In this paper, a single-frequency real-time kinematic positioning (RTK) robust adaptive Kalman filtering algorithm is proposed in order to realize real-time dynamic high-precision positioning of smartphone global navigation satellite systems (GNSSs). A robust model is established by using the quartile method to dynamically determine the threshold value and eliminate the gross error of observation. The Institute of Geodesy and Geophysics Ⅲ (IGG Ⅲ) weight function is used to construct the position and speed classification adaptive factors to weaken the impact of state mutation errors. Based on the analysis of the measured data of Xiaomi 8 and Huawei P40 smartphones, simulated dynamic tests show that the overall accuracy of the Xiaomi 8 is improved by more than 85% with the proposed robust RTK algorithm, and the overall positioning error is less than 0.5 m in both open and sheltered environments. The overall accuracy of the Huawei P40 is improved by more than 25%. Furthermore, the overall positioning accuracy is better than 0.3 m in open environments, and about 0.8 m in blocked situations. Dynamic experiments show that the use of the robust adaptive RTK algorithm improves the full-time solution planar positioning accuracy of the Xiaomi 8 by more than 15%. In addition, the planar positioning accuracy under open and occluded conditions is 0.8 m and 1.5 m, respectively, and the overall positioning accuracy of key nodes whose movement state exhibits major changes improves by more than 20%.

With the completion of the BeiDou Global Navigation Satellite System (BDS-3), the multi-system precise point positioning ambiguity resolution (PPP-AR) has been realized. The satellite phase fractional cycle bias (FCB) is a key to the PPP-AR. Compared to the combined ionosphere-free (IF) model, the undifferenced and uncombined (UDUC) model retains all the information from the observations and can be easily extended to arbitrary frequencies. However, the FCB is difficult to apply directly to the UDUC model. An observable-specific signal bias (OSB) can interact directly with the original observations, providing complete flexibility for PPP-AR for multi-frequency multi-GNSS. In this study, the OSB product generation for the GPS (G), Galileo (E), and BDS-3 (C) systems is performed using 117 globally distributed multi-GNSS experiment (MGEX) stations, and their performances are evaluated. Then, the PPP-AR comparison and analysis of the two positioning models of the UDUC and IF are conducted. The results show that the stability of OSB products of the three systems is better than 0.05 ns. For the precise point positioning (PPP) ambiguity fixed solution, with comparable positioning accuracy and convergence time to the products of both the Wuhan University (WUM) and the Centre National d’Etudes Spatials (CNES) institutions, an average fixed-ambiguity rate is over 90%. Compared to the PPP float solution, the PPP-AR has the most significant improvement in positioning accuracy in the E-direction. The average improvements in the positioning accuracy under the IF and UDUC models in the static and kinematic modes are higher than 45% and 40%, respectively. The convergence times of the IF and UDUC models are improved on average by 48% and 60% in the static mode and by 40% and 55% in the kinematic mode, respectively. Among the IF and UDUC positioning models, the former has slightly better positioning accuracy and convergence time than the latter for the PPP float solution. However, both models have comparable positioning accuracy and convergence time after the PPP-AR. The GCE multi-system combination is superior to other system combinations. The average convergence time for the static PPP fixed solution is 8.5 min, and the average convergence time for the kinematic PPP fixed solution is 16.4 min.

As an indispensable type of information, location data are used in various industries. Ultrawideband (UWB) technology has been used for indoor location estimation due to its excellent ranging performance. However, the accuracy of the location estimation results is heavily affected by the deployment of base stations; in particular, the base station deployment space is limited in certain scenarios. In underground mines, base stations must be placed on the roof to ensure signal coverage, which is almost coplanar in nature. Existing indoor positioning solutions suffer from both difficulties in the correct convergence of results and poor positioning accuracy under coplanar base-station conditions. To correctly estimate position in coplanar base-station scenarios, this paper proposes a novel iterative method. Based on the Newton iteration method, a selection range for the initial value and iterative convergence control conditions were derived to improve the convergence performance of the algorithm. In this paper, we mathematically analyze the impact of the localization solution for coplanar base stations and derive the expression for the localization accuracy performance. The proposed method demonstrated a positioning accuracy of 5 cm in the experimental campaign for the comparative analysis, with the multi-epoch observation results being stable within 10 cm. Furthermore, it was found that, when base stations are coplanar, the test point accuracy can be improved by an average of 63.54% compared to the conventional positioning algorithm. In the base-station coplanar deployment scenario, the upper bound of the CDF convergence in the proposed method outperformed the conventional positioning algorithm by about 30%.

