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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]

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]

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]

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]

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.

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 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]

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]

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]

To analyze the performance of Global Positioning System (GPS) Precise Point Positioning (PPP) Ambiguity Resolution (AR) under various ionospheric scintillation environments, we selected GPS data of ionospheric scintillation monitoring receivers (ISMR) and geodetic receivers from high-latitude and low-latitude regions during 2021–2023. We conducted GPS Kinematic PPP using Canadian Spatial Reference System (CSRS) PPP and used the maximum and average values of σ φ and S 4 as indicators to characterize the intensity of phase scintillation and amplitude scintillation for ISMRs, while the maximum and average values of Rate of Total Electron Content Index (ROTI) to characterize the intensity of ionospheric scintillation for geodetic receivers. We also used ambiguity resolved percentage (ARP) and the 3-Dimensional Root Mean Square (3D RMS) of positioning errors as performance metrics for PPP-AR and PPP. As the maximum and average values of ionospheric scintillation indices increase, the PPP-ARP for high-latitude ISMRs decreases to 90.0 %, and the 3D RMS can reach 0.204 m. During ionospheric quiet conditions, positioning accuracy of GPS PPP can reach the cm-mm level. As the geomagnetic latitude decreases, the scintillation effects on PPP-AR and PPP become more pronounced for high-latitude ISMRs. Compared with high-latitudes, ISMRs located at low-latitudes are more severely affected by scintillation, with PPP-ARP at the station HNLW in China and the station UFBA in Brazil dropping to 80.0 % and 60.0 %, respectively. The 3D RMS can reach 0.288 m and 0.341 m. The results of geodetic receives are consistent with those of ISMRs, with 3D RMS of positioning errors up to 0.240 m and 0.256 m for CYNE and MAL2, respectively, while PPP-ARP drops to 60.4 % and 79.6 %. Additionally, we observed a strong positive correlation between ionospheric scintillation duration and the maximum values of σ φ , S 4 and ROTI. [ABSTRACT FROM AUTHOR]

This study aims to investigate the comparative performance of PPP technique in evaluating the precision of three distinct geoid models and to quantify the contribution of GLONASS constellation to GPS as well as the effect of observation length. We use recently and concurrently measured GNSS and levelling data crossing rough topography with steep geoid slope in Türkiye. The RMSE statistics about the mean of the geometric minus gravimetric geoid heights reveal that at least 4-hours of static data should be collected regardless of the constellation. We find out encouraging results with 8-hours of GPS + GLONASS solutions having RSME values of 3.0, 5.0 and 21.5 cm in validating national, globally combined and satellite-only geoid models, respectively. The multi-GNSS PPP processing with a relatively long observation period yields comparable results to relative positioning though the latter still performs slightly better. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) technology has emerged as a powerful tool for unraveling Earth's dynamic nature, offering continuous and precise monitoring of geodetic positions with global coverage. This study quantifies the noise magnitude and velocity uncertainty estimates using GNSS-derived coordinate time series data from 31 IGS global stations. It assessed the relationship between the noise level and the uncertainties related to the derived velocities and systematically evaluated the influence of different coordinate solution time spans, satellite orbit/clock products, and GNSS constellation on the noise level and velocity uncertainties. The result gives insights into GNSS velocity estimation, noise characteristics, and the influence of ambiguity resolution. The results suggested that resolving ambiguities and using specific GNSS constellation satellite orbits and clocks solutions enhances the precision of velocity estimates and reduces noise magnitude. The noise levels are observed to be consistently above --0.7 in 5-year solution sets and below --0.8 in 8-year solution sets. There is an average of 30 and 42% reduction in velocity uncertainties due to 3 year increment in solution span using JPL and ESA orbits, respectively. GPS-only solution set appeared to be favorable for high-precision GNSS-based geodynamic applications with increased favourability when the ambiguities are resolved. The identified noise model, GGM+WN, demonstrated the most appropriate noise model in most cases which is not out of place to have been used in quantifying the noise magnitude and velocity uncertainties in this study. [ABSTRACT FROM AUTHOR]

Approaching the peak year of the 25th solar activity cycle, the frequency of strong geomagnetic storms is gradually increasing, which seriously affects the navigation and positioning performance of GNSS. Based on the globally distributed GNSS station data and FORMOSAT-7/COSMIC-2 occultation data, this paper explores for the first time the effects of the G4-class geomagnetic storm that occurred on 23–24 April 2023 on the global ionosphere, especially the ionospheric equatorial anomalies and F-layer perturbations. It reveals the precise point positioning (PPP) accuracy degradation during a geomagnetic storm. The results show that the ionospheric rate of total electron content index (ROTI) and near high latitude GNSS phase scintillations index have varying levels of perturbation during geomagnetic storms, with the maximum ROTI and phase scintillations index exceeding 0.5 TECU/min and 0.8, respectively. The equatorial ionization anomaly (EIA) shows an enhanced state (positive ionospheric storms) during geomagnetic storms, and the cause of this phenomenon is most likely the equatorward neutral wind. The variation of the S4 index of the FORMOSAT-7/COSMIC-2 satellite reveals the uplift of the F-layer during geomagnetic storms. During geomagnetic storms, the PPP accuracy degrades most seriously at high latitudes, the maximum MAE exceeds 2.3 m, and the RMS in the three-dimensional (3D) direction exceeds 2.0 m. These investigations can provide case support for space weather and GNSS studies of the impact of geomagnetic storms during peak solar activity years. [ABSTRACT FROM AUTHOR]

