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The thermal expansion effects of GNSS stations are influenced by not only temperature variations, but also bedrock depths and types. Unfortunately, the current studies treat the subsurface GNSS monument and their nearby bedrock as a whole, without taking into account the inconsistencies among bedrock depths and types, while the existing full-spectrum finite element method (FEM) cannot be easily extended to consider the bedrock information. To solve this problem, we propose a refined full-spectrum temperature-induced subsurface thermal expansion model (FSHBDT) that considers both seasonal and non-seasonal temperature variations as well as bedrock information based on the half-space harmonic model. Results show that the full-spectrum half-space harmonic model (FSH), which considers only seasonal and non-seasonal temperature variations, can obtain comparable results to the FEM and even outperform the FEM for inland stations. In addition, the depth and type of bedrock have significant effects on the annual amplitude and phase of thermal expansion-induced vertical displacement. In particular, we find that the station displacement increases by more than 1 mm and the annual phase delays by up to 10° for high-latitude and deeper bedrock stations when bedrock depths are taken into account. The FSHBDT improves the correlation coefficient between GNSS height and mass load displacements by up to 42.3% compared to the FEM and explains up to 8.2% of the nonlinear variation in the GNSS height time series. Our work confirms the advantage of rigorous subsurface thermal expansion modeling to correct the nonlinear variations of global GNSS stations, which might provide a potential opportunity to improve the terrestrial reference frame toward the goal of 1 mm accuracy. [ABSTRACT FROM AUTHOR]

The new generation of BDS-3 broadcasted open service signals B1C and B2a, which are compatible and interoperable with GPS and Galileo overlapping frequency signals, are suitable for multi-constellation global navigation satellite system (multi-GNSS) precise point positioning ambiguity resolution (PPP-AR). However, multipath errors caused by an actual complex environment can affect the ability of ambiguity resolution, thereby restricting the positioning performance of multi-GNSS. Due to different orbital repeat periods of GNSS systems, the implementation complexity of a multipath correction method based on time-domain repeatability is relatively high, while that based on spatial-domain repeatability are research hotspot at present, thanks to the advantages of simple algorithms, easy implementation, and real-time correction. Based on the original multipath hemispherical map (MHM) and trend-surface analysis MHM (TMHM) methods, four multipath processing schemes, namely, the independent modeling and correction (I-MHM, I-TMHM), together with the joint modeling and correction (C-MHM, C-TMHM) of different GNSS systems are proposed in this paper. We find that the residuals of GPS, BDS-3, and Galileo overlapping frequency show a strong correlation at the same spatial position after considering the GNSS inter-system biases in static PPP-AR modes, while the multipath joint modeling and correction method can improve the positioning performance more than the independent modeling and correction. This can be attributed to the ability of multi-GNSS to improve the space coverage within grids, making the modeling results more explanatory. Compared to C-MHM, the C-TMHM derived positioning accuracy and convergence time of combined GCE in 3D component can be improved by up to 29.3% and 40.7%, respectively. In addition, through using multi-GNSS data for multipath modeling, the modeling time can be shortened by more than half to obtain a correction effect similar to that of full orbit period modeling, specifically, 3-day data for GC modeling, while 4-day data for GE, CE, and GCE modeling. Finally, the performances of our improved multipath modeling method were verified and evaluated by using the observation data in environment with fewer blind areas. Compared with the uncorrected cases, the positioning accuracies of GC, GE, CE, and GCE in 3D component improve by 51.7, 63.8, 59.7, and 65.7%, after correcting the multipath error by the proposed C-TMHM method, while the convergence time can also be shortened by 55.3, 51.0, 52.2, and 64.2%, respectively. This research has significant applicability for mitigating multipath errors in various scenarios to improve positioning accuracy and reliability. [ABSTRACT FROM AUTHOR]