## 3 Recent Developments and Progress  
### GNSS Positioning Performances  
Multi-GNSS has been widely applied in navigation and positioning, as well as in tropospheric Zenith Tropospheric Delay (ZTD) estimation, e.g., using the low-cost Centipede-RTK network [29]. To ensure that the results were not influenced by any specific software, the researchers compared the ZTD calculations using two different open-source scientific software programs: RTKLIB (specifically, demo version 5) and CSRS-PPP (version 3). The findings from this evaluation were quite informative with revealing that the ZTD estimates derived from the Centipede-RTK network and the EPN were closely aligned when processed through the CSRS-PPP software. The maximum mean difference observed between the estimates from these two networks was approximately 3.5 cm. This close agreement highlighted the reliability and the coherence of the ZTD calculations obtained from both systems, thereby suggesting the effectiveness of the methodologies employed in the research [29]. Furthermore, the GNSS positioning capabilities were enhanced through case studies of GNSS RTK with the selection of basis functions for the adjustment of unmodelled errors and a required step aiming to deliver a conceptual basis and technical recommendations for the subsequent implementation of specific time-varying models. To achieve this goal, three fundamental functions--sinusoidal, polynomial, and combinatorial--were examined to fit unmodeled errors in differential placements. The datasets were obtained and tested by the IGS and the NOAA's IFCRS (US National Oceanic and Atmospheric Administration) [30]. A different study examined the precision of the tilt compensation feature in GNSS/IMU receivers within an open-air setting. [PERSON] et al. [31] sought to inform professionals and researchers about the specifications and limitations associated with employing GNSS/IMU technology for precise measurements, so as to avoid compromising the accuracy of coordinates in GNSS RTK surveys. The experiment utilized seven GNSS/IMU receivers, which had compensation angles \(\alpha\) ranging from 30\({}^{\circ}\) to 45\({}^{\circ}\). Figure 2: Geometric model of GNSS multipath reflectometry (GNSS-R). The precision positioning status of low-cost GNSS receivers and geodetic GNSS receivers under different working conditions were evaluated, using fast and real-time satellite products for experiments, respectively [32]. In motion mode, the combined GNSS PPP utilizing GPS and GLONASS, along with the 'WHU' fast product, achieved centimeter-level positioning accuracy across various directions. An analysis of convergence times indicates that the PPP based on either GPS or BDS, when employing 'WHU' products alongside geodetic receivers, requires approximately 38.2 min. In contrast, when employing a dual system, this time is reduced to approximately 18.5 min, and with a triple system, it can be further reduced to 14.8 min. When utilizing static data, the influence of multi-GNSS combinations on convergence time is limited, and mainly depends on the accuracy of the products employed. For motion-based PPP that utilizes low-cost GNSS receivers, achieving an extreme precision of below 0.1 m typically necessitates over two hours, which is considerably longer than the convergence times observed at the MGEX site. It is noted that the convergence time for multi-GNSS PPP is shorter when compared to single-system PPP (see Figure 3), and the convergence time for fixed solutions is superior to that of floating-point solutions (see Figure 4). Figure 3: Convergence time using different system combinations and ‘GBM’ products with the average floating-point solution (**top**) and fixed solution (**bottom**) at each site (Reprinted from Ref. [32]). [PERSON] et al. [33] established a high-precision tropospheric delay model using ground-based GNSS stations and the MOFC model, and applied it to PPP, which improved the positioning accuracy and convergence time of PPP-AR (Figure 5).