The aim of the new generation of Global Geodetic Observing System is a millimeter-level accuracy in positioning, with a crucial role to be played by Global Navigation Satellites Systems (GNSS) in the Precise Point Positioning (PPP) mode. This is of course because GNSS constellations and receivers provide an efficient stand-alone technique with a homogeneous performance over large areas (positions, navigation and meteorology) when used in conjunction with the PPP mode, with also an ever-increasing data flow and different satellite line-of-sights. The requirement of accuracies reaching the millimeter or sub-millimeter implies a knowledge at this level of each line in the GNSS-PPP error budget, including, but not restricted to: clock biases, troposphere and ionosphere delays, multipath and ground deformations. In this review study, we consider this millimeter-/submillimeter level GNSS-PPP error budget, and possible mitigations and improvements in the frame of the existing global constellations: GPS, Galileo, GLONASS and BDS, in view of augmented constellations and/or Low Earth Orbit constellations, which will be available in the near future. We also pay a special attention to systematic biases that can/could exist between constellations. [ABSTRACT FROM AUTHOR]

The precise point positioning (PPP) technique generally takes tens of minutes to converge, severely limiting its use. This longer convergence time is mainly due to the slower variation of satellite geometry in space and the stronger correlation of unknown parameters to be estimated. Fortunately, the lower orbit altitude of Low Earth Orbit (LEO) satellites contributes to the fast variation of the satellites' spatial geometry. In addition, high-precision atmospheric delay information has become readily available, which can help decrease unknown parameters' correlation. This study proposes a double-augmentation PPP approach with accelerated convergence by tightly integrating the LEO/atmosphere-augmented information. The GNSS observations in both mid-latitude and low-latitude areas, and simulated LEO observations under a Walker/polar mixed constellation, are used to validate the double-augmentation PPP approach. Test results in both areas indicate that the double-augmentation PPP can converge within 0.8 min, improving the convergence time by over 73%, and over 83% compared to the LEO-only augmented PPP and atmosphere-only augmented PPP. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) is an important alternative to real-time kinematic (RTK) positioning for deformation monitoring. Global Navigation Satellite System (GNSS) multi-frequency and multi-system integration can benefit PPP dynamic deformation monitoring due to increased measurement redundancy and facilitated ambiguity resolution (AR). This study investigates the performance of GNSS multi-frequency uncombined (UC) PPP-AR with GPS triple-frequency, BDS-3 triple-frequency, and Galileo five-frequency signals for monitoring high-rate vibrations based on 20-Hz observations from a shaking table. The GNSS multi-frequency UC fractional cycle bias (FCB) estimation method and PPP-AR method are developed. The results of vibration tests indicate that the displacement monitoring accuracy of GPS/BDS-3/Galileo multi-frequency PPP-AR solution is 5.3–8.4 mm. BDS-3 dual-frequency PPP-AR, BDS-3 triple-frequency PPP-AR, and GPS/BDS-3/Galileo multi-frequency PPP-AR solutions improve the accuracy by 8%, 17%, and 46% over the BDS-3 dual-frequency float solutions, respectively. GNSS multi-frequency UC PPP-AR can accurately identify the vibration frequency and amplitude, but the PPP-derived displacement is nosier than that of RTK. [ABSTRACT FROM AUTHOR]

The Real-Time Kinematic (RTK) positioning method of the Global Navigation Satellite System (GNSS) has been widely used for landslide monitoring. The stability of its reference station is crucial to obtain accurate and reliable monitoring results. Unstable reference stations due to the geological environment and human activities are difficult to detect and in practical applications often ignored. As a result, it affects the positioning solutions and subsequently the interpretation and detection of landslide motions, which must be addressed in GNSS landslide monitoring. To solve this problem, we propose using the Precise Point Positioning (PPP) technique to analyze the stability of the reference station by verifying its position. The deformations of the monitoring stations are then compensated. First, the reference station coordinates are obtained by the PPP technique and tectonic motion is considered in data processing. The change or breakout of the reference station position is then determined using a cumulative sum control chart method. Finally, each monitoring station's displacements are compensated according to the displacements of the reference station. According to the results of the Tengqing landslide experiment, the PPP technique can be used in GNSS landslide monitoring to analyze the stability of reference stations. With PPP, millimeter-level accuracy for the coordinates of reference stations is achieved. Compared to the traditional deformation series, the compensated displacement series more reliably reflects the landslide motions. This study will increase the reliability of monitoring results and contribute to implementing GNSS in monitoring landslides. [ABSTRACT FROM AUTHOR]

