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Using two ionospheric scintillation monitoring receivers (ISMRs) and four geodetic receivers from April 1, 2022 to March 31, 2023, this study investigates ionospheric scintillation effects at low-latitudes on BDS-3 and GPS PPP accuracy and ambiguity resolved percentage (ARP). Experimental results indicate that during scintillation periods, the positioning errors of BDS-3 PPP can reach several metres and some cases can reach more than 10 m, while during non-scintillation periods, the positioning errors can maintain a centimetre level. Compared with BDS-3, the positioning errors of GPS PPP are generally smaller than 1 m under ionospheric scintillation. For BDS-3 PPP-ARP statistics, the values are around 71-99% under non-scintillation conditions, while these values are degraded to about 27-70% under ionospheric scintillation. It is found that when the average of S4 (ROTI) increases, the 3D RMS results of BDS-3 and GPS PPP show an increasing trend, while the PPP-ARP exhibits a decreasing trend. [ABSTRACT FROM AUTHOR]

Objectives: The satellite attitude quaternion products have been proposed by International GNSS Service in the third data reprocessing campaign (repro3). These satellite attitude quaternion products are not only contributed to combining the precise satellite products during the eclipse season, but also can improve the reliability of precision point positioning (PPP) when satellites are in abnormal yaw attitude. Methods: The four final and rapid BeiDou-3 satellite navigation system (BDS-3) satellite attitude products provided by Wuhan University (WHU), Geo Forschungs Zentrum and Center for Orbit Determination in Europe have been compared. Attitude model characteristic of BDS-3 with different type from different analysis centers have been also analyzed in the eclipse seasons, and the effect of different satellite model on satellite clock and kinematic PPP have been investigated. Results: The results demonstrate that the BDS-3 yaw angle difference can reach up about 120° from different analysis centers when the sun elevation angle is approximately 0°. In this period, different analysis centers used different attitude models. Furthermore, when the satellite attitude quaternions are used from different analysis centers, the PPP positing accuracy can be improved during the eclipse season. In detail, a significant improvement rate is achieved by using WHU rapid products, compared with nominal attitude strategy, the 3D positioning accuracy of kinematic PPP solutions with satellite attitude quaternions can be improved approximately 18. 4%. Conclusion: Although the positioning accuracy of PPP solutions can be improved by using the publicly BDS-3 attitude model, various attitude strategies may be adopted in different analysis centers. Therefore, in order to obtain reliable PPP results, the satellite attitude quaternions should be used. [ABSTRACT FROM AUTHOR]

Array Precise Point Positioning (PPP) is a concept that utilizes GNSS observations from multiple antennas in an array of known geometry to realize improved GNSS parameter estimation. This paper proposes a new model of Array PPP entirely based on undifferenced observations, called undifferenced Array PPP model. First, it represents the attitude as a quaternion and formulates how to derive the attitude from the GNSS undifferenced observations in the antenna array. Then, the estimated undifferenced ambiguities are extracted from float solutions, constructed as double-differenced ambiguities between the antennas, and resolved to integers. Finally, it applies Lie theory to keep the rotation parameters always lying on a 3D unit-sphere manifold, indicated as Special Orthogonal group S O 3 . The undifferenced Array PPP model has equivalent performances with the mix Array PPP model based on mix observations containing undifferenced and double-differenced GNSS observations. The difference is that the mix Array PPP model considers the cross-correlation between different antennas in its stochastic model, while the undifferenced Array PPP model incorporates the cross-correlation in its functional model. The independence of the satellite observations in the undifferenced Array PPP model brings benefits in adjusting available satellites, frequency bands and error detection, resulting in better performances in the dynamic scenarios under complex environments. Last but not the least, the new model represents the attitude as quaternion and estimates its perturbations in the measurement update phase of Kalman filter, having the potential to achieve tight integration with Inertial Measurement Unit (IMU) and then increase the continuity and availability of solutions, especially in a GNSS-denied environment. [ABSTRACT FROM AUTHOR]

Asymmetric troposphere modeling is crucial in Precise Point Positioning (PPP). The functional model of the asymmetric troposphere has been thoroughly studied, while the stochastic model lacks discussion. Currently, there is no suitable stochastic model for asymmetric tropospheric conditions, potentially degrading the positioning accuracy and the reliability of Zenith Total/Wet Delay (ZTD/ZWD) estimates. This paper introduces an Azimuth-Dependent Weighting (ADW) scheme that utilizes information from asymmetric mapping functions to adaptively weight Global Navigation Satellite System (GNSS) observations affected by azimuth-dependent errors. The concept of ADW has been validated using Numerical Weather Prediction data and International GNSS Service data. The results indicate that ADW effectively improves the coordinate repeatability of the PPP solution by approximately 10 % in the horizontal and 20 % in the vertical direction. Additionally, ADW appears to be capable to improve the ZWD estimates during the PPP convergence period and yields smoother ZWD estimates. Consequently, it is recommended to adopt this new weighting scheme in PPP applications when an asymmetric mapping functions is employed. [ABSTRACT FROM AUTHOR]

GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial–temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the Expectation–Maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by 2 mm / hour . [ABSTRACT FROM AUTHOR]

Zenith Tropospheric Delay (ZTD) is one of the main atmospheric errors in the Global Navigation Satellite System (GNSS). In this study, we propose a novel ZTD forecasting model based on the deep-learning method named Informer-based ZTD (IBZTD) forecasting model using the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth generation reanalysis data (ERA5) from 2011 to 2021. With 72-hour historical GNSS-derived ZTDs as prior information, the subsequent 24-hour ZTDs can be forecasted. The IBZTD forecasting model achieves the best regression fit with post GNSS-derived ZTDs compared with GPT3 (Global Pressure and Temperature 3) and HGPT2 (Hourly Global Pressure and Temperature 2) models, especially in winter with a Root Mean Square Error (RMSE) of 1.51 cm and a Mean Absolute Error (MAE) of 1.15 cm. With the post GNSS-derived ZTDs as reference, in terms of the overall 24-hour forecasting accuracy for 9 GNSS stations in 2022, IBZTD forecasting model achieves a MAE of 1.66 cm and a RMSE of 2.21 cm, significantly outperforming the GPT3 model (MAE: 2.60 cm, RMSE: 3.37 cm), HGPT2 model (MAE: 3.23 cm, RMSE: 4.03 cm) and Long Short-Term Memory (LSTM) model (MAE: 2.65 cm, RMSE: 3.65 cm). An average time improvement of 17.8% and comparable forecasting precisions are achieved in the IBZTD forecasting model compared with the Transformer-based ZTD (TBZTD) forecasting model. Using predicted ZTD as prior constraints in Precise Point Positioning (PPP), the vertical convergence speed exhibits a significant improvement of 14.20%, 20.24%, 18.48%, and 19.39% in four seasons. [ABSTRACT FROM AUTHOR]

