In order to facilitate high-precision and real-time Precise Point Positioning (PPP), the International GNSS (Global Navigation Satellite System) Service (IGS), BDS-3 (BeiDou-3 Navigation Satellite System), and Galileo navigation satellite system (Galileo) have provided real-time satellite clock correction, which is updated at a high-frequency. However, the frequent updates pose the challenges of increasing the computational burden and compromising the timeliness of these correction parameters. To address this issue, an improved Real-Time Service (RTS) method is developed using an extrapolation algorithm and a linear model. The results indicate that a 1 h arc length of the satellite clock correction series is optimal for fitting a linear model of the RTS. With this approach, the 1 h extrapolation results for BDS-3 and Galileo are superior to 0.09 ns. Moreover, when these model coefficients are transmitted and updated at the intervals of 1, 2, 5, and 10 min, the corresponding PPP can converge at the centimeter-level. It is evident that these improved RTS methods outperform the current approach with high-frequency interval transmission, as they effectively mitigate the challenges associated with maintaining the timeliness of correction parameters.

The tropospheric delay is one of the main error sources that degrades the accuracy of Global Navigation Satellite Systems (GNSS) Single Point Positioning (SPP). Although an empirical model is usually applied for correction and thereby to improve the positioning accuracy, the residual tropospheric delay is still drowned in measurement noise, and cannot be further compensated by parameter estimation. How much this type of residual error would sway the SPP positioning solutions on a global scale are still unclear. In this paper, the biases on SPP solutions introduced by the residual tropospheric delay when using nine conventionally Zenith Tropospheric Delay (ZTD) models are analyzed and discussed, including Saastamoinen+norm/Global Pressure and Temperature (GPT)/GPT2/GPT2w/GPT3, University of New Brunswick (UNB)3/UNB3m, European Geostationary Navigation Overlay System (EGNOS) and Vienna Mapping Functions (VMF)3 models. The accuracies of the nine ZTD models, as well as the SPP biases caused by the residual ZTD (dZTD) after model correction are evaluated using International GNSS Service (IGS)-ZTD products from around 400 globally distributed monitoring stations. The seasonal, latitudinal, and altitudinal discrepancies are analyzed respectively. The results show that the SPP solution biases caused by the dZTD mainly occur on the vertical direction, nearly to decimeter level, and significant discrepancies are observed among different models at different geographical locations. This study provides references for the refinement and applications of the nine ZTD models for SPP users.

High-accuracy, real-time precipitable water vapor (PWV) products with high spatiotemporal resolution are of great significance for precipitation forecasting, extreme weather monitoring and early warning. Global reanalysis data and Global Navigation Satellite System (GNSS), face limitations in providing real-time, high spatiotemporal resolution PWV products owing to the latency of reanalysis data and the uneven distribution of GNSS stations. To overcome these challenges, a novel PWV retrieval approach was developed. The Huawei Cloud Pangu-Weather system was introduced to predict hourly real-time PWV globally, namely Pangu PWV, with a horizontal resolution of 0.25° from 2018 to 2020. The estimation result of Pangu PWV was evaluated using PWV dataset from 540 radiosonde stations and 12,292 GPS stations worldwide. In this work, the gridded PWV product from MERRA-2 was incorporated for comparison. To mitigate evaluation uncertainties, the previously developed Global PWV Vertical Correction Model (GPWV-H) was employed to adjust the gridded PWV for both products. The mean bias and root mean square error (RMSE) for MERRA-2 and Pangu PWV are -2.59/0.59 mm and 3.67/3.67 mm against radiosonde records, respectively, and mean bias and RMSE are -2.20/-0.01 mm and 3.17/3.37 mm against GPS PWV data, respectively. In addition, Pangu PWV has close performance to MERRA-2 PWV, further demonstrating that Pangu PWV is well-suited for meteorological applications. Besides, the performance of the two products was tested under extreme weather conditions in a specific region. The mean bias and RMSE for MERRA-2 and Pangu PWV are -6.14/0.19 mm and 7.05/3.76 mm, respectively, indicating that the Pangu PWV still yield stable performance during extreme weather events. Thus, the Pangu PWV, exhibiting the merits such as real-time, great precision, and high spatiotemporal resolution on a global scale, holds great potential for applications in extreme weather monitoring and precipitation forecasting.