Multi-frequency observations are now available from GNSSs, thereby bringing new opportunities for precise point positioning (PPP). However, they also introduce new challenges, such as inter-frequency clock bias (IFCB) between the new frequencies and the original dual-frequency observations due to triple-frequency observations, which severely impact the PPP. In this paper, we studied the estimation and correction methods of uncombined inter-frequency clock bias of GPS, BDS-3, and Galileo, analyzed the time-varying characteristics and short-term stability of IFCB, and analyzed the influence of IFCB on the positioning of the GPS, BDS-3, and Galileo, based on a triple-frequency un-differential non-combined PPP model. The obtained results show that the amplitude of Block IIF satellites of the GPS can reach up to 10–20 cm, and the IFCB in BDS-3, Galileo, and GPS Block III satellites can be neglected. After correction by IFCB, the 3D positioning accuracy of the GPS triple-frequency PPP was 1.73 cm and 4.75 cm in the static and kinematic modes, respectively, while the convergence time was 21.64 min and 39.61 min. Compared with the triple-frequency GPS PPP without any correction with IFCB, the static and kinematic 3D positioning accuracy in this work was improved by 27.39% and 17.34%, and the corresponding convergence time was improved by 10.55% and 15.22%, respectively. Furthermore, the delayed IFCB was also used for positioning processing, and it was found that a positioning performance comparable to that of the same day can be obtained. The standard deviation of IFCB for a single satellite was found to be no more than 1 cm, when the IFCB value of a neighboring day was subtracted from the IFCB value of same day, which proves the short-term stability of IFCB.

Dynamic deformation monitoring is a crucial component of the structural health monitoring of an offshore oil platform. Given the insensitivity of the Global Navigation Satellite System (GNSS) to high-frequency vibration information, a combination of GNSS and accelerometer is used for vibration monitoring of platform structures. A hybrid filter based on complementary ensemble empirical mode decomposition (CEEMD) combined with a Chebyshev filter is proposed to process the monitoring data. The extracted GNSS low-frequency displacement is fused with the high-frequency displacement obtained from acceleration integration to obtain the overall dynamic displacement of the platform. The experimental analysis shows that the combination of t-test and correlation coefficient can select the required intrinsic mode function (IMF), the proposed hybrid filter can reduce the noise error to a certain extent, and the quadratic frequency domain integration of the acceleration data can avoid the influence of the integration trend term. The correlation coefficient between the overall reconstructed displacement and the original GNSS monitoring data was 0.8576, and the signal correlation after denoising and refactoring was more than 85%, thereby preserving the essential information components. Integrated GNSS and accelerometer monitoring systems complement each other’s advantages, compensating for their shortcomings in monitoring the dynamic deformation of a structure.

Many Beidou navigation satellite system (BDS) receivers or boards provide dual-frequency measurements to conduct precise positioning and navigation for low-power consumption. Cycle-slip processing is a primary work to guarantee consistent, precise positioning with the phase data. However, the cycle-slip processing of BDS dual-frequency phases still follows with those of existing GPS methods. For single-satellite data, cycle-slip detection (CSD) with the geometry-free phase (GF) is disturbed by severe ionospheric delay variations, while CSD or cycle-slip repair (CSR) with the Melbourne–Wubbena combination (MW) must face the risk of the tremendous disturbance from large pseudorange errors. To overcome the above limitations, a new cycle-slip repair method for BDS dual-frequency phases (BDCSR) is proposed: (1) An optimal model to minimize the variance of the cycle-slip calculation was established to the dual-frequency BDS, after correcting the ionospheric variation with a reasonable and feasible way. (2) Under the BDS dual-frequency condition, a discrimination function was built to exclude the adverse disturbance from the pseudorange errors on the CSR, according to the rankings of the absolute epoch-difference GFs calculated by the searched cycle-slip candidates after correcting the ionospheric variation. Subsequently, many compared CSR tests were implemented in conditions of low and medium elevations during strong geomagnetic storms. Comparisons from the results of different methods show that: (1) The variations of ionospheric delays are intolerable in the cycle-slip calculation during the geomagnetic storm, and the tremendous influence from the ionospheric variation should be corrected before calculating the cycle-slip combination with the BDS dual-frequency data. (2) Under the condition of real dual-frequency BDS data during the geomagnetic storm, the actual success rate of the conventional dual-frequency CSR (CDCSR) by employing the optimized combinations, but absenting from the discrimination function, is lower than that of BDCSR by about 2%; The actual success rate of the CSD with MW (MWCSD), is lower than that of BDCSR by about 2%. (3) After adding gross errors of 0.7 m to all real epoch-difference pseudoranges epoch-by-epoch, results of CDCSR and MWCSD showed many errors. However, BDCSR achieved a higher actual success rate than those of CDCSR and MWCSD, about 43% and 16%, respectively, and better performance of refraining the disturbance of large pseudorange error on the cycle-slip determination was achieved in the BDCSR methodology.