Factor graph optimization has been widely used for state estimation in robotic SLAM community. Extensive algorithms have been proposed for camera/LiDAR/INS based SLAM. However, GNSS positioning based on factor graph optimization is limited, which prevents the introduction of high precise GNSS to robotic SLAM community. The current implementations are focused on pseudorange or RTK based positioning. PPP with ambiguity resolution (AR) is the state-of-the-art positioning technique for the past decade. Therefore, the PPP AR based on factor graph optimization is proposed, in which the pseudorange and carrier phases factors are constructed from the error equations of raw observations, while the ambiguity resolution factor is built from the ambiguity resolution. Results from 80 MGEX stations show that the average accuracy of static PPP is improved from 1.25, 0.61 and 2.29 cm to 0.81, 0.5 and 2.1 cm, corresponding to improvements of 35.1%, 18.7% and 8.7% in east, north, and up directions, respectively. As for kinematic PPP, the average accuracy is improved from 2.62, 2.21 and 5.8 cm to 1.64, 1.74 and 5.37 cm, corresponding to improvements of 37.5%, 21.6% and 7.4% in east, north, and up directions, respectively. The kinematic PPP was also verified with real-world data collected from a moving vehicle. After the first ambiguity fixing, the accuracy of PPP is improved from 3.7, 2.1 and 10.1 cm to 1.6, 2.0 and 9.0 cm for east, north and up component, respectively, corresponding to improvements of 32%, 5% and 11%. The above results confirm the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Galileo supports global precise point positioning (PPP) service by delivering precise products via satellites, which is known as high accuracy service (HAS). To improve reception efficiency, the Galileo HAS employs a high-parity vertical reed-solomon encoding scheme, increasing the complexity of HAS corrections recovery. To promote research and application of the HAS, an open-source C/C + + decoding package, HASPPP, has been developed for seamless embedding into the prevalent C/C++-based software, such as RTKLIB. HASPPP provides interfaces for effortless decoding support of raw HAS binary data from various manufacturers. The HASPPP manual offers code analysis along with simple to complex examples to aid users in swiftly mastering decoding. HASPPP has undergone rigorous validation of its decoding accuracy and reliability. [ABSTRACT FROM AUTHOR]

The modernization of the Global Navigation Satellite Systems (GNSS) has brought many new features and capabilities, one of which is programmable power output capability, also known as flex power. Flex power capability allows for an increase in the signal strength of the individual signals to better fulfil operational constraints, but it may also cause biases in the pseudorange and carrier phase observations. This study focuses on the flex power capability characteristics of the second-generation Beidou Navigation and Positioning System (Beidou-2). We summarized the Beidou-2 flex power activation periods from January 2021 to April 2024 and analyzed the impact of flex power on phase biases and precise point positioning with ambiguity resolution (PPP-AR). The results show that Beidou-2 flex power would affect both pseudorange and phase observations on the B3I signals simultaneously. In addition, Hatch–Melbourne–Wübbena (HMW) combinations with single-epoch exhibit obvious discontinuities due to this mode of Beidou-2 flex power. Furthermore, the differences in estimated wide-lane (WL) biases can reach up to approximately 0.4 cycles when the Beidou-2 flex power is switched on or off. During this time, regarding the WL biases estimation with the daily constant strategy, the WL ambiguity residuals of Beidou-2 PPP-AR users are only approximately 70% within ± 0.25 cycles. In contrast, with the piecewise constant strategy, the WL ambiguity residuals above the threshold can reach approximately 90%. Considering flex power in kinematic PPP-AR, the position biases root mean square (RMS) values of 0.8, 0.8 and 2.5 cm can be achieved for the east, north and up components, respectively, while the corresponding position biases RMS without careful consideration of flex power are 1.0, 0.9 and 2.8 cm. Therefore, to achieve more reliable positioning results, it is advisable to incorporate flex power into high-precision GNSS data processing, especially for bias products of PPP-AR. [ABSTRACT FROM AUTHOR]

Since the full system deployment of BDS-3 in July 2020, it has provided stable and reliable positioning, navigation and timing (PNT) services for users around the world. It is an urgent task to explore the potential performance of precise point positioning (PPP) based on the full constellation of BDS-2/BDS-3. This research presented the global satellite visibility of BDS-2/BDS-3, analyzed the stability and accuracy of BDS-2 and BDS-3 rubidium clocks and hydrogen clocks, jointly estimated the BDS-2 and BDS-3 fractional cycle biases (FCB) and evaluated the PPP performance with ambiguity resolution (AR). Due to the fact that International GNSS Service (IGS) precise products have a great impact on narrow-lane (NL) FCB estimation, the FCB obtained by using the precise products from CODE (Center for Orbit Determination in Europe) and GBM (Deutsches GeoForschungsZentrum) in two different analysis centers and the FCB obtained by using GBM precise products with different calculation strategies are analyzed. In addition, the experimental data from Multi-GNSS Experiment (MGEX), EUREF (EPN) and Germany (GPN) observation networks are used to evaluate the influence of orbital errors on BDS FCB estimation. For wide-lane (WL) FCB, MGEX WL FCB has the highest accuracy, followed by EPN and GPN. On the contrary, for NL FCB, MGEX NL FCB has the worst accuracy, followed by EPN, and GPN is the best. Eventually, numerous experiment results showed that compared with the static float solution, the PPP fixed solutions in East (E), North (N) and Up (U) directions are improved by 32.9%, 27.7%, 13.8% for BDS-3 and 10.0%, 7.5%, 3.8% for BDS-2/BDS-3. Compared with the kinematic float solution, the PPP fixed solutions in E, N and U directions are improved by 27.9%, 23.4%, 16.6% for BDS-3 and 15.9%, 8.9%, 5.3% for BDS-2/BDS-3. [ABSTRACT FROM AUTHOR]

The open access to raw Global Navigation Satellite System (GNSS) measurements from Android smartphones brings new possibilities to high-accuracy positioning with precise point positioning (PPP) technique. However, decimeter or even centimeter level positioning accuracy is still challengeable mainly due to the low completeness of dual-frequency observations and specific observation errors from a smartphone. Huawei P40 released in 2020 is the first module that can track multi-GNSS multi-frequency signals. Based on GNSS observations from P40 and a co-located geodetic-grade receiver, a method is proposed to extract and model the P40 code-carrier inconsistency errors. The P40 observation inconsistency presents a linear drift pattern with respect to time at each frequency and can even reach hundreds of meters. A correction model is then established which reduces the code-carrier differences to a level of few meters. Regarding to the P40 code-carrier inconsistency error signature, an uncombined precise point positioning (PPP) algorithm is developed with the inconsistency error treated with different schemes, including correction using established model, parameterization as a linear function, or estimated as an independent clock offset for carrier-phase observation. Meanwhile, to cope with the dual-frequency data deficiency of P40, the PPP algorithm is designed based on pure single-frequency processing which can handle mixed single- and dual-frequency observations. Positioning performances of three schemes are validated in both static and kinematic scenarios. With applying the code-carrier inconsistency schemes, P40 positioning precision reaches 0.2 m and 1.0 m for static and kinematic experiments, respectively, which is improved by an order of magnitude against the case without. Furthermore, precision can be even improved when P40 is equipped with an external geodetic-grade antenna. It reaches 5.8 and 18.2 cm in the static and kinematic tests, respectively, revealing improvements of 28.7% and 54.4% against the case without considering the inconsistencies, respectively. Such result is very encouraging and indicate a positioning accuracy level close to a geodetic receiver. [ABSTRACT FROM AUTHOR]

