The third generation of the Beidou navigation satellite system (BDS-3) broadcasts navigation signals of five frequencies. Focusing on the deep integration of five-frequency signals, we applied the joint BDS-3 five-frequency undifferenced and uncombined precise point positioning (UC-PPP) to analyze the receiver inter-frequency biases (IFB). Firstly, 12 Multi-GNSS Experiment tracking (MGEX) stations are selected to investigate the time-varying characteristics of receiver IFB and, according to random characteristics, three random modeling schemes are proposed. Secondly, the effects of three stochastic modeling methods on zenith tropospheric delay, ionospheric delay, floating ambiguity, and quality control are analyzed. Finally, the effects of three IFB stochastic modeling methods on positioning performance are evaluated. The results showed that the amplitude in the IFB for B2b is 5.139 m, B2a is 1.964 m, and B1C is 0.950 m by measuring one week’s observation data. The IFB stochastic modeling method based on random walks can shorten the PPP convergence time by 4~12%, diminish the false alarm of quality control, and improve the positioning accuracy. The random walk model is recommended to simulate the variation of IFB, which can not only overcome the disadvantage of the time constant model being unable to accurately describe the time-varying characteristics of the IFB, but also avoid reducing the strength of the kinematic PPP positioning model due to the large process noise of the white noise model.

Ocean tidal variation is a key parameter for ensuring coastal safety, monitoring marine climate, and maintaining elevation datum. Recently, the ground-based global navigation satellite system reflectometry (GNSS-R) technique has been applied for regional tidal measurements, which is somewhat restricted in terms of temporal and spatial resolutions. A convenient method to improve temporal resolution of measurements is to combine multi-GNSS observations. This paper proposes a new sea-surface altimetry method using the posterior errors (PE) of dual-frequency carrier-phase signals derived from the ionosphere-free Precise Point Positioning (IF-PPP). Considering that the number of initial retrievals is obviously unsuitable for minute-level tidal measurements, both the time sliding window based on the Lomb–Scargle periodogram and a weighted cubic spline smoothing function are significant processing steps for estimating the reflector heights between the sea surface and antenna center. Measurements from two coastal GNSS stations with different tidal amplitudes are used to test the proposed method and compare it with the tide gauge and the signal-to-noise ratio (SNR) methods, respectively. The experimental results show that the multi-GNSS PE combination method can be used to estimate a minute-level sea level time series, and its root-mean-squared errors (RMSE) are about 12.5 cm. In terms of correlation, for all results, the corresponding coefficients exceed 0.97. Moreover, this combined PE method demonstrates a significant advantage in increasing temporal resolution, which is beneficial for application on high-frequency sea-level monitoring.

High-spatiotemporal-resolution Precipitable Water Vapor (PWV) derived from Global Navigation Satellite Systems (GNSS) is a critical parameter for meteorological monitoring and numerical weather prediction. However, traditional PWV retrieval methods rely heavily on the weighted mean temperature (T_m), which typically necessitates external meteorological data or empirical models, thereby limiting the efficiency and real-time capability of GNSS meteorology in data-sparse regions. To address this limitation, this study proposes a real-time meteorology-free Spatial Sliding Window-based Direct Grid Model (SSW-DGM) for retrieving PWV directly from zenith wet delay (ZWD). The model formulates the ZWD-PWV relationship as a time-varying function incorporating seasonal harmonic terms, trained using ERA5 reanalysis profiles from 2016 to 2019. A unique spatial sliding window strategy is employed to capture the atmospheric heterogeneity over complex terrain. Validated in the Loess Plateau of China using data from 2020, the experimental results indicate that: (1) Internal Consistency: The SSW-DGM achieves exceptional agreement with ERA5 data, with a station-specific mean Root Mean Square Error (RMSE) of 0.23 mm; (2) External Accuracy: Compared to traditional GNSS-PWV (T_m-based, derived using ERA5 meteorological parameters) and radiosonde-PWV, the model demonstrates high external accuracy, maintaining strong correlations and robust seasonal stability; (3) Real-time Applicability: In a simulated real-time scenario based on Precise Point Positioning (PPP) derived ZWD, the proposed model exhibits performance comparable to traditional methods, with 91.4% of retrievals showing consistent agreement with reference values. These findings suggest that the SSW-DGM can realize high-precision, real-time PWV retrieval without auxiliary meteorological sensors, offering a promising solution for operational GNSS meteorology in complex environments.