To address the uneven spatial distribution and significant variations in observation data quality among multi-GNSS experiment (MGEX) stations, this paper proposes an adaptive station selection method (comprehensive adaptive site selection, CAS) for uncalibrated phase delay (UPD) estimation that incorporates observation data quality, thereby overcoming the limitations of traditional methods that neglect station geometry and data quality. A position dilution of precision (PDOP) and UPD error propagation model is developed. Using marginal benefit theory, the optimal number of stations is determined. A multi-indicator evaluation system based on Dempster-Shafer (D-S) evidence theory is established to assess data quality, enabling a dynamic grid algorithm that balances spatial geometry and data quality. The experiments are conducted using BeiDou‑3 navigation satellite system (BDS‑3) data. Experimental results demonstrate that the proposed method selects 80 optimal stations, accounting for only 30% of the global stations. The estimated Narrow-Lane (NL) UPD products achieve an accuracy better than 0.05 cycles, with a discrepancy of less than 0.002 cycles compared to the full-station solution, indicating comparable precision. Furthermore, the computational time is reduced by 54.1%.

Monitoring surface deformation at reclaimed airports under construction is crucial for ensuring construction safety. However, significant variations in surface scattering characteristics cause severe decorrelation, limiting the effectiveness of conventional single-polarization Interferometric Synthetic Aperture Radar (InSAR). To address the issue of insufficient coherent pixels, we propose a dual-polarization sequential InSAR technique and compare its performance with traditional Persistent Scatterer Interferometry (PSI) and Distributed Scatterer Interferometry (DSI) at the Dalian Jinzhou Bay International Airport (DJBIA). Using 89 Sentinel-1A dual-polarization (VV-VH) images (August 2022 to October 2025), the results demonstrate that VV and VH polarizations exhibit significant spatial complementarity, highlighting the necessity of multi-polarization data. Further, to address the issue of long-term changes in scattering characteristics, we applied the Sequential Estimation and Total Power-Enhanced Expectation Maximization Inversion (SETP-EMI) method, which dynamically integrates dual-polarization information and performs adaptive phase optimization. This approach significantly enhances monitoring capability in low-coherence areas of the airport under construction, effectively suppressing phase noise, improving interferogram quality, and yielding a more complete and reliable deformation field. Overall, this study systematically validates the SETP-EMI method with dual-polarization information for deformation monitoring at reclaimed airports under construction, providing technical support for engineering safety control and research on reclamation subsidence mechanisms.

Targeting the issues of uneven spatial distribution and significant variations in observation data quality among Multi-GNSS Experiment (MGEX) stations, this paper proposes an adaptive station selection method for Uncalibrated Phase Delay (UPD) estimation that incorporates observation data quality, overcoming the limitations of traditional methods which often overlook station geometry and data quality. A Position Dilution of Precision (PDOP) and UPD error propagation model is developed. Using marginal benefit theory, the optimal number of stations is determined. A multi-indicator evaluation system based on Dempster-Shafer (D-S) evidence theory is established to assess data quality, enabling a dynamic grid algorithm that balances spatial geometry and data quality. Experimental results demonstrate that the proposed method selects 80 optimal stations, accounting for only 30% of the global stations. The estimated narrow-lane UPD products achieve an accuracy better than 0.05 cycles, with a discrepancy of less than 0.002 cycles compared to the full-station solution, indicating comparable precision. Furthermore, the computational time is reduced by 54.1%.