The time-varying characteristic of the bias in the GPS code observation is investigated using triple-frequency observations. The method for estimating the combined code bias is presented and the twelve-month (1 January–31 December 2016) triple-frequency GPS data set from 114 International GNSS Service (IGS) stations is processed to analyze the characteristic of the combined code bias. The results show that the main periods of the combined code bias are 12, 8, 6, 4, 4.8 and 2.67 h. The time-varying characteristic of the combined code bias, which is the combination of differential code bias (DCB) (P1–P5) and DCB (P1–P2), shows that the real satellite DCBs are also time-varying. The difference between the two sets of the computed constant parts of the combined code bias, with the IGS DCB products of DCB (P1–P2) and DCB (P1–P2) and the mean of the estimated 24-h combined code bias series, further show that the combined code bias cannot be replaced by the DCB (P1–P2) and DCB (P1–P5) products. The time-varying part of inter-frequency clock bias (IFCB) can be estimated by the phase and code observations and the phase based IFCB is the combinations of the triple-frequency satellite uncalibrated phase delays (UPDs) and the code-based IFCB is the function of the DCBs. The performances of the computed the IFCB with different methods in single point positioning indicate that the accuracy for the constant part of the combined code bias is reduced, when the IGS DCB products are used to compute. These performances also show that the time-varying part of IFCB estimated with phase observation is better than that of code observation. The predicted results show that 98% of the predicted constant part of the combined code bias can be corrected and the attenuation of the predicted accuracy is much less evident. However, the accuracy of the predicted time-varying part decreases significantly with the predicted time.

In consideration of contributions from both carrier phase and pseudorange observations during computation, this study introduces a reconstructed method for estimating the multi-frequency global navigation satellite system (GNSS) inter-frequency clock biases (IFCB). Diverging from conventional approaches that separately calculate the time-varying and constant parts of IFCBs using carrier phase and pseudorange observations, the reconstructed method directly utilizes their combination to estimate satellite IFCBs. To validate the efficacy of the presented approach, 7 d observations from 87 International GNSS Service (IGS) stations are analyzed, with a specific focus on triple-frequency GPS, multi-frequency BDS-3, and Galileo IFCBs, aiming to scrutinize their distinctive characteristics. Furthermore, the performances of satellite IFCB estimation are investigated in both precise point positioning (PPP) and single-point positioning (SPP) using 35 IGS stations over 3 d. The results demonstrate that IFCBs of GPS BLOCK IIIA satellites exhibit centimeter-level variations, distinguishing them from BLOCK IIF counterparts. The Galileo IFCBs vary from millimeter to centimeter level, while those of BDS-3 reach a centimeter level. These variations significantly impact GPS PPP convergence performances but have minimal effects on Galileo and BDS-3 PPP. SPP performances are slightly enhanced when the time-varying IFCB part are taken into account. Additionally, we note disparities in the constant parts of satellite IFCBs computed with differential code bias (DCB) products, reconstructed, and pseudorange observation-based methods, particularly for BDS-3 C2I/C6I-C1P/C5P and C2I/C6I-C1P/C6I combinations. The differences of IFCB estimated with different strategies, SPP and PPP performances show that the reconstructed method is better than others, and the IFCB accuracy decreases when computed with satellite DCB products.

The continuity and accuracy of real-time (RT) global satellite navigation system (GNSS) sensing of atmospheric water vapor can be seriously affected by a lack of connectivity. To mitigate this issue, a method has been developed that utilizes the International GNSS Service (IGS) ultra-rapid (IGU) satellite orbit and an established RT service (RTS) for satellite clock correction. This method ensures the accuracy of RT atmospheric water vapor estimation even when communication is interrupted. The established RTS utilizes variations in historical clock correction data from the user side to extrapolate its RT high-precision value. Through experimentation, it has been determined that using a quadratic polynomial and an eighth-order harmonic-based function along with 1-hour historical clock correction data is optimal for establishing this RTS method. The 2D and 3D accuracies of static Precise Point Positioning (PPP) can achieve centimeter to millimeter levels, and the estimated average Root Mean Square (RMS) of zenith tropospheric delay (ZTD) is equivalent to the RT archived products. When compared to the precipitable water vapor (PWV) results obtained from IGS ZTD products, the averaged RMS values of GPS, Galileo, and BDS-3 PWV reach 3.12 mm, 4.41 mm, and 6.43 mm, respectively, which can meet the accuracy requirements of general numerical weather forecasting and other applications during communication interruptions.