This study examines the accuracy and stability of three prominent Precise Point Positioning (PPP) services: AUSPOS, Trimble RTX, and OPUS, across varying observation periods from 30 to 180 minutes. Static GNSS data was collected at eight different locations over a three-hour timeframe. The analysis focused on comparing the geocentric coordinates (X, Y, Z) obtained from each service, utilizing metrics such as Root Mean Square Error (RMSE) and standard deviations to assess performance. The results revealed that processing time significantly influences accuracy, with Trimble RTX demonstrating the highest precision across all intervals. AUSPOS displayed considerable variations at shorter observation periods, while OPUS exhibited larger discrepancies, indicating potential challenges in stability. These findings underscore the strengths and weaknesses of each service, offering critical insights for selecting the most appropriate GNSS processing option tailored to specific geodetic applications. By highlighting the relationship between observation duration and positioning accuracy, this study contributes valuable knowledge to the field of geodesy and PPP service utilization. [ABSTRACT FROM AUTHOR]

Objectives: The BeiDou-3 satellite navigation system (BDS-3) can provide real-time precise point positioning (PPP) services to China and neighboring regions through PPP-B2b signals. Because PPPB2b signals do not contain ionospheric model products, the current positioning research mainly adopts ionospheric-free combination. The positioning accuracy can reach decimeter level, but requires about 30 min of convergence time. In this paper, aiming at the long convergence time of PPP-B2b positioning, the improvement of positioning convergence performance based on ionospheric model products is analyzed. Methods: Quasi-4-dimensional ionospheric modeling is introduced into regional ionospheric delay modeling in China and four schemes of 50,100,150 and 200 reference stations uniformly distributed in China (day of year 201—207) are adopted for ionospheric modeling. Results: The results show that when the number of stations used in ionospheric modeling increases from 50 to 200, the accuracy of ionospheric model products increases from 2-3 TECU to better than 0.8 TECU. Compared with the current ionospheric-free combined PPP, the convergence time of BDS-3 dynamic PPP can be deceased by 77%. In addition, the convergence time of GPS+BDS-3 dynamic PPP is reduced from 13.51 min to 4.45 min. Conclusions: High-precision ionospheric model products can significantly shorten the convergence time of PPP-B2b. [ABSTRACT FROM AUTHOR]

This paper investigates time‐lag effects of ionospheric response to two severe geomagnetic storms (Kp = 8) on the degradation of kinematic precise point positioning (PPP) solutions, utilizing over 5500 Global Navigation Satellite Systems (GNSS) stations distributed worldwide. Focusing on these two severe geomagnetic storms that occurred during solar cycle 24, the study employs an open‐source positioning software package, namely RTKLIB, to derive the PPP solutions. The findings reveal significant variations in time lags across different magnetic latitudes. These variations are driven by ionospheric responses to a southward interplanetary magnetic field and subsequent decreases in the SMY‐H index during the 2015 St. Patrick's Day Storm and the 2017 September 7–8 Storm. Specifically, at high latitudes, PPP degradation primarily manifests during the main phase of the storm, resulting in delays spanning from several minutes to 1–2 hr after the sudden onset of the storm. In contrast, mid‐ and low latitudes exhibit a wider range of delays extending up to tens of hours. Notably, rapid positioning degradation is observed predominantly at the magnetic local time noon and midnight sectors. The study discusses these time lag effects concerning the intensity of various ionospheric disturbances triggered by the interactions among the solar wind, magnetosphere, and ionosphere during geomagnetic storms. The insights obtained from this research have the potential to be integrated into physics‐based and machine‐learning models to enhance forecasting capabilities of space weather impacts. Plain Language Summary: This paper presents space weather impact on Global Navigation Satellite Systems positioning solutions. Specifically, it examines the time‐lag effects of the ionospheric response to severe geomagnetic storms. The study finds that the time it takes the positioning system to degrade varies depending on the device latitude. At high latitudes, the degradation happens quickly, within minutes to an hour after the storm starts. At mid‐ and low latitudes, the degradation takes longer, sometimes up to tens of hours after the storm onset. The differences in the time lag are related to how the ionosphere reacts to changes in the Earth's magnetic fields during these storms. This study is significant because it quantifies the time difference between the start of a storm and the degradation in the positioning system. The information gained from this research will help improve forecasting space weather impacts. Key Points: Initial attempt to quantify the time lags between the sudden onset of a geomagnetic storm and the degradation in precise point positioning on a global scaleTime lags in high latitudes typically vary from a few minutes to less than 2 hrMiddle and low latitudes responses show a wider range of time lags of up to several tens of hours [ABSTRACT FROM AUTHOR]

BeiDou navigation satellite system with global coverage (BDS-3) has been fully operational since July 2020, currently providing the positioning, navigation and timing service together with regional BDS-2. In addition to the legacy signals of B1I and B3I, the BDS-3 also transmits several new signals such as BIC, B2a and B2b, which brings new opportunities for rapid ambiguity resolution (AR) of BDS precise point positioning (PPP). In this contribution, a multi-frequency (MF) rapid PPP-AR method with regional network augmentation was proposed. Firstly, BDS five-frequency observations were introduced into uncombined double-differenced models to retrieve regional augmentation corrections at the server. Thereafter, a cascade PPP-AR strategy using extra-wide-lane, wide-lane and narrow-lane ambiguity was employed at the user. Once ambiguities were fixed to integers, the phase correction accuracy could reach about 3 cm on average overall BDS frequencies in the network with inter-station distances of 100–200 km. Subsequently, the statistical results of seven-day simulated kinematic experiments showed that over 99% of epochs on average realized PPP-AR. Correspondingly, the positioning accuracy of the MF fixed solution reached 1.8, 1.9, 4.7 cm in the east, north and up components, respectively, improving by 5–15% compared with the dual-frequency scheme. Moreover, several vehicle-borne experiments under different urban scenarios were also conducted. Under an open-sky or a relatively open highway scene, the BDS-MF scheme similarly exhibited good performance, and over 98% of epochs achieved rapid PPP-AR with a positioning accuracy better than 3 cm. More encouragingly, for this BDS-challenged experiment with an average satellite number of 8.6, although only 72.06% of epochs were available due to serious signal blockages caused by overpass, tunnels or tall buildings, the horizontal positioning accuracy could still remain 7 cm on average.