The tropospheric zenith wet delay (ZWD) serves as a pivotal parameter for atmospheric water vapour inversion. By converting it into precipitable water vapour, high-temporal-resolution atmospheric humidity monitoring becomes feasible, providing crucial support for enhancing short-term rainfall forecast accuracy. However, ZWD exhibits significant non-stationarity due to complex influencing factors, and traditional models struggle to achieve precise predictions across all scenarios owing to limitations in local feature extraction. This article employs a ZWD prediction method based on the dynamic temporal decomposition module of TimesNet, re-constructing one-dimensional high-frequency ZWD time series into two-dimensional tensors to overcome the technical limitations of conventional models. Comprehensively considering topographical characteristics, climatic features, and seasonal factors, experiments were conducted using 30 s ZWD data from 20 IGS stations. This dataset comprised four consecutive days of PPP solutions for each season in 2023. Through comparative experiments with CNN-ATT and Informer models, the global prediction accuracy, seasonal adaptability, and topographical robustness of TimesNet were systematically evaluated. Results demonstrate that under the input-prediction window configuration where each can achieve the optimal accuracy, TimesNet achieves an average seasonal Root Mean Square Error (RMSE) of 5.73 mm across all seasonal station samples, outperforming Informer (7.89 mm) and CNN-ATT (10.02 mm) by 27.4% and 42.8%, respectively. It maintains robust performance under the most challenging conditions—including summer severe convection, high-altitude terrain, and climatically variable maritime zones—while achieving sub-5 mm precision in stable environments. This provides a reliable algorithmic foundation for short-term precipitation forecasting in Global Navigation Satellite System (GNSS) real-time meteorology.

With the improvement of satellite orbit and clock products and the continuous development of precise point positioning with ambiguity resolution (PPP-AR), the positioning performance of PPP-AR has significantly advanced. However, the uncertainty of atmospheric delays—especially tropospheric wet delay, which is strongly affected by weather changes, temperature, and other factors—still results in long convergence times, severely limiting the wider application of PPP-AR. To improve positioning accuracy and convergence performance, this study proposes a local tropospheric wet delay grid modeling approach in a southern province of China, aiming to provide a tropospheric delay-enhanced PPP-RTK service. Due to the varied elevations of reference stations, an exponential function-based height normalization is first applied. Based on the normalized wet delay values, several interpolation methods are used to generate grid products, which are then used to estimate wet delays at user stations. The interpolated values are compared with user station-derived tropospheric delays (treated as ground truth), and the accuracy of each method is assessed using RMSE, bias, and correlation metrics. The results show that the RMSEs of inverse distance weighting (IDW) and ordinary Kriging interpolation are 10.01 mm and 9.19 mm, respectively, while those of BP neural network and LSTM-based methods are 12.26 mm and 13.04 mm. The proposed Kriging + LSTM hybrid method achieves the best performance, with an RMSE of 6.65 mm, and also outperforms other methods in terms of bias and correlation. To further verify the impact of wet delay grid model accuracy on positioning performance, the study evaluates convergence and accuracy in standard PPP-AR and in a simulated kinematic PPP-RTK mode with additional wet delay constraints. Compared to standard PPP-AR, the vertical (U) direction accuracy improves from 12.04 mm to 11.02 mm (7.74% improvement), and convergence time is reduced from 24.2 minutes to 18.4 minutes (23.97% improvement). Additionally, the ambiguity fixing rate increases by an average of approximately 1.09% with the inclusion of wet delay constraints.

Estimation and correction of Global Navigation Satellite System (GNSS) satellite uncalibrated phase delays (UPDs) is crucial for ambiguity resolution (AR) in precise point positioning (PPP). The estimation accuracy of narrow-lane (NL) UPD may vary depending on the GNSS data processing methods. However, a comprehensive evaluation and comparison of different estimation schemes is still lacking. Utilizing 30 consecutive days of observation data from 109 globally distributed multi-GNSS stations, this study evaluates the performance of NL UPD estimated based on five schemes derived from precise orbit determination (POD), precise clock estimation (PCE), and PPP. The evaluation criteria include the daily stability of NL UPD, the distribution of fractional cycle residuals of NL ambiguities, the distribution of fractional cycle residuals of single-difference NL ambiguities in PPP AR, and the positioning accuracy of PPP AR. The results indicate that the fixed-solution POD and PCE schemes perform the best, followed by the PPP scheme. The float-solution PCE scheme underperforms compared to the PPP scheme, while the float-solution POD scheme performs the worst, significantly lagging behind the other four schemes. These findings provide valuable insights for selecting optimal UPD estimation scheme in GNSS data processing.

