.22%, 17.53%, and −3.69%, respectively. Moreover, ISB_CV and ISB_RW models have the better frequency transfer stability. Consequently, we recommended the optimal ISB_CV or suboptimal ISB_RW model for BDS-2 and BDS-3 combined precise time and frequency transfer when processing the old as well as the new signals.

The requirement of timeliness is increasing while obtaining precise tempo-spatial information with the development of global navigation satellite systems (GNSSs). Due to the poor network environment and communication conditions in some regions or application scenarios, it is difficult for users to receive real-time (RT) precise products. The hourly updated ultra-rapid products with low latency and high accuracy are of great interest in GNSS real-time and near-real-time fields. However, it is difficult to achieve the high-rate one-hourly updated precise clock estimation (PCE); since many ambiguity parameters need to be estimated, the computation is time-consuming. At present, the highest time resolution of ultra-rapid clock offsets is 15 min. The low samplings affect the prediction accuracy of clock offsets and the precise point positioning (PPP) performances. To meet these requirements, we proposed an efficient method and design a new framework for high-rate one-hourly updated ultra-rapid PCE. We modified the epoch-difference (ED) PCE model in the parameter estimation. According to the characteristics of the modified ED PCE model, the Open Multi-Processing (OpenMP) and Intel Math Kernel Library (MKL) technologies are used to construct a parallel system to realize the parallelism among satellites, epochs, and stations. The comprehensive assessment in the precision of clock offsets and PPP performances is conducted. The result demonstrates that the one-hourly updated multi-GNSS clock offsets with 30 s sampling can be obtained within 20 min. The estimated clock offsets accuracy increases with the improvement of the time resolution. The STD and RMS are improved by (0.97 to 9.09% and 0.12 to 5.56%) in the observation session, (2.82 to 23.08% and 0.95 to 9.09%) in the first hour of the prediction session, and (0.11 to 3.85% and 0.12 to 4.19%) in the second hour of the prediction session compared with low-rate products, respectively. The high-rate one-hourly updated ultra-rapid clock offsets significantly improves the RT-PPP performances. The positioning accuracy can be improved by 1.52~25.74%, and the convergence time can be improved by 21.96~65.75%. The RT-PPP performances are basically the same as GeoForschungsZentrum Potsdam (GFZ) rapid products and slightly better than the Center National d’Etudes Spatiales (CNES) RT products (CLK93). The one-hourly updated ultra-rapid products with low latency, high accuracy, and not limited by network conditions can be well applied to real-time or near real-time applications and research.