This study investigates the impact of observation session duration and station latitude on the precision of Precise Point Positioning (PPP). Global Positioning System-only Receiver Independent Exchange files from 516 continuous stations spanning latitudes from 90°N to 90°S across the Americas (30°–130°W) were binned into sessions of 1, 2, 3, 4, 6, and 12 h and processed using the GPSPACE PPP software. These sub-daily solutions, along with the original 24 h ones, were compared against a reference coordinate derived from an extended linear trajectory model for each station. Analysis of the results, considering both accuracy and precision, was conducted across the entire latitude range of the study. We found that the precision of a PPP solution approximately follows a power-law relationship with observation duration. Parameters for these power-law relationships were determined for all latitude ranges that allow users to predict a result’s uncertainty as a function of session length. Findings indicate that longer observation sessions lead to reduced positioning errors, with vertical scatter decreasing with increasing latitude. Since all these stations are characterized by good to excellent sky view, our power-law rule-of-thumb provides a lower bound on the occupation time needed to achieve target positioning precision at locations with poorer sky visibility.

Abstract With the rapid development of technologies such as autonomous driving and robotic navigation, the demand for accurate and reliable positioning results with BDS has increased. The current status and future development of BDS high precision services are reviewed. The operational PPP-B2b of BDS-3 achieves positioning accuracy at decimeter-level within 14 min and has the drawbacks in regional coverage and long convergence time compared with the international counterparts, such as CLAS of QZSS and HAS of Galileo. A development frame for multi-layer BDS high-precision services is proposed by considering its construction cost, compatibility of user terminal, operating maintenance burden, and service level. The global high-precision service with the improved orbit and clock accuracy enhanced with the inter-satellite link is taken as the most fundamental layer. By incorporating inter-satellite link observations, the orbit errors URE and clock errors are significantly reduced to approximately 0.05 m and 0.16 ns, respectively, which will expand PPP service to global. Based on this, the regional PPP-AR and PPP-RTK services with improved convergence performance are taken as the second layer. With PPP-AR, the convergence time drops to 10 min. With PPP-RTK, the convergence time would be further shortened to less than 3 min. The LEO enhanced PPP service is taken as the third layer which overcomes both drawbacks of the long convergence time of the inter-satellite link enhanced service (the first layer) and the regional coverage of the PPP-AR/PPP-RTK services (the second layer). The simulation results show that by introducing a LEO constellation of 288 satellites, the LEO enhanced PPP can achieve positioning accuracy better than 5 cm within approximately 1 min. In addition, the integration of LEO constellation and PPP-RTK is further proposed to enable instantaneous convergence. The implementation challenges are also presented.

Abstract Satellite navigation positioning has become an indispensable component of everyday life, where precise pinpointing and rapid convergence are crucial in delivering timely and accurate location information. However, due to the damping of integer ambiguities and system residual errors, the rapid convergence of Precise Point Positioning (PPP) implementation is a significant challenge. To address this, this paper proposes a novel Carrier Phase Zero-Baseline Self-Differencing Precise Point Positioning (CZS-PPP) technique and its ionosphere-free fusion model. By employing the proposed CZS-PPP approach in separate scenarios involving BDS-3, GPS, and dual-system settings, we systematically validate the efficacy of the method. The experimental results indicate that the convergence time of the method is less than 4 min in a single-system scenario. Furthermore, in a dual-system scenario, the method can achieve rapid convergence in less than 3 min. The CZS-PPP technique presented demonstrates the elimination of integer ambiguities and the effective suppression of system residuals, in comparison to the conventional method. The proposed approach has demonstrated remarkable performance across different systems, offering a promising new pathway for achieving PPP fast convergence in BDS/GNSS.

Ambiguity resolution (AR) can markedly enhance the precision of precise point positioning (PPP) and accelerate the convergence process. The decoupled clock model represents a pivotal approach for ambiguity resolution, yet current research on this topic is largely confined to GPS. Consequently, in this study, we extend the investigation of the decoupled clock model to multi-GNSS. Firstly, based on the conventional model, we derive the multi-GNSS decoupled clock estimation model and the precise point positioning with ambiguity resolution (PPP-AR) model. Secondly, we provide a detailed explanation of the estimation process for the multi-GNSS decoupled clock estimation. To validate the efficacy of the proposed model, we conduct multi-GNSS decoupled clock estimation and PPP-AR experiments using six days of observation data. The results demonstrate that the decoupled clocks of GPS, Galileo, and BDS-3 can all achieve high accuracy, thus fully meeting the requirement of ambiguity resolution. In terms of positioning performance, the joint three systems have higher positioning accuracy, reaching 3.10 cm and 6.13 cm in horizontal and vertical directions, respectively. Furthermore, the convergence time (CT) and time to first fix (TTFF) are shortened, to 23.13 min and 13.65 min, respectively. The experimental findings indicate that the proposed multi-GNSS decoupled clock model exhibits high precision and rapid positioning service capabilities. [ABSTRACT FROM AUTHOR]

The accurate measurement of water vapor is essential for research about and the applications of meteorology, climatology, and hydrology. Based on the BeiDou PPP-B2b service, real-time precipitable water vapor (PWV) can be retrieved with the precise point positioning (PPP) software (XTW-PPP version 0.0). The experiment was conducted in Beijing in January 2023. Three solutions were designed with PPP using the BeiDou system only, the GPS system only, and the BeiDou-GPS combined solution. Real-time PWVs for the three solutions were validated with the ERA5 reanalysis data. Between the PWV values from the single BeiDou and ERA5, there was a bias of 0.7 mm and an RMSE of 1.8 mm. For the GPS case, the bias was 0.73 mm and the RMSE was 1.97 mm. The biases were less than 1 mm and RMSEs were less than 2 mm. Both the BeiDou and the GPS processing performed very well. But little improvement was found for the BeiDou-GPS combined solution, compared with the BeiDou system-only and the GPS system-only solution. This may be due to the poor handling of two different kinds of errors for the GPS and the BeiDou systems in our PPP software. A better PWV estimation with the two systems is to estimate PWV with a single system at the first step and then obtain the optimization by Bayesian model averaging. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube's performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime. [ABSTRACT FROM AUTHOR]

