With satellite phase bias products, integer ambiguity resolution (AR) enabled precise point positioning (PPP) can be achieved, that is, PPP-real-time kinematic (RTK). However, PPP-AR still requires minutes to converge to centimeter-level accuracy, as atmospheric delay parameters need to be estimated in the user un-combined (UC) model. To shorten the convergence time, reference-network-derived atmospheric delay corrections are often directly corrected for raw code/phase observables, without considering their uncertainties, thereby causing model errors. In this study, we propose a new ionosphere-weighted model, in which an elevation-dependent weight is adopted. To evaluate the proposed model, on-board kinematic experiments were conducted based on GPS/Galileo/BDS2/ BDS3 dual-frequency measurements. Compared with the positioning results of the traditional determined variance weight, the proportion of horizontal errors less than 5 cm is increased from 70% to 80%, and horizontal accuracy is improved by 22% and 9.8% at the 68th and 95th percentile, respectively, indicating that the proposed model can improve the PPP-RTK performance.

With the global service of the BeiDou Navigation Satellite System (BDS), the Galileo Navigation Satellite System (Galileo), and the modernization of the Global Positioning System (GPS), achieving high-precision positioning through triple-frequency-only observations in medium baseline real-time kinematics (RTK) is anticipated. This study investigates the impacts of double-difference (DD) troposphere delay and ionosphere delay on ambiguity resolution (AR) based on six medium baselines at a latitude of 30°. Additionally, it evaluates positioning accuracy, fixing rate, convergence time, and computational time using triple-frequency-only (B1I/B2a/B3I, E1/E5a/E5b, L1/L2/L5) data, comparing these results to those obtained from dual-frequency (B1I/B2a, E1/E5a, L1/L2) and combined dual-frequency and triple-frequency data. The experimental findings suggest that, for geometry-based wide-lane (WL) AR, the DD troposphere delay and ionosphere delay can be disregarded. However, they cannot be overlooked when aiming to resolve the raw ambiguity. Triple-frequency-only RTK exhibits comparable positioning accuracy to dual-frequency RTK, with its primary advantage lying in faster convergence. The probability of achieving convergence within 180 s is approximately 8.0% higher for triple-frequency-only RTK compared to dual-frequency RTK. In terms of computational time, the use of triple-frequency-only data reduces the required time by 8.26 s compared to the approach that simultaneously employs both dual-frequency and triple-frequency data, resulting in a computational time reduction of approximately 20%. Therefore, when conducting medium baseline RTK positioning, it is recommended to adopt the ambiguity resolution method proposed in this paper based on triple-frequency-only observations.

The rapid economic expansion has spurred extensive construction near subway networks, impacting the stability of their track foundations. Consequently, it’s crucial to monitor and predict settlement in subway track foundations. However, the dynamic deformation patterns often exhibit nonlinearity and non-stationarity, posing challenges for traditional linear regression models. To tackle this, our study integrates the BiLSTM (bi-directional long short-term memory) network with the AdaBoost ensemble learning algorithm. Using settlement data from Shanghai metro monitoring points, the model is trained and evaluated employing R² (coefficient of determination), MAE (mean absolute error), and RMSE (root mean square error). Results show that our proposed model displays superior predictive accuracy compared to the LSTM and the BiLSTM, with an average training set R² of 0.99, test set R² of 0.78, average MAE of 0.32 mm, and average RMSE of 0.4 mm. Consequently, for forecasting subway track foundation deformations, employing our network model ensures highly accurate predictive capabilities.

The real-time kinematic (RTK) technology has been widely used as the high-precision positioning method in the offshore area. However, RTK requires a bi-directional communication and groups measurement errors together, thereby limiting its mass-market applications. Combining the advantages of precise point positioning (PPP) and RTK, PPP-RTK has become one of the hotspot technologies in the mass market. In this contribution, we propose the uncombined multi-GNSS PPP-RTK model using uncalibrated phase delays (UPDs) estimated from the legacy ionosphere-free and Melbourne-Wübbena combination. With the UPDs estimated based on 14 regional stations, we conduct PPP ambiguity resolution (AR) at 3 augmentation stations and derive precise atmospheric corrections, i.e., RMS of zenith tropospheric and slant ionospheric correction can be up to 4.89 mm and 2.20 cm, respectively. After applying atmospheric correction, the correct fixed solution of four on-board kinematic experiments can be better than 95% and the positioning accuracy can be better than 5 cm in both horizontal and vertical direction, showing the encouraging performance similar to RTK in the offshore area.

In dense urban environment, Multipath (MP) and Non-line-of-sight (NLOS) signals will degrade the performance of BeiDou Navigation Satellite System (BDS) Position, Velocity and Timing (PVT). In order to mitigate this negative impact, a Constrained Robust Unscented Kalman Filter (CRUKF) is implemented based on pseudorange/Doppler shift measurements. An equivalent weight function based on the innovation vector is constructed, which can overcome the problem of performance degrading of traditional robust methods caused by the inaccurate initial state vector. Then, the motion information, navigation direction and elevation, is included to further constrain the Robust UKF (RUKF) solution. The performance of CRUKF is analyzed using two real car tests in a dense building area, Tokyo. It is shown that there is a clear correlation between MP/NLOS errors and Position Dilution of Precision (PDOP), which seriously lows the positioning accuracy. Regarding the horizontal position, the Root Mean Square Error (RMSE) of CRUKF is 5.6 m, while those of Robust Iterative Least Square (RILS) and RUKF are 15.3 m and 6.4 m, respectively. Similar improvements are presented in vertical position and velocity and hence show the superior positioning performance of CRUKF. In addition, without sensor aiding or coupling, CRUKF can be suitable for real-time application of low-cost receiver.