Real-time dynamic displacement and spectral response on the midspan of Jiangyin Bridge were calculated using Global Navigation Satellite System (GNSS) and a speedometer for the purpose of understanding the dynamic behavior and the temporal evolution of the bridge structure. Considering that the GNSS measurement noise is large and the velocity/acceleration sensors cannot measure the low-frequency displacement, the Variational Mode Decomposition (VMD) algorithm was used to extract the low-frequency displacement of GNSS. Then, the low-frequency displacement extracted from the GNSS time series and the high-frequency vibration calculated by speedometer were combined in this paper in order to obtain the high precision three-dimensional dynamic displacement of the bridge in real time. Simulation experiment and measured data show that the VMD algorithm could effectively resist the modal aliasing caused by noise and discontinuous signals compared with the commonly used Empirical Mode Decomposition (EMD) algorithm, which is guaranteed to get high-precision fusion data. Finally, the fused displacement results can identify high-frequency vibrations and low-frequency displacements of a mm level, which can be used to calculate the spectral characteristics of the bridge and provide reference to evaluate the dynamic and static loads, and the health status of the bridge in the full frequency domain and the full time domain.

As one of the main errors that affects Global Navigation Satellite System (GNSS) positioning accuracy, ionospheric delay also affects the improvement of smartphone positioning accuracy. The current ionospheric error correction model used in smartphones has a certain time delay and low accuracy, which is difficult to meet the needs of real-time positioning of smartphones. This article proposes a method to use the real-time regional ionospheric model retrieved from the regional Continuously Operating Reference Stations (CORS) observation data to correct the GNSS positioning error of the smartphone. To verify the accuracy of the model, using the posterior grid as the standard, the electron content error of the regional ionospheric model is less than 5 Total Electron Content Unit (TECU), which is about 50% higher than the Klobuchar model, and to further evaluate the impact of the regional ionosphere model on the real-time positioning accuracy of smartphones, carrier-smoothing pseudorange and single-frequency Precise Point Positioning (PPP) tests were carried out. The results show that the real-time regional ionospheric model can significantly improve the positioning accuracy of smartphones, especially in the elevation direction. Compared with the Klobuchar model, the improvement effect is more than 34%, and the real-time regional ionospheric model also shortens the convergence time of the elevation direction to 1 min. (The convergence condition is that the range of continuous 20 s is less than 0.5 m).

For long baseline in a network, the traditional combined ionosphere-free (IF) + wide-lane (WL) strategy is commonly used, but the residual tropospheric delays and larger noise hamper the basic ambiguity resolution (AR). With the completion of the BeiDou global navigation satellite system (BDS-3) and the quad-frequency signals provided by BDS-3 satellites, we can construct more combinations that are conducive to ambiguity resolution. Compared with ionosphere-free linear combinations, we estimated ionospheric delay using three independent WL observations, and formed an ionosphere-weighted model using uncombined code and phase observations, which proved to be quite effective. Based on the real quad-frequency BDS-3 observations of two CORS (Continuously Operating Reference Stations) and two user stations, we processed eight days of data to study the formal and empirical ambiguity success rates and user positioning errors. The rounding success rate of WL ambiguity was significantly improved with ionospheric correction. The success rate of the basic ambiguity increased from 94.4 and 96.1% to 98.0% using the quad-frequency ionosphere-weighted (QFIW) model compared with the double-frequency ionosphere-free (DFIF) model and the triple-frequency geometry-based (TFGB) model. Furthermore, the user E/N/U positioning accuracy improved by 20.6/31.5/13.1% and 6.3/22.9/5.8%, respectively.

An inter-system model for multi-GNSSs (global navigation satellite systems) makes the interoperability among different GNSS constellations possible. In recent years, inter-system models for geodetic receivers have been extensively studied. However, the precise positioning of smartphones suffers from various problems, and the current research mostly focuses on how to achieve the GNSS ambiguity resolution. Based on the research of receiver channel-dependent bias, in this study, we will research the temporal behaviors of differential inter-system bias (DISB) and implement an inter-system model for smartphones. A representative Huawei P40 (HP40) smartphone was used in the experiments, and the results show the following: (1) For the HP40, the frequencies of Code Division Multiple Access (CDMA) systems are free of receiver channel-dependent phase bias, which provides the chances for further interoperability among these systems. However, the code observations of the HP40 are influenced by receiver channel-dependent code bias; it is therefore suggested to set a large initial standard deviation (STD) value for code observations in the positioning. (2) GPS L1/QZSS L1 and BDS-2 B1I /BDS-3 B1I are free of phase DISB, and there is obvious phase DISB between GPS L1 and Galileo E1; even so, the valuations are sufficiently stable and the STD is close to 0.005 cycles. However, the phase DISB of GPS L1/BDS B1I is unstable. (3) For kinematic positioning, when the stable phase DISB is introduced, a 3–38.9% improvement in the N/E/U directions of the positioning accuracies in the inter-system differencing is achieved compared with the intra-system differencing.

A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm.

The need for high-precision and dependable navigation and positioning services is rising in the mass market as a result of the BDS-3’s completion and the performance development of smartphone chips. However, compared with the geodesic receiver, the positioning accuracy of smartphones is severely degraded due to the low antenna gain and poor anti-interference ability. In March 2022, Redmi released K50 smartphones that support BDS tri-frequency, providing conditions for further improvement of smartphone positioning. First, we collected the multi-constellation and multi-frequency data of the K50 to evaluate the availability of tri-frequency observations. Then, we compared the observations between different frequencies and found that the pseudorange data quality of the L5/E5a is better than that of L1/E1. For the BDS, the pseudorange data quality of the B2a is obviously better than that of the other two frequencies. For carrier observations, expect for the initial phase biases of B1C, there is no significant difference in data quality between different frequencies. It means that the traditional random model cannot accurately reflect the pseudorange quality of smartphone observation. We used the zero-baseline double difference residual method to calculate the smartphone observation accuracy and refined the random model. Finally, we verified the performance of the refined model through location tests. The results show that the model refinement can significantly improve positioning accuracy and reliability in the single point positioning test and shorten the convergence time in relative positioning. In kinematic positioning, the improved model can obtain the positioning accuracy of a single epoch centimeter-level even when the signal is slightly blocked, which is of great significance for high-precision navigation of smartphones in urban environments.