To support real-time global navigation satellite systems (GNSS) precise applications, satellite clock corrections need to be precisely estimated at a high-rate update interval, which remains a challenge due to the rapid development of multi-GNSS constellations. In this study, we developed an undifferenced (UD) ambiguity resolution (AR) procedure to improve both the accuracy and computational efficiency for real-time multi-GNSS clock estimation realized by a square root information filter. In the proposed method, UD ambiguities are resolved after correcting the simultaneously estimated uncalibrated phase delays (UPD) and the fixed UD ambiguity parameters are eliminated immediately from the filter, so that the computational burden is significantly reduced. Moreover, based on the linear relationship between double-differenced (DD) and UD ambiguities, we investigated the difference between DD and UD AR in clock estimation. We found that the major reason why DD AR contributes little to the clock estimation while UD AR can speed up the convergence remarkably is that UD AR additionally provides a stable clock datum compared with DD AR. GNSS observations from about 100 globally distributed stations were processed with the proposed method to generate simulated real-time clocks and UPDs for GPS, Galileo, and BDS satellites over a one-month period. The results show that the percentage of wide-lane (WL) UPD residuals within ± 0.25 cycles and narrow-lane (NL) UPD residuals within ± 0.15 cycles are over 97.0% and 90.0%, respectively, which contributes to an ambiguity fixing rate of more than 90% for three systems. The mean daily standard deviation (STD) of the clocks of the UD-fixed solution with respect to Center for Orbit Determination in Europe 30 s final products is 0.021, 0.020, and 0.035 ns for GPS, Galileo, and BDS satellite, respectively, which is improved by 78.1%, 58.3%, and 79.8% compared to the float solution. Benefiting from the removal of fixed ambiguities, the average computation time per epoch was reduced from 3.88 to 1.05 s with a remarkable improvement of 72.9%. The quality of the satellite clock and UPD products was also evaluated by the performance of kinematic precise point positioning (PPP). The results show that fast and reliable multi-GNSS PPP-AR can be achieved with the derived UD-fixed clocks and UPDs, which outperforms that using DD-fixed clock and off-line UPD products with an average improvement of 7.9% and 19.9% in terms of convergence time and positioning accuracy, respectively. Furthermore, we demonstrated the effectiveness of the proposed UD AR method through a 7-day real-time clock estimation experiment. [ABSTRACT FROM AUTHOR]

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This study presents an innovative approach to improving the accuracy and reducing the error convergence time of static Precise Point Positioning (PPP) in Global Positioning System (GPS) navigation. The research focuses on the impact of the high spatial and temporal resolution of a regional ionospheric data assimilation model on PPP over Taiwan. The study further evaluates the performance of both static PPP with the ionospheric information using commonly used models such as Klobuchar and International Reference Ionosphere (IRI), as well as a global ionospheric data assimilation model. Compared to the default IRI, the data assimilated IRI model can improve the overall ionospheric total electron content by approximately 83%. Additionally, it can significantly reduce horizontal positioning errors and shorten the error convergence time more than 52% for static PPP, even during geomagnetic storm events. The study concludes that the high resolution of a regional ionospheric data assimilation model can enhance the accuracy and reduce the error convergence time of PPP navigation and positioning. This research provides valuable insights for future studies in this field, especially in the development of more precise and efficient models for correcting ionospheric delay in GPS navigation. Plain Language Summary: The study concludes that regional ionospheric data assimilation models can enhance the accuracy and error convergence time of PPP navigation and positioning. This research provides valuable insights for future studies in this field, particularly in developing more accurate and efficient models for correcting ionospheric delay in GNSS navigation. Key Points: This study examines the impacts of high‐resolution regional ionospheric data assimilation models on PPP in GPS positioningThe EnKF/IRI model improves ionospheric TEC, recuses PPP errors, and shortens PPP convergence timeThis study concludes that regional ionospheric data assimilation model enhances PPP accuracy and provide valuable insights [ABSTRACT FROM AUTHOR]

Relative GNSS positioning, a longstanding measurement standard, often incurs high manpower and equipment costs. Online Precise Point Positioning (PPP) presents a cost-effective alternative by minimizing these expenses. However, transitioning from the ITRF2014 to the TWD97[2010] coordinate system presents unique challenges. This study evaluates the efficacy of five PPP services – AUSPOS, OPUS, CSRS-PPP, magicGNSS, and RTX-PP – using 2018 Continuously Operating Reference Stations (CORS) data. Following a seven-parameter transformation, we systematically compared these services to identify the optimal solution for Taiwan’s geodetic survey needs. Our analysis reveals that RTX-PP offers superior performance, achieving 1 cm accuracy over 24 h and 4 cm accuracy over 1 h. Most stations met these accuracy standards, even during short observation intervals from September 9, 2018. Nonetheless, there is a 24.1 % likelihood of exceeding the 6 cm accuracy threshold due to variations in GNSS data quality. To address this, we employed G-Nut software to analyze station data quality across regions, recommending station selection based on data ratio and cycle slips to improve PPP solution accuracy effectively. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP) augmentation corrections can enhance the accuracy of Global Navigation Satellite System (GNSS) positioning. Three prominent PPP augmentation services: the third generation of BeiDou Navigation Satellite System (BDS-3) PPP-B2b, Europe's Galileo High Accuracy Service (HAS) and Quasi-Zenith Satellite System (QZSS) Centimeter Level Augmentation Service (CLAS), are evaluated and compared, contributing to the optimal utilization of these services. Based on a 25-day dataset in March 2023, all the three services have made significant improvements in GPS orbit accuracy compared to the broadcast ephemeris. Galileo HAS achieved the highest three-dimension (3D) orbit accuracy for both GPS and Galileo (10.5 and 10.4 cm), followed by CLAS (48.1 and 16.3 cm) and PPP-B2b (GPS: 73.0 cm, BDS-3: 44.6 cm). This distinct performance of PPP-B2b orbits is found for the first time to be related to the large constellation rotation errors, which accounts for roughly half of the orbit errors of along and cross components. Regarding clock errors, PPP-B2b and HAS enhanced GPS clock accuracy to 0.20 ns (70 %) and 0.17 ns (74 %), respectively, over the broadcast clock (0.66 ns), while CLAS shows a much smaller improvement. Moderate correlations of 0.3–0.8 between orbit and clock errors are observed for the three augmentation corrections. For signal in space ranging error (SISRE), HAS (GPS:5.5 cm, Galileo:4.9 cm) outperforms PPP-B2b (GPS:14.3 cm, BDS-3:8.9 cm) and CLAS (GPS:23.6 cm, Galileo:13.7 cm). The 2-hourly kinematic positioning results with an accuracy of better than 20 cm (95th percentile) for the horizontal and vertical component, could be achieved for both PPP-B2b and HAS within 20 min within their service area. It is not recommended rely solely on the orbit/clock/code bias of CLAS for precise positioning, as the positioning accuracy is influenced by the SISRE. PPP-RTK of CLAS achieves horizontal 10 cm (95th percentile) and rapid convergence of mostly less than a minute by incorporating phase bias and atmospheric corrections. [ABSTRACT FROM AUTHOR]