To address the lack of publicly available inter-frequency clock bias (IFCB) products and the impact of IFCB on real-time or near-real-time multi-frequency precision positioning, a MATLAB-based software for multi-GNSS IFCB estimation and forecast (M_IFCB) was produced for multi-frequency users. This software can estimate the IFCB of GPS, BDS-2, Galileo and BDS-3 satellites and provide three alternative forecast models for GPS satellites with large IFCB amplitude variations. To verify the availability of M_IFCB, 194 and 41 globally evenly distributed MGEX continuous tracking stations were used for IFCB estimation and GPS triple-frequency uncombined precise point positioning (PPP) performance evaluation, respectively. The results show that the precision of the static solutions of the triple-frequency uncombined PPP increased by about 20.4% in the horizontal direction and 18.5% in the vertical direction, respectively. Incorporating the predicted IFCB correction, the precision of the static solutions increased by about 19.9% in the horizontal direction and 17.6% in the vertical direction, respectively.

To address the performance of BeiDou satellite clocks after global network has been built, the BeiDou-3（BDS-3） satellite observation data from 120 international global navigation satellite system（GNSS） service（IGS） tracking stations uniformly distributed around the world were used to solve the BeiDou satellite clock bias in this paper. The method of evaluating the BeiDou satellite clock bias was used to analyze the accuracy level of the new generation of BeiDou satellite clocks. The results were obtained as follows: the accuracy of BeiDou satellite clocks was within 0.1 ns for middle earth orbit（MEO）,0.15 ns for inclined geosynchronous orbit（IGSO）,and 0.2～0.9 ns for geosynchronous eearth orbit（GEO）;the long-term sequence of the frequency of BDS within 10 000 s was relatively stable at the level of 1×10 -14 ;when performing precise single-point positioning solution, the root mean squared（RMS） error of GPS and BDS were both at the centimeter level. Based on the experimental results of satellite clock difference, it was shown that: MEO was more accurate and stable than IGSO satellite clock bias; the rubidium clock（Rb-Ⅱ） and passive hydrogen maser（PHM） carried by BDS-3 were more stable than the Rb of BDS-2;aging hardware of earlier satellites affected satellite clock performance; there were large fluctuations in phase and frequency; the accuracy and convergence speed of BDS in upper direction were slightly insufficient; GPS+BDS combined positioning could improve the single-point positioning performance in the upper direction. It showed that the stability of BeiDou satellite clocks had reached the demand for clock bias forecasting and real-time precision single-point positioning applications.

针对全国全球导航卫星系统(GNSS)基准站建设时间及密度不同,全国GNSS基准站网空间分布不均的问题,该文在系统掌握全国GNSS基准站升级改造的基础上,将全国按照省(自治区、市)、地理区划、胡焕庸线、东经108°、三大阶梯以及长江流域、黄河流域进行区域划分,并运用Delaunay三角网对区划内的GNSS基准站进行统计分析.研究发现,全国2 300余座GNSS基准站间距均值为65.19 km,处于胡焕庸线东南半壁的华北、华中、华东和华南四地的GNSS基准站平均间距均低于55 km,胡焕庸线西北半壁的GNSS基准站平均间距达到了 107.42 km,全国GNSS基准站分布总体上呈现东南较西北密集的分布特征.

To address the problem of long convergence time of PPP-AR（precise point positioning-ambiguity resolution） due to the estimated tropospheric delay, a bilinear quadratic interpolation method was used to construct virtual observations of tropospheric delay with elevation compensation based on the GGOS（global geodetic observing system） grid product, and a PPP-AR method with elevation compensation and tropospheric constraints was proposed in this paper. It was compared with the traditional PPP-AR for estimating tropospheric delay and the PPP-AR with additional IGS tropospheric product constraint in terms of localization accuracy, convergence time and ambiguity fixation rate, respectively. The results showed that compared with the traditional estimation of tropospheric delay, the proposed method could significantly improve the localization accuracy in the U-direction by 2.94 cm and 11.2% on average; shorten the convergence time by 14.5% on average; and improve the ambiguity fixation rate by 1.9% on average.