The antenna phase center correction is an important error source in GNSS precise positioning. The discussion on the difference of antenna phase center model based on different reference frames and its influence on post-static positioning position parameter estimation is helpful to obtain the consistent positioning results of the reference frame and improve the positioning reliability. Firstly, the difference of satellite/ground antenna phase center correction was analyzed under different reference frames, and then the IGS core station with uniform global distribution was selected; the estimated position difference caused by satellite/ground antenna phase center correction based on different reference frames was calculated and analyzed. The results show that the site difference caused by phase center correction under different reference frames is millimetre in plane direction and centimetre in elevation direction, and the average value of site difference is 7.1 mm; the influence of satellite antenna phase center correction on the estimated position of stations under different reference frames is greater than that of ground antenna phase center correction, the influence of the same type of antenna on different stations is basically the same. [ABSTRACT FROM AUTHOR]

Stochastic models play an important role in achieving high accuracy in positioning, the ideal estimator in the least-squares (LS) can be obtained only by using the suitable stochastic model. This study investigates the role of variance component estimation (VCE) in the LS method for Precise Point Positioning (PPP). This estimation is performed by considering the ionospheric-free (IF) functional model for code and the phase observation of Global Positioning System (GPS). The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes: a) antenna type, b) receiver type, c) the tropospheric effect, and d) the ionosphere effect. The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model. This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions. Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE. The position error difference for the east-west, north-south, and height components was 1.5 cm, 4 mm, and 1.8 cm, respectively. Therefore, weight estimation with LS-VCE can provide more appropriate results. Eventually, the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight. According to the results, the LS-VCE has a higher convergence rate than the nominal weight. The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11, 13, 12, and 9 min, respectively.

Precise Point Positioning (PPP) with Integer Ambiguity Resolution (IAR) is an effective way of improving the overall performance of the PPP technique both in terms of convergence time and accuracy. Even though PPP-IAR has seen a tremendous development in the last two decades, there is still room for improvement. Specifically, the search stage of candidate carrier phase ambiguities is characterized as an NP-hard problem that requires a long processing time, leading to limitation in the reliability of the identified optimal solution. A field that would have an impact on the search process of carrier phase ambiguities, and is addressed conceptually in this paper, is Artificial Intelligence (AI). [ABSTRACT FROM AUTHOR]

The Galileo High-Accuracy Service (HAS) is providing free Precise Point Positioning (PPP) corrections for Galileo and GPS satellites through the E6b signal and the internet. Currently, HAS should provide a horizontal and vertical 95% accuracy below 20 centimetres and 40 centimetres, respectively. To assess the accuracy of the current HAS corrections, software has been developed to receive, decode and use HAS corrections. HAS corrections were acquired in the Munich area (Germany) during two sessions in November 2022 and April 2023. The decoder was validated by comparing recorded corrections to data from the Galileo High Accuracy Reference Algorithm and User Terminal (HAUT). Then, the availability and quality of HAS corrections were analysed. The use of orbit and clock corrections significantly improves the broadcast product accuracy; for instance, the Galileo orbit RMS error decreases up to 43% and the GPS RMS up to 80%. The code bias accuracy is at sub-nanosecond level. Finally, to validate the use of HAS corrections, PPP positioning has been achieved. For the used station network, we reached a 95% horizontal and vertical accuracy of 19 cm and 34 cm, respectively, for the kinematic and bi-constellation positioning matching with targeted HAS performances. [ABSTRACT FROM AUTHOR]

The Galileo High-Accuracy Service (HAS) was declared operational (initial service) in January 2023 after an intense testing phase aimed at assessing its service performance through the transmission of live HAS corrections. The HAS performance at high latitudes is evaluated by analyzing data collected at the Polish Polar Station located in Hornsund, in the Norwegian Svalbard archipelago. At such a location, the reception conditions can be affected by poor satellite geometries and ionospheric scintillation may degrade the signal quality. In this respect, data affected by scintillation events were identified and used for the performance analysis. The assessment is carried out by comparing the HAS corrections with the International GNSS Service (IGS) precise products. Moreover, the retrieved HAS corrections are used to assess the Precise Point Positioning (PPP) performance. [ABSTRACT FROM AUTHOR]

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time. [ABSTRACT FROM AUTHOR]