The global navigation satellite system (GNSS) is a crucial technical tool used for precisely determining the orbit of low earth orbit (LEO) satellites. However, due to the short arc length of spaceborne GNSS observations and the presence of numerous outliers, there is a high rate of misjudgment of cycle slips, which leads to a decrease in orbit determination accuracy. To address this issue, we propose a linear-fit forward and backward moving window averaging (LFBMWA) algorithm and a modified second-order time-difference phase Ionospheric residual (MSTPIR) algorithm to minimize cycle slip misjudgment by suppressing the impact of outliers. Simulation experiments show that the traditional method using FBMWA and STPIR has an 85.53% misjudgment rate, while the proposed method using LFBMWA and MSTPIR reduces it to 13.79%, representing a reduction of over 70 percentage points. Additionally, the proposed method successfully detects all cycle slips. For the GRACE-C and GRACE-D satellites from day 1 to day 250 of 2022, the three-dimensional orbit errors using the proposed method are 3.35 cm and 3.24 cm, respectively, representing a reduction of 30.9% and 32.8% compared to traditional methods. Therefore, the proposed method performs well and can be used as an effective tool for cycle slip detection. [ABSTRACT FROM AUTHOR]

The analysis of altimetric profiles in Antarctica and their evolution over the years is a sensitive topic for the scientific community since it helps understand the effects of climate change that the continent undergoes. Different geomatic techniques, including the GNSS technology, can be employed to obtain altimetric profiles. However, the GNSS differenced approaches, such as the Post Processing Kinematic, are hardly usable to define long profiles in Antarctica because of the low number of CORS stations. In these conditions, the Precise Point Positioning (PPP) approach is a valid alternative to avoid processing very long baselines. The aim of this article is to define a standard procedure for the processing of historical GPS data, thanks to the availability of a dataset from the International Trans-Antarctic Scientific Expedition, which took place between 1998 and 1999 (ITASE98-99). This expedition focused on mapping the Antarctic territory, subdividing it by nations of influence, using geophysical and geodetic technologies, including GPS. The altimetric profiles had already been calculated in 2002 by the Geomatics group of the University of Bologna using the Gipsy-OASIS II software. In this work, the new version of the JPL software, GipsyX, is used to apply the newly implemented models and reprocessed products. The calibration of the processing parameters leading to the final PPP solution is described in the paper, including details on the implementation of a post-processing filtering procedure. The average a posteriori elevation error is 4.6 cm, while 99% of them are within 27 cm. The comparison of the new results to both the previous processing and the REMA elevation model shown that about double the number of solutions are now available, meter-level elevation spikes have been avoided, and a half meter bias is now reduced to a few centimeters. Given the almost 15 years difference between the 1999.0 expedition epoch and the REMA reference epoch, the obtained results can be used to study accumulation/erosion effects on the Antarctica ice sheet. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) meteorology, in which the zenith total delay (ZTD) and precipitable water vapor (PWV) are retrievable from GNSS signals, is a well-established tool for weather and climate monitoring. The real-time provision of ZTD/PWV products has always been challenging in GNSS meteorology, which is basically limited by the timely accessibility to precise satellite ephemerides. GNSS open service is based on the broadcast ephemerides. The accuracy of Galileo broadcast ephemerides has been improved to a high level, enabling real-time retrieval of ZTD/PWV using Galileo open service and being independent of network communication environments and devices. Moreover, building additional data processing systems and dense ground tracking networks is no longer necessary (excluding issues necessitating extremely accurate real-time ZTD/PWV retrievals, such as the PWV along coastal boundaries). We propose the real-time precise point positioning (PPP) technology with Galileo broadcast ephemerides to retrieve the high-accuracy ZTD/PWV. The data sets from 22 globally distributed stations spanning a year are used for analysis. Results indicate that the accuracy of real-time ZTD estimates derived from ambiguity-float solutions can reach to 2 cm after an average initialization time of 52.9 min. Taking international GNSS service (IGS) and radiosonde results as the reference, the mean bias of ZTD and PWV errors is usually less than 6 and 2 mm, respectively, while the standard deviation (STD) is 15.7 and 2.5 mm. The performance of ZTD/PWV estimates is nearly comparable to that of IGS real-time data streams, while it is worse than that of IGS post-processed precise products. [ABSTRACT FROM AUTHOR]

To mitigate multipath effects in multi-GNSS and multi-frequency precise point positioning (PPP), we constructed multi-GNSS and multi-frequency multipath models using the multipath hemispherical map (MHM) method. We investigated multi-GNSS and multi-frequency multipath effects by analyzing the impact of multipath corrections on observation residuals and PPP performance. In general, greater code rates and signal strengths lead to smaller observation residuals and multipath corrections, and signals with better anti-multipath performance are obtained. Notably, the observation residuals and multipath corrections of the GPS L5 signals are the smallest among those of the triple-frequency signals, and those of the GLONASS G1 signals are smaller than those of the G2 signals. Among the Galileo five-frequency signals, those of the E1 and E5 signals are the largest and smallest, respectively. Among the BDS-3 five-frequency signals, those of the B1I and B1C signals are greater than those of the other signals. Additionally, overlapping frequency signals with the same code rates and similar signal strengths display similar observation residuals and multipath corrections. In particular, the BDS-3 B1C signal has large phase residuals in the high-elevation region, possibly due to inaccurate receiver antenna phase center corrections applied. Surprisingly, the MHM method works well on it, possibly because the phase multipath corrections include elevation-specific errors. After multipath correction, the low-frequency multipath errors of multi-GNSS and multi-frequency observations are efficiently mitigated, significantly reducing the observation residuals and improving the observation accuracy. As a result, the three-dimensional convergence time of multi-GNSS and multi-frequency float kinematic PPP is reduced by 24.1%, with a 13.8% improvement in the positioning accuracy. [ABSTRACT FROM AUTHOR]

Smartphone global navigation satellite system measurements in suburban environments suffer from severe multipath and noise, posing a challenge in dealing with the potential outliers. Using the range errors derived from smartphones, the characteristics of range errors can be further utilized to optimize the stochastic model and improve outlier diagnosis in user environments. Compared to existing algorithms, a new adaptive phase/code precision ratio scheme is proposed. Furthermore, a scale factor is utilized to deal with the over-optimization issue in the fitted weighting scheme functions, and adaptive a posteriori residual rejection method which considers the number of rejected measurements is introduced. The positioning improvements brought by the proposed algorithm are validated step by step. The proposed adaptive phase/code precision ratio can reduce the 68th and 95th horizontal positioning errors by 4 cm and 3 cm, respectively, compared to a ratio of 100. The percentage of horizontal positioning errors within 1 m can be improved by 7% (from 50 to 58%). Compared to the conventional carrier-to-noise (C/N0)-based weighting scheme, the proposed weighting scheme can reduce the 68th and 95th percentile horizontal positioning errors by 14 cm and 15 cm, representing improvements of 11% and 8%, respectively. Applying the new residual rejection method, the percentage of positioning errors within 1 m improves from 42 to 54% compared to C/N0-based weighting scheme. The results demonstrate great potential for achieving overall sub-meter level horizontal positioning performance with smartphones in suburban environments. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The smartphone-based precise point positioning (PPP) technique is usually used in limited satellite visibility environments, resulting in discontinuities in carrier phase observations. This study proposes an approach to improve the smartphone-based PPP performance by predicting the missed carrier phase observations with Doppler observations. Kinematic smartphone-based PPP experiments in the tree canopy and high-building environments are conducted, and results show that the proposed PPP approach improves the horizontal positioning accuracy by over 31% and 14% and vertical positioning accuracy by over 23% and 10% when compared to the PPP approaches without predictions and with linear predictions, respectively. [ABSTRACT FROM AUTHOR]