针对全球升温、极端天气增加、我国西北短时暴雨增多等现象,该文结合ERA5降水数据和气象站采集的实际降水量,利用我国西北干旱地区GPS观测数据反演的GPS/PWV对一次短时强降水过程进行分析.结果表明:①GPS/PWV的积累和变化与实际降水发生时刻及降水量具有密切联系,特别是GPS/PWV在陡升陡降及高位震荡与降水实际发生具有较强的对应关系,对GPS/PWV应用于我国西北干旱地区短时强降水预报及防灾减灾等具有一定的参考意义;②ERA5数据记录的降水事件与气象站记录的实际降水的发生存在较好的对应关系,但降水发生时刻及降水量与实际降水相比准确性较差.该研究对于增强数值同化和机器学习在短时暴雨及极端天气等预报具有重要意义.

Objectives: In order to make full use of the observed value information of each frequency, an undifferenced and uncombined integer ambiguity resolution method between BeiDou satellite navigation system（BDS） long-range reference stations is proposed. Methods: First, the error observation equation is established directly by using the observations of different frequencies, and the relative zenith tropospheric wet delay error and ionospheric delay error are estimated by random walk strategy to increase the constraint between epochs. Second,a linear calculation method of undifferenced integer ambiguity real-time is used to obtain the undifferenced integer ambiguity of all satellites in the current epoch of the reference network. It solves the problem that ambiguity needs to be inherited or re-superimposed on normal equations in the reference star transformation. Because the information of each frequency observation is fully utilized, the influence of linear combination amplification noise on integer ambiguity fixing is avoided, and the ambiguity fixing success rate of uncombined method is much higher than that of ionosphere-free combination method.Results and Conclusions: The results show that the average fixed speed of ambiguity of each reference station is 20 epochs（sampling interval 1 s）. The integer ambiguity resolution of the carrier phase of the reference station can be realized quickly.

针对当前智能手机原始观测数据不稳定导致实时定位精度不高,且未对电离层延迟进行较好修正等问题,该文研究了 2类3种不同芯片智能手机多普勒平滑伪距对实时广域差分定位影响,可改善数据质量,提升定位精度;在此基础上对比了广播电离层参数改正、实时电离层产品、电离层格网预测文件3种电离层产品对手机广域差分定位精度的影响.结果表明,多普勒平滑伪距可提升广域差分定位精度,相较于平滑前二维和三维精度分别提升了 49.3％、47.8％;其次,3种电离层改正产品均能不同程度改善Mi8、P30、P40平面与高程精度,其中,电离层格网预测文件提升U方向定位精度最为明显,对Mi8的高程提升了 31.3％.

The time-varying biases within carrier phase observations are integrated into satellite clock offset parameters for precise clock estimation. Consequently, when the precise satellite clock bias is applied to the third frequency observation for precise point positioning (PPP), a new type of inter-frequency clock bias (IFCB) with satellite dependence should be noticed. If the IFCB is estimated together with the receiver coordinates, tropospheric wet delay, ambiguity and other parameters, it will increase the computational burden and lead to more time consumption. In order to solve this problem, the IFCB of GPS Block IIF satellites were estimated using 162 global uniformly distributed Multi-GNSS Experiment (MGEX) stations. By analyzing the time-varying characteristic of each satellite IFCB and combining the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function is proposed. The feasibility of this method was verified through the Student’s t-distribution, comparison with the measured IFCB, the posteriori residual of the third frequency carrier phase and the kinematic/static PPP solutions. The results showed that since the IFCB period was not a complete 24 h, the difference in the IFCBs time series on different days was increasingly significant with the passage of lag time, and the correlation constantly decreased. The peak-to-peak amplitudes of the IFCB difference reached 1.13, 3.44, 6.86 and 11.25 cm when the lag time was 1, 9, 19 and 29 days, respectively. In addition, based on the lag characteristic of final precise ephemerides released by the International GNSS Service (IGS) analysis centers, the prediction accuracy of the IFCB was evaluated with a time lag of 7 days. The root mean square of the posteriori residuals at the third-frequency observation decreased by approximately 51.3% compared to that without considering for IFCB correction. The triple-frequency uncombined PPP in the horizontal and vertical directions improved by approximately 33.2% and 17.2% for the static PPP solutions and 50.2% and 39.7% for the kinematic PPP solutions, respectively. In general, the accuracy and convergence time of the triple-frequency uncombined PPP were equivalently improved when the predicted IFCB and the measured IFCB were used.