In this study, a precise single-receiver differential code bias (DCB) estimation method using the precise point positioning (PPP) model is presented. The first step is to extract the high-precision ionospheric observations, including DCBs, based on the PPP model. Then, the satellite DCBs are corrected using International GNSS Service (IGS) products. Lastly, the algorithm for the minimization of the standard deviation of vertical total electron content (VTECmstd) is employed to determine the value of receiver DCB. To check the method, GNSS data from more than 200 IGS stations around the globe on four days with various geomagnetic and solar activity circumstances are processed. The receiver DCBs are compared to those obtained using previous carried-to-code level (CCL) models. The experimental results show that, compared to the CCL model, the values of VTECmstd for most stations are significantly reduced, the mean number of stations with negative ionospheric measurements is reduced by 40% after correcting the receiver DCBs, and the mean error of estimated receiver DCBs is reduced by approximately 0.6 ns using the PPP model. These results suggest that this method can provide more high-precision receiver DCB estimation. [ABSTRACT FROM AUTHOR]

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future. [ABSTRACT FROM AUTHOR]

Differential Code Bias (DCB) is a crucially systematic error in satellite positioning and ionospheric modeling. This study aims to estimate the BeiDou-3 global navigation satellite system (BDS-3) satellite DCBs by using the single-frequency (SF) uncombined Precise Point Positioning (PPP) model. The experiment utilized BDS-3 B1 observations collected from 25 International GNSS Service (IGS) stations located at various latitudes during March 2023. The results reveal that the accuracy of estimating B1I-B3I DCBs derived from single receiver exhibits latitude dependence. Stations in low-latitude regions show considerable variability in the root mean square (RMS) of absolute offsets for satellite DCBs estimation, covering a wide range of values. In contrast, mid- to high-latitude stations demonstrate a more consistent pattern with relatively stable RMS values. Moreover, it has been observed that the stations situated in the Northern Hemisphere display a higher level of consistency in the RMS values when compared to those in the Southern Hemisphere. When incorporating estimates from all 25 stations, the RMS of the absolute offsets in satellite DCBs estimation consistently remained below 0.8 ns. Notably, after excluding 8 low-latitude stations and utilizing data from the remaining 17 stations, the RMS of absolute offsets in satellite DCBs estimation decreased to below 0.63 ns. These enhancements underscore the importance of incorporating a sufficient number of mid- and high-latitude stations to mitigate the effects of ionospheric variability when utilizing SF observations for satellite DCBs estimation. [ABSTRACT FROM AUTHOR]

The incorporation of multi-frequency signals into global navigation satellite systems (GNSS) has presented new possibilities for precise positioning and rapid ambiguity resolution. Inter-frequency clock bias (IFCB) pertains to the time-varying biases among distinct frequencies within carrier phase observations in GNSS signals. The appropriate handling of IFCB is critical in enhancing the accuracy and convergence time of precise point positioning (PPP) solutions. The focus of this study is on the proper modeling of phase IFCB in multi-GNSS multi-frequency PPP. In this paper, the optimal IFCB power spectral density value of 0.6 m/sqrt(s) is first determined. To obtain the optimal stochastic model for IFCB, a thorough comparison and analysis of the product correction and parameter estimation methods is conducted. Additionally, experiments are conducted on the effect of IFCB modeling on the performance of undifferenced and uncombined PPP using data from 130 multi-GNSS experiment stations across the globe over a period of one week in January 2022. The study reveals that the optimal power spectral density for IFCB is within [60, 0.006] m/sqrt(s), modeling IFCB as a random walk is feasible, and the PPP is comparable for the three IFCB processing schemes of product correction, random walk, and white noise. Meanwhile, it is not reasonable to treat IFCB as a random constant or neglect it in the multi-GNSS multi-frequency PPP. In the absence of product correction or for users who require immediate and continuous positioning solutions, modeling IFCBs as random walks can lead to more reliable positioning results and improved convergence performance. [ABSTRACT FROM AUTHOR]

Low Earth orbit (LEO) satellites have high signal strength and faster geometry changes over short periods, offering unique advantages in navigation augmentation. Integrating LEO satellites into the navigation system can help augment the performance of the global satellite navigation system and break the dilemma of the existing navigation system with limited services in challenging environments. Constellation design is the key before establishing a complete LEO navigation augmentation platform. Therefore, in this study, two LEO navigation augmentation constellations, Polar/Walker (S1) and Walker/Walker (S2) with different inclinations, are designed and optimized using the non-dominated sorting genetic algorithm III (NSGA-III). The global average geometric dilution of precision (GDOP) of BDS-3 is reduced from 1.56 to 0.92 and 0.95, and the average visible satellite number is improved from 11.74 to 27.83 and 25.72 with the navigation augmentation of the optimized constellations. To further validate the navigation augmentation effect of two LEO constellations on BDS-3 precision point positioning (PPP), nine stations at different latitudes were selected for LEO augmented