With the rapid development of technologies such as autonomous driving and robotic navigation, the demand for accurate and reliable positioning results with BDS has increased. The current status and future development of BDS high precision services are reviewed. The operational PPP-B2b of BDS-3 achieves positioning accuracy at decimeter-level within 14 min and has the drawbacks in regional coverage and long convergence time compared with the international counterparts, such as CLAS of QZSS and HAS of Galileo. A development frame for multi-layer BDS high-precision services is proposed by considering its construction cost, compatibility of user terminal, operating maintenance burden, and service level. The global high-precision service with the improved orbit and clock accuracy enhanced with the inter-satellite link is taken as the most fundamental layer. By incorporating inter-satellite link observations, the orbit errors URE and clock errors are significantly reduced to approximately 0.05 m and 0.16 ns, respectively, which will expand PPP service to global. Based on this, the regional PPP-AR and PPP-RTK services with improved convergence performance are taken as the second layer. With PPP-AR, the convergence time drops to 10 min. With PPP-RTK, the convergence time would be further shortened to less than 3 min. The LEO enhanced PPP service is taken as the third layer which overcomes both drawbacks of the long convergence time of the inter-satellite link enhanced service (the first layer) and the regional coverage of the PPP-AR/PPP-RTK services (the second layer). The simulation results show that by introducing a LEO constellation of 288 satellites, the LEO enhanced PPP can achieve positioning accuracy better than 5 cm within approximately 1 min. In addition, the integration of LEO constellation and PPP-RTK is further proposed to enable instantaneous convergence. The implementation challenges are also presented. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) signals experience delays when passing through the atmosphere due to the presence of free electrons in the ionosphere and air density in the non-ionized part of the atmosphere, known as the troposphere. The Precise Point Positioning (PPP) technique demonstrates highly accurate positioning along with Zenith Tropospheric Delay (ZTD) estimation. ZTD estimation is valuable for various applications including climate modelling and determining atmospheric water vapor. Current GNSS network resolutions are not completely sufficient for the scale of a few kilometres that regional climate and weather models are increasingly adopting. The Centipede-RTK network is a low-cost option for increasing the spatial resolution of tropospheric monitoring. This study is motivated by the question of whether low-cost GNSS networks can provide a viable alternative without compromising data quality or precision. This study compares the performance of the low-cost Centipede-RTK network in calculating the Zenith Tropospheric Delay (ZTD) to that of the existing EUREF Permanent Network (EPN), using two alternative software packages, RTKLIB demo5 version and CSRS-PPP version 3, to ensure robustness and software independence in the findings. This investigation indicated that the ZTD estimations from both networks are almost identical when processed by the CSRS-PPP software, with the highest mean difference being less than 3.5 cm, confirming that networks such as Centipede-RTK could be a reliable option for dense precise atmospheric monitoring. Furthermore, this study revealed that the Centipede-RTK network, when processed using CSRS-PPP, provides ZTD estimations that are very similar and consistent with the EUREF ZTD product values. These findings suggest that low-cost GNSS networks like Centipede-RTK are viable for enhancing network density, thus improving the spatial resolution of tropospheric monitoring and potentially enriching climate modelling and weather prediction capabilities, paving the way for broader application and research in GNSS meteorology. [ABSTRACT FROM AUTHOR]

Satellite navigation positioning has become an indispensable component of everyday life, where precise pinpointing and rapid convergence are crucial in delivering timely and accurate location information. However, due to the damping of integer ambiguities and system residual errors, the rapid convergence of Precise Point Positioning (PPP) implementation is a significant challenge. To address this, this paper proposes a novel Carrier Phase Zero-Baseline Self-Differencing Precise Point Positioning (CZS-PPP) technique and its ionosphere-free fusion model. By employing the proposed CZS-PPP approach in separate scenarios involving BDS-3, GPS, and dual-system settings, we systematically validate the efficacy of the method. The experimental results indicate that the convergence time of the method is less than 4 min in a single-system scenario. Furthermore, in a dual-system scenario, the method can achieve rapid convergence in less than 3 min. The CZS-PPP technique presented demonstrates the elimination of integer ambiguities and the effective suppression of system residuals, in comparison to the conventional method. The proposed approach has demonstrated remarkable performance across different systems, offering a promising new pathway for achieving PPP fast convergence in BDS/GNSS. [ABSTRACT FROM AUTHOR]

The Global Navigation Satellite System (GNSS) can be utilized for long-distance and high-precision time transmission. With the ongoing development of low Earth orbit (LEO) satellites and the rapidly changing geometric relationships between them, the convergence rate of ambiguity parameters in Precise Point Positioning (PPP) algorithms has increased, enabling fast and reliable time transfer. In this paper, GPS is used as an experimental case, the LEO satellite constellation is designed, and simulated LEO observation data are generated. Then, using the GPS observation data provided by IGS, a LEO-enhanced PPP model is established. The LEO-augmented PPP model is employed to facilitate faster and more reliable high-precision time transfer. The application of the LEO-augmented PPP model to time transfer is examined and discussed through experimental examples. These examples show multiple types of time transfer links, and the experimental outcomes are uniform. GPS + LEO is compared with exclusive GPS time transfer schemes. The clock offset of the time transfer link for the GPS + LEO scheme converges more swiftly, meaning that the time required for the clock offset to reach a stable level is the briefest. In this paper, standard deviation is employed to assess stability, and Allan deviation is utilized to assess frequency stability. The results show that the clock offset stability and frequency stability achieved by the GPS + LEO scheme are superior within the convergence time range. Controlled experiments with different numbers of satellites for LEO enhancement indicate that time transfer performance can be improved by increasing the number of satellites. As a result, augmenting GPS tracking data with LEO observations enhances the time transfer service compared to GPS alone. [ABSTRACT FROM AUTHOR]