北斗导航卫星系统于2020年7月正式建成并开通,BDS-3卫星在B1I和B3I基础上,增加B1C、B2a民用频率,为验证BDS-3不同频率与GPS组合定位性能,分别对BDS-3(B1C+B2a)+GPS与BDS-3(B1I+B3I)+GPS组合PPP定位性能进行分析,并与BDS-3单系统进行对比.结果表明,在静态定位中,BDS-3(B1C+B2a)+GPS组合在高程方向精度优于2 cm,低于BDS-3(B1I+B3I)+GPS组合;在水平方向精度相当,优于1 cm,收敛时间减少9％;与BDS-3相比,定位精度提高10％～25％,收敛时间减少17％～24％.在动态定位中,BDS-3(B1C+B2a)+GPS与BDS-3(B1I+B3I)+GPS定位精度相当,收敛时间减少14％;与BDS-3相比,BDS-3(B1C+B2a)+GPS动态PPP在高程方向精度优于4 cm,水平方向精度优于3 cm,定位精度提高31％～38％,收敛时间减少52％～58％.

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.

针对智能手机GNSS观测数据质量差无法满足高精度定位需求的问题,该文首先分析了智能手机的数据质量,在此基础上提出了基于多普勒平滑伪距的广域差分方法,提升了智能手机实时定位的精度.实验表明:静态模式下,广域差分定位和多普勒平滑伪距广域差分定位相比伪距单点定位平面分别为47.7％、64.4％,高程方向分别提高55.2％和68.9％;动态模式下,直行时平面可达1.5m,转弯时精度变差,约为2.5m.

A suitable stochastic model is important for parameter estimation in processing undifferenced and uncombined precise point positioning (UC-PPP). Since only when the correct stochastic model is applied can one obtain minimum variance estimations of the precise positioning in the linear adjustment model. However, current multi-frequency UC-PPP stochastic models were established mainly based on an empirical ionosphere-free combined PPP model, which makes it difficult for the established stochastic model to reflect the noise level of the raw observations objectively and truly. In order to solve this problem, an optimized stochastic model suitable for multi-frequency UC-PPP was constructed by considering the variance component factors (VCF) on the diagonal and the cross-correlation coefficients (CCC) between observations of the same type in the (co)variance matrix based on the empirical stochastic model, and a two-step evaluation and optimization procedure for the VCF and CCC was proposed based on the posterior estimation method of the variance–covariance components. To evaluate the stochastic models, 54 GPS dual-frequency observations from the multi-GNSS experiment (MGEX) stations with receivers of four mainstream brands were processed. The results show that all four types of receivers exhibited higher accuracy of observations at L2 frequency than at L1 frequency, and the VCF of the pseudorange was about 8–15 times higher than that of the carrier phase based on the empirical stochastic model. The accuracy of the pseudorange and carrier phase observations varied with the receiver brands. For example, the accuracy of the carrier phase of Leica receiver at L2 frequency was clearly higher than that at L1 frequency, while SEPT receivers showed more significant differences between the pseudorange values at these two frequencies. In terms of Javad and Trimble receivers, the accuracy of pseudorange observations at two frequencies was basically the same, while the carrier phase showed a larger difference. In addition, these four types of receivers presented smaller cross-correlations between observations at different frequencies with the coefficient below 0.04. To assess the UC-PPP performance, three different stochastic models were tested and analyzed. The test results indicate that the proposed stochastic models exhibited better performance with an increase in the positioning accuracy along east, north and vertical directions, i.e., 18.4%, 10.7% and 8.6% for static positioning, and 18.7%, 17.9% and 14.8% for dynamic positioning. However, UC-PPP accuracy and convergence time did not show significant variations when the covariance-related information was incorporated into the stochastic model.

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.