Valid multipath error model is the prerequisite for high-performance GNSS integrity monitoring. It is indispensable to civil aviation and other Safety-of-Life (SoL) users. The model must perfectly bound multipath error while preventing the constructed model from being too conservative. Nevertheless, no sound methodologies to meet both the requirements have been introduced in previous literatures, and subsequently, practices always require iterative manual trade-offs. To improve the efficiency of multipath modeling, we propose a new automatic multipath error modeling methodology. It quantifies the above requirements in the objective function of multiobjective genetic algorithm (GA) so that multipath modeling can be managed automatically. Moreover, through introducing a new model that is based on two inflation factors, conservatism of modeling results can be significantly reduced. Experiments based on a 4-month dataset of BDS-3 Medium Earth Orbit (MEO) satellites show that constructed multipath models effectively bound actual error in each elevation bin. In addition, the new model form with two inflation factors brings average CDF difference reduction of 67.4% at B1I and 50.6% at B3I, which means significantly mitigation in terms of conservatism.

High-precision real-time satellite orbit products are prerequisite for achieving high-performance navigation and positioning services. This study develops an integrated precise orbit determination approach that combines GPS and low Earth orbit (LEO) satellites using the square root information filtering algorithm to improve the convergence time and accuracy of GPS real-time satellite orbits. By collecting data from varying numbers of global ground stations and LEO satellites (Sentinel-3A/B, GRACE-C/D, Swarm-A/B/C), GPS and LEO satellite orbits were determined synchronously. Orbit convergence time and accuracy were evaluated against the official reference products. Results show that, with 9 ground stations, adding 7 LEO satellites decreases the GPS orbit convergence time in the along-track, cross-track, and radial directions from 28.0, 28.3, and 21.8 h to 1.9, 3.9, and 14.3 h, respectively, achieving remarkable improvements of 93%, 86%, and 34%. Increasing the number of ground stations to 79 further reduces the convergence time to 0.7, 1.4, and 10.9 h in the three directions. For LEO satellites, increasing ground stations from 9 to 79 decreases the average convergence time across all three directions by 44%–70%. In terms of GPS orbit accuracy after convergence, the configuration of 7 LEO satellites with 9 ground stations reaches accuracies of 6.5, 3.8, and 3.0 cm in the along-track, cross-track, and radial directions, which is improved by 64%, 66%, and 48%, respectively, compared to the results without LEO satellites. When 79 ground stations are used, the GPS orbit accuracy is further improved to 5.0, 2.5, and 2.6 cm in the three directions. Notably, the three-dimensional GPS orbit accuracy reaches 6.8 cm with 19 ground stations and 7 LEO satellites, which outperforms the accuracy level of 7.4 cm obtained utilizing only 79 ground stations. These results indicate that the optimal deployment of LEO satellites can effectively compensate for ground network limitations while maintaining high-precision real-time orbit determination.

Satellite laser ranging (SLR) is an important technique that determines geodetic parameters, and its observation processing often calibrates range bias corrections to offset systematic errors. However, the impact of different range bias calibration methods on estimating the BDS-3 satellite orbit and Earth Rotation Parameters (ERP) has not been fully studied. The aim of this study is to explore the impact of employing different SLR range bias corrections on the accuracy of SLR-based BDS-3 satellite orbit and ERP. Eight months of experimental analysis revealed that the station–satellite-pair-dependent range bias correction resulted in the optimal orbit accuracy. Regarding orbit differences relative to precise ephemerides and overlap differences, the 3D root-mean-square (RMS) of satellites manufactured by the China Academy of Space Technology (CAST) are 1.00 and 0.94 m, respectively. The corresponding values of satellites manufactured by the Shanghai Engineering Center for Microsatellites (SECM) are 0.98 and 0.90 m, respectively. The station–satellite-pair-dependent range bias correction performed the best in terms of pole coordinate accuracy. The RMS of the X _P and Y _P differences relative to the International Earth Rotation and Reference Systems Service (IERS) 20 C04 product are 1.32 and 1.41 mas, respectively. The solution using satellite-dependent range bias corrections has the optimal length of day (LOD) accuracy, with a 44.92 μs rms of the LOD difference. However, due to the apparent satellite-related error characteristic reflected in the SLR residual, the station-dependent range bias correction is unsuitable for simultaneously processing the SLR observations of all BDS-3 satellites.

Data processing of the Global Navigation Satellite System using uncombined (UC) observations has been a hot topic in recent years. However, the computation complexity and time consumption of the UC approach is much higher than those of the linear combination approach due to there being more parameters of interest. Concerning this issue, we propose a three-step approach by combining the ionosphere-free (IF) observation model and the UC observation model in a network scheme to reduce computation complexity. The first two steps are based on the IF observation model to detect cycle slips and gross errors using preprocessing and post-fit residual screening algorithms, respectively, while the third step is based on the UC observation model in which the ambiguities estimated from the IF model are used for UC ambiguity resolution (IF-IF-UC). To validate this approach, a network of 140 globally distributed stations is chosen and 1 year of GPS/GALILEO/BDS-3 dual-frequency data in 2021 is processed. The 1D RMSs of satellite orbit difference and the average STDs of satellite clock differences with respect to ESA’s products for GPS, Galileo and BDS-3 are 1.8, 2.4 and 4.1 cm and 0.024, 0.019 and 0.028 ns, respectively. Compared with the GIM products provided by the Center for Orbit Determination in Europe, the mean RMSs of the VTEC differences for GPS, Galileo and BDS-3 are 2.38, 2.30 and 3.09 TECU. For comparison purposes, the approach where all three-steps are based on the UC model is also conducted (UC-UC-UC). Results show that satellite orbits, clocks and VTECs from the IF-IF-UC approach are almost the same as those from the UC-UC-UC approach. By introducing high-performance linear algebra libraries, the elapsed time of the proposed IF-IF-UC approach is about 1 h, which is an improvement of 36% when compared to the UC-UC-UC approach. Nevertheless, the elapsed time is nearly 6 d when the UC-UC-UC approach is conducted without introducing high-performance linear algebra libraries.