Satellite product combination has been a major effort for the International GNSS Service Analysis Center Coordinator to improve the robustness of orbits, clocks and biases over original AC-specific contributions. While the orbit and clock combinations have been well documented, combining phase biases is more of a challenge since they have to be aligned with the clocks precisely to preserve the exactitude of integer ambiguities in precise point positioning (PPP). In the case of dual-frequency signals, frequency-specific phase biases are first translated into an ionosphere-free form to agree with the IGS satellite clocks, and they can then be integrated as integer clocks to facilitate a joint combination. However, regarding multi-frequency phase biases, forming their ionosphere-free counterparts would be cumbersome as they are linearly dependent. We therefore propose a concept of “frequency-specific integer clock” where all third-frequency phase biases are integrated individually with satellite clocks to enable an efficient frequency-wise combination. The resultant combined product will ensure all-frequency PPP ambiguity resolution over any frequency choices and observable combinations. Our combination test based on the GPS/Galileo satellite products from four IGS-ACs in 2020 showed that the mean phase clock/bias consistencies among ACs for all third-frequency signals (i.e., GPS L5, Galileo E6 and E5b) were as high as 10 ps, and the ambiguity fixing rates were all around 95%. Both quantities reached the same levels as those for the baseline frequencies (i.e., GPS L1/L2 and Galileo E1/E5a). The combined products outperformed AC-specific products since outlier contributions were excluded in the combination. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Time transfer technology using PPP relies onhigh-precision clockproducts of GPS satellites. When the observation we use is different that of the clock products, a SCB will be incorporated into the calculation of clock.For analyze the effect of SCB, we first derive the principles of correcting SCB. Thenthe effect of SCB on GPS PPP time transfer under three different conditionsis analyzed. The results indicate that the SCB can significantly improve the frequency stability, precision and PPP time transfer convergence speed.The precision of time transfer is improved by approximately 7% and the 5000s-200000s frequency stabilityis improved significantly, up to 20%. [ABSTRACT FROM AUTHOR]

This study proposes a model using 5G time-of-arrival data to assist global navigation satellite system precise point positioning ambiguity resolution. Specifically, the model addresses the problem of PPP requiring a long convergence time in partially satellite-occluded GNSS environments, such as urban canyons. First, we apply the ionosphere-free PPP model to estimate uncalibrated phase delays. Next, we combine real 5G data with GNSS data to determine whether introducing 5G observations will decrease the convergence time of the PPP solution. Experimental results reveal that the 5G-assisted PPP model can effectively improve the convergence efficiency of the float solution, lower the fixed time, and achieve greater positional reliability. Notably, the combination of GPS, BDS, and 5G with a sampling interval of 1 s obtains a fixed solution in an average of 1.12 min. Moreover, 5G-assisted GNSS positioning effectively compensates for partial satellite occlusion, optimizes the PDOP value, and speeds up ambiguity fixing. The introduction of three and more 5G base stations helps to obtain fixed solutions within 9 min when it is difficult to obtain fixed solutions relying only on GNSS. Our findings have important implications for improving the widespread applicability and effectiveness of satellite-based navigation systems in light of increasing urbanization and the rise of signal-occluding environments. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP), coupled with the ambiguity resolution (AR) method, has demonstrated substantial potential in fields like agricultural navigation and airborne mapping. However, there remains a notable deficiency in the comprehensive comparative evaluation of its performance when using rapid and real-time satellite products, especially for mass low-cost receivers. Stations equipped with geodetic and low-cost receivers are analyzed in kinematic and static mode. In the kinematic mode, the GPS+Galileo-combined PPP, employing ambiguity fixing with "WHU" rapid products, achieves the highest positioning accuracy of 0.9 cm, 0.9 cm, and 2.6 cm in the North, East, and Up components, respectively. Real-time PPP using "CNT" products attains accuracies of 2.1 cm, 2.7 cm, and 4.8 cm for these components, utilizing GPS ambiguity-fixed PPP. BDS positioning accuracy is inferior to standalone GPS, but improves when the number of visible BDS satellites exceeds 10. Convergence time analysis shows that approximately 38.2 min are required for single GPS or BDS PPP using the "WHU" products and geodetic receivers, which can be reduced to 18.5 min for dual-system combinations and further to 14.8 min for triple-system combinations. The time can be further reduced by ambiguity fixing. In the static mode, multi-GNSS combination does not significantly impact convergence times, which are more influenced by the precision of the products used. Real-time products require approximately 22 min to achieve horizontal accuracy below 0.1 m, while rapid products reach this accuracy within 10 min. For PPP using low-cost GNSS receivers, more than two hours are necessary to achieve an accuracy better than 0.1 m for kinematic PPP, which is considerably longer than the convergence time observed at MGEX stations. However, the accuracy achieved after convergence, as well as the performance of static PPP, is comparable to that of MGEX stations. [ABSTRACT FROM AUTHOR]

Ionospheric irregularities remain as a challenging concern among space scientists and engineers as it can pose severe threats to satellite-based services by introducing amplitude and phase scintillations in the transionospheric radio signals. The scintillations may cause degradation of the positioning, navigation, and timing (PNT) services or even complete system failure under extreme conditions. The present work focuses on understanding the ionospheric irregularities during the space weather event on May 12, 2021, witnessing the first strong geomagnetic storm in the 25th solar cycle. This particular event commenced around 13.00 UT, apparently altering the regular development of equatorial plasma bubbles around the local post-sunset terminator. We selected three global positioning system (GPS) stations, one at the near-magnetic equator (CUSV) and two at far low-latitude locations with a longitudinal separation (THKK and HWKS) over the Southeast Asian longitudes to investigate the characteristics of ionospheric plasma irregularities on the storm day. The results showed that the amplitude of ROTI was highest at the low-latitude CUSV, followed by the THKK and HKWS stations. The increased ROTI at CUSV is due to its latitudinal location close to the geomagnetic equator in the equatorial ionization anomaly (EIA) region which often witnesses more fluctuations than the inter-mediate latitudes. The strong TEC fluctuation occurrences were comparatively minimal at HWKS station on the storm day (May 12, 2021), whereas both intermediate and relatively higher TEC fluctuation occurrences were found at THKK and CUSV stations, respectively. Moreover, the occurrence rate of moderate irregularities was the highest at CUSV, followed by THKK and HKWS, while that of weak irregularities was maximum at HKWS, followed by THKK and CUSV. This happens because the systematic longitudinal time delay observed at the onset of ionospheric scintillations corresponds to the rise of PBs velocity at the magnetic equator that strongly depended upon the F-region dynamo electric fields in the east–west direction. Furthermore, the three-dimensional (3-D) positioning errors were estimated at a 30-sec interval to understand the impact of storm-induced irregularity on the positioning solution. An excellent agreement is realized between the ROTI pattern and positioning errors at all stations, irrespective of latitudinal extent from the magnetic equator. In order to model the amplitude of the scintillation index against the SNR measurements, the linear, quadratic, and cubic regression curve fittings are utilized that indicate the cubic polynomial manifesting the best fitted SNR measurements with the weak as well as moderate scintillation index. The continuous wavelet transformation (CWT) method was implemented to mitigate the ionospheric scintillation effects on positioning accuracy. The CWT estimation reveals the hidden information in positioning error due to the scintillation index, which makes it easy to understand the ionospheric scintillation effects on positioning. The attempt in this work is aligned with the efforts towards reliable PNT operations over equatorial and low latitudes. [ABSTRACT FROM AUTHOR]