The tropospheric Zenith Wet Delay (ZWD) is one of the primary sources of error in Global Navigation Satellite Systems (GNSS). Precise ZWD modeling is essential for GNSS positioning and Precipitable Water Vapor (PWV) retrieval. However, the ZWD modeling is challenged due to the high spatiotemporal variability of water vapor, especially in low latitudes and specific climatic regions. Traditional ZWD models make it difficult to accurately fit the nonlinear variations in ZWD in these areas. A hybrid deep learning algorithm is developed for high-precision ZWD modeling, which considers the spatiotemporal characteristics and influencing factors of ZWD. The Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) are combined in the proposed algorithm to make a novel architecture, namely, the hybrid CNN-LSTM (CL) algorithm, combining CNN for local spatial feature extracting and LSTM for complex sequence dependency training. Data from 46 radiosonde sites in South America spanning from 2015 to 2021 are used to develop models of ZWD under three strategies, i.e., model CL-A without surface parameters, model CL-B with surface temperature, and model CL-C introducing surface temperature and water vapor pressure. The modeling accuracy of the proposed models is validated using the data from 46 radiosonde sites in 2022. The results indicate that CL-A demonstrates slightly better accuracy compared to the Global Pressure and Temperature 3 (GPT3) model; CL-B shows a precision increase of 14% compared to the Saastamoinen model, and CL-C exhibits accuracy improvements of 30% and 12% compared to the Saastamoinen and Askne and Nordius (AN) model, respectively. Evaluating the models’ generalization capabilities at non-modeled sites in South America, data from six sites in 2022 were used. CL-A shows overall better performance compared to the GPT3 model; CL-B’s accuracy is 19% better than the Saastamoinen model, and CL-C’s accuracy is enhanced by 33% and 10% compared to the Saastamoinen and AN model, respectively. Additionally, the proposed hybrid algorithm demonstrates a certain degree of improvement in both modeling accuracy and generalization accuracy for the South American region compared to individual CNN and LSTM algorithm.

Accuracy and resolution are the two primary challenges that impose limitations on the practical implementation of classical tide-level remote sensing. To improve the accuracy and applicability and increase the temporal resolution of the inversion point near the shore area, the influence of coastal reflection signals in the signal-to-noise ratio (SNR) residual sequence should be weakened significantly. This contribution proposes an anti-interference GNSS Multipath Reflectometry (GNSS-MR) algorithm called VMD_SNR, which is enhanced using variational mode decomposition (VMD). Compared with wavelet decomposition and empirical mode decomposition (EMD) methods, VMD_SNR exhibits superior capabilities in reducing the interference caused by noisy signals. The measurements of ground-based GNSS stations are used to verify the performance improvement in the VMD_SNR algorithm. The results show that the proposed algorithm is better than the wavelet decomposition method and EMD method in terms of accuracy and stability in the shore area, where the effective number is higher than 99% of the total number, and the accuracy is better than 13.80 cm. Moreover, the accuracy improvement is more significant in the high-elevation range, which is 30.16% higher than the wavelet decomposition method and 38.34% higher than the EMD method.

Since the observation precision of the Global Navigation Satellite System (GNSS) carrier phase is on the order of millimeters, if the phase ambiguity is correctly solved, while calibrating the receiver inter-frequency bias, time synchronization on the order of tens of picoseconds is expected. In this contribution, a method that considers the prior constraints of the between-receiver inter-frequency bias (IFB) and its random variation characteristics is proposed for the estimation of the between-receiver clock difference, based on the uncombined GNSS carrier phase and pseudorange observations of the zero and short baselines. The proposed method can rapidly achieve the single-difference ambiguity resolution of the zero and short baselines, and then obtain the high-precision relative clock offset, by using only the carrier phase observations, along with the between-receiver IFBs being simultaneously determined. Our numerical tests, carried out using GNSS observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, show that the method can fix the between-receiver single-difference ambiguity successfully within an average of fewer than 2 epochs (interval 30 s). Then, a clock difference between two receivers with millimeter precision is obtained, achieving time synchronization on tens of picoseconds level, and deriving a frequency stability of 5 × 10⁻¹⁴ for averaging times of 30,000 s. Furthermore, the proposed approach is compared with the precise point positioning (PPP) time transfer method. The results show that, for different types of receivers, the agreement between the two methods is between −6.7 ns and 0.2 ns.

Fast and reliable cycle slip determination can ensure successive ambiguity resolution and precise positioning. Generally, it is not difficult to determine big cycle slips using the linear combination of observations, for instance, the geometry-free (GF) combination and the Hatch–Melbourne–Wübbena (HMW) combination. However, the participation of pseudorange observations may fail to identify small cycle slips. This contribution proposes an integration scheme combining the improved geometry-free (IGF) combination and time-difference carrier phase (TDCP) model to determine simultaneous cycle slips for undifferenced kinematic data. The IGF combination, which is improved from the modified geometry-free (MGF) combination and utilizes the Gauss floor function to take the decimal part of GF, can directly determine small cycle slips on a specific frequency. The TDCP model is used to estimate the differences of position and clock error between adjacent epochs by least-square adjustment using clean phase observations, and repair the remaining cycle slips by the predicted TDCP measurements obtained from the predetermined parameters. The proposed method is tested against 1 Hz kinematic dataset with simulation and highway dataset with real cycle slips. In the simulation test, all cycle slips can be correctly repaired by IGF for L1/L5, E1/E5 and E1/E5a. These combinations are unavailable for MGF. Compared to the HMW-GF method, the repair success rate of IGF improves from 96.80% to 99.16%, and the number of incorrect cases reduces from 9650 to 2535. The IGF-TDCP integration scheme can further improve the performance of IGF, whose repair success rate is more than 99.97% and incorrect cases are 38. The highway test shows that the proposed method effectively processes simultaneous cycle slips on more than half of the tracking satellites caused by the overpasses, even in the case of simultaneous 3 second data gaps on 5 satellites of 6 tracking satellites.

The integration of global navigation satellite system (GNSS) and inertial navigation system (INS) provides the fundamental location-based service for autonomous driving and intelligent transportation systems. However, traditional Gaussian assumption-based integration methods cannot provide stable localization performance in complex urban environments. Therefore, the GNSS position error distribution is remodeled in this study to enhance the robustness of vehicle localization. Firstly, the distribution characteristics of GNSS positioning errors across multiple scenarios are systematically analyzed, based on which a Gaussian–Student’s t mixture distribution is used to refine the error representation and construct a hierarchical linear Gaussian state-space model. Subsequently, a low-complexity adaptive optimization mechanism is designed to fine-calibrate the prior measurement stochastic model. Finally, joint iterative estimation of state parameters and auxiliary variables is conducted through the variational Bayesian framework. This method ensures rapid responsiveness to environmental changes while achieving a synergistic optimization between adaptability and robustness. Field experiments conducted in typical urban environments demonstrate that the proposed algorithm can achieve superior overall performance, better than traditional robust methods with improvements of 38.1% and 28.8% in position and velocity respectively. Especially in representative challenging scenarios, ^i.e. urban canyon and bridge underpass, the proposed method achieves position RMSE improvements of over 22.6% and 46.1% compared with traditional approaches, respectively. It highlights the strong adaptability and robustness in complex urban environments.