In response to the issue of poor network real-time kinematic (NRTK) service performance in regions with significant height differences, an improved tropospheric height correction (ITHC) method is proposed. Precise point positioning (PPP) is employed to compute the troposphere delay at base stations. Subsequently, a tropospheric vertical profile fitting model (TVPFM) is established for the vertical reduction of the troposphere in regions with significant height differences. In this case, the tropospheric errors introduced by the height differences between the base and rover stations can be calculated. Finally, the tropospheric error can be corrected during the generation of virtual observations, ensuring high-accuracy positioning of NRTK rovers. With the troposphere delay computed based on the PPP approach, datum errors introduced by inaccurate tropospheric correction methods are mitigated. To reduce the dependence of the troposphere delay on height, ECMWF reanalysis v5 (ERA5) data are employed to fit the TVPFM. Experimental analysis demonstrates that the troposphere exhibits distinct vertical variation characteristics, allowing for its segmentation into three layers. Consequently, a piecewise TVPFM is established. Observations obtained from the continuously operating reference stations network located in Yunnan, China, are utilized for validation. The selected stations exhibit a maximum height difference of approximately 2 km. The experimental results exhibit a notable enhancement in correction accuracy with the ITHC in comparison to conventional correction methodologies. Specifically, the ambiguity fixing rate demonstrates a noteworthy improvement of 13.3%, accompanied by a substantial increase in positioning accuracy by 51.4%.

The long convergence time and non-robust positioning accuracy are the main factors limiting the application of precision single-point positioning (PPP) in kinematic vehicle navigation. Therefore, a dual/triple-frequency multi-constellation PPP-RTK method with atmospheric augmentation is proposed to achieve cm-level reliable kinematic positioning. The performance was assessed using a set of static station and kinematic vehicle positioning experiments conducted in Wuhan. In the static experiments, instantaneous convergence within 1 s and centimeter-level positioning accuracy were achieved for PPP-RTK using dual-frequency observation. For the kinematic experiments, instantaneous convergence was also achieved for dual-frequency PPP-RTK in open areas, with RMS of 2.6 cm, 2.6 cm, and 7.5 cm in the north, east, and up directions, respectively, with accuracy similar to short-baseline real-time kinematic positioning (RTK). Horizontal positioning errors of less than 0.1 m and 3D positional errors of less than 0.2 m were 99.54% and 98.46%, respectively. Additionally, after the outage of GNSS and during satellite reduction in obstructed environments, faster reconvergence and greater accuracy stability were realized compared with PPP without atmospheric enhancement. Triple-frequency PPP-RTK was able to further enhance the robustness and accuracy of positioning, with RMS of 2.2 cm, 2.0 cm, and 7.3 cm, respectively. In summary, a performance similar to RTK was achieved based on dual-frequency PPP-RTK, demonstrating that PPP-RTK has the potential for lane-level navigation.

GNSS attitude determination has been widely adopted due to its high efficiency, absence of cumulative errors, and ease of installation. However, practical navigation and attitude determination systems often rely on low-cost receivers that struggle with substantial multipath effects, frequent cycle slips, and satellite signal loss, significantly impairing attitude determination accuracy in challenging urban environments. To address this issue, this contribution proposes a constrained dynamic prediction model (C-Dynamics), which enables more accurate initial coordinates and thereby increases the effectiveness of the constrained LAMBDA (CLAMBDA) technique. To evaluate the practical performance of C-Dynamics, two sets of real-world data collected from a vehicle platform were analyzed. The results demonstrate that C-Dynamics significantly enhances the accuracy of initial coordinate estimations across various environments. Compared with the lambda method, the CLAMBDA method + C-Dynamics method (CLAMBDA+CD) improves the fixing rate in the urban environment by 5.6%, and the accuracy of the heading angle, pitch angle, and baseline length improved by 66%, 70.9%, and 84.2%, respectively. Moreover, in challenging high obstruction environments, the fixing rate increased by 43.5%, while the accuracy of heading angle, pitch angle, and baseline length improved by 76.4%, 69.2%, and 94%, respectively. The proposed algorithm effectively addresses the low fixing rate and insufficient accuracy of the LAMBDA method in high obstruction environments and holds practical value for widespread adoption in the mass market.

Tropospheric delay is a major error source in Global Navigation Satellite System (GNSS), and the accuracy of its modeling critically influences positioning performance. In this study, we evaluate the performance of the real-time tropospheric correction model, VMF3-FC, under diverse geographic and climatic conditions. Both site-wise and grid-wise products at multiple spatial resolutions are assessed, with a particular focus on the widely used 1°×1° and 5°×5° products. Using IGS-ZTD as the reference, results show that the root mean square (RMS) of ZTD is approximately 1.58 cm for site-wise products, 1.67 cm for the 1°×1° products, and 2.34 cm for the 5°×5° products. VMF3-FC maintains stable performance across seasonal changes and during typhoon events, with no significant accuracy degradation as forecast duration increases. Further GNSS evaluation reveals that incorporating VMF3-FC as tropospheric constraints significantly enhances integer ambiguity resolution (PPP-IAR) performance, yielding a 23% improvement in vertical accuracy and a 4.27% reduction in convergence time. For traditional Precise Point Positioning (PPP) float solutions, the improvements are modest, with horizontal accuracy gains below 0.2%, vertical improvement of 5.2%, and a 1.1% reduction in convergence time. Overall, VMF3-FC demonstrates high accuracy and robustness, making it a reliable correction model for GNSS positioning and atmospheric studies. Its broad applicability underscores its value in geospatial information science and real-time navigation systems.