The multi-constellation Global Navigation Satellite Systems (GNSS) offers promising potential for the retrieval of real-time (RT) atmospheric parameters to support time-critical meteorological applications, such as nowcasting or regional short-term forecasts. In this study, we processed GNSS data from the globally distributed Multi-GNSS Experiment (MGEX) network of about 30 ground stations by using the precise point positioning (PPP) technique for retrieving RT multi-GNSS tropospheric delays. RT satellite orbit and clock product streams from the International GNSS Service (IGS) were used. Meanwhile, we assessed the quality of clock and orbit products provided by different IGS RT services, called CLK01, CLK81, CLK92, GFZC2, and GFZD2, respectively. Using the RT orbit and clock products, the performances of the RT zenith total delays (ZTD) retrieved from single-system as well as from multi-GNSS combined observations were evaluated by comparing with the U.S. Naval Observatory (USNO) final troposphere products. With the addition of multi-GNSS observations, RT ZTD estimates with higher accuracy and enhanced reliability compared to the single-system solution can be obtained. Compared with the Global Positioning System (GPS)-only solution, the improvements in the initialization time of ZTD estimates are about 5.8% and 8.1% with the dual-system and the four-system combinations, respectively. The RT ZTD estimates retrieved with the GFZC2 products outperform those derived from the other IGS-RT products. In the GFZC2 solution, the accuracy of about 5.05 mm for the RT estimated ZTD can be achieved with fixing station coordinates. The results also confirm that the accuracy improvement (about 22.2%) can be achieved for the real-time estimated ZTDs by using multi-GNSS observables, compared to the GPS-only solution. In the multi-GNSS solution, the accuracy of real-time retrieved ZTDs can be improved by a factor of up to 2.7 in the fixing coordinate mode, compared with that in the kinematic mode.

The Real-Time Global Navigation Satellite System (GNSS) Precise Positioning Service (RTPPS) is recognized as the most promising system by providing precise satellite orbit and clock corrections for users to achieve centimeter-level positioning with a stand-alone receiver in real-time. Although the products are available with high accuracy almost all the time, they may occasionally suffer from unexpected significant biases, which consequently degrades the positioning performance. Therefore, quality monitoring at the system-level has become more and more crucial for providing a reliable GNSS service. In this paper, we propose a method for the monitoring of real-time satellite orbit and clock products using a monitoring station network based on the Quality Control (QC) theory. The satellites with possible biases are first detected based on the outliers identified by Precise Point Positioning (PPP) in the monitoring station network. Then, the corresponding orbit and clock parameters with temporal constraints are introduced and estimated through the sequential Least Square (LS) estimator and the corresponding Instantaneous User Range Errors (IUREs) can be determined. A quality indicator is calculated based on the IUREs in the monitoring network and compared with a pre-defined threshold. The quality monitoring method is experimentally evaluated by monitoring the real-time orbit and clock products generated by GeoForschungsZentrum (GFZ), Potsdam. The results confirm that the problematic satellites can be detected accurately and effectively with missed detection rate $4\times {10}^{-6}$ and false alarm rate $1.2\times {10}^{-5}$. Considering the quality alarms, the PPP results in terms of RMS of positioning differences with respect to the International GNSS Service (IGS) weekly solution in the north, east and up directions can be improved by 12%, 10% and 27%, respectively.

For the precise orbit determination (POD) of global navigation satellite systems (GNSS) constellation, it is very difficult to precisely model the solar radiation pressure (SRP) force acting on GNSS satellites. For GPS satellites, the ECOM model developed by the Center for Orbit Determination in Europe has been utilized by most of International GNSS Service (IGS) analysis centers. However, it should be adapted and optimized to the characteristics of satellites of each GNSS system or even individual satellites. It was extended to the ECOM2 model for GLONASS satellites and then for Galileo satellites by employing a box–wing model. Since November 2020, the third generation of the BeiDou satellite system (BDS-3) has been in its full operation and there are about 200 globally distributed IGS ground stations tracking BDS-3 signals, which creates a great potential to evaluate and optimize its SRP modeling. From the POD processing carried out in this study, we found significant fluctuations of up to 20 cm in overlapping orbit differences for satellites over eclipses in the radial direction and of about 20 and 50 cm in the cross and along directions for ECOM2 and ECOM models. Then, based on numerical analyses we demonstrate that the fourth- and sixth-order sine terms in the Sun direction can significantly reduce the overlapping orbit differences of ECOM. Therefore, an adapted SRP model by adding the fourth- and sixth-order sine periodical terms in the Sun direction to the ECOM model is presented. The adapted model is then validated for BDS-3 POD and orbit prediction. Results show that fluctuations in the amplitude of overlapping estimated orbits using ECOM models are reduced from 20 to < 10 cm in the radial-track component and satellite laser ranging residuals are reduced to half by the adapted SRP model. For the predicted BDS-3 satellite orbits, the RMS values over deep eclipses can be improved from about 7, 14 and 26 cm to about 3, 5 and 12 cm, in the radial, cross and along directions, respectively, compared to the ECOM model.

The computational efficiency is critical with the increasing number of GNSS satellites and ground stations since many unknown parameters must be estimated. Although only active parameters are kept in the normal equation in sequential least square estimation, the computational cost for parameter elimination is still a heavy burden. Therefore, it is necessary to optimize the procedure of parameter elimination to enhance the computational efficiency of GNSS network solutions. An efficient parallel algorithm is developed for accelerating parameter estimation based on modern multi-core processors. In the parallel algorithm, a multi-thread guided scheduling scheme, and cache memory traffic optimizations are implemented in parallelized sub-blocks for normal-equation-level operations. Compared with the traditional serial scheme, the computational time of parameter estimations can be reduced by a factor of three due to the new parallel algorithm using a six-core processor. Our results also confirm that the architecture of computers entirely limits the performance of the parallel algorithm. All the parallel optimizations are also investigated in detail according to the characteristics of CPU architecture. This gives a good reference to architecture-oriented parallel programming in the future development of GNSS software. The performance of the multi-thread parallel algorithm is expected to improve further with the upgrade of new multi-core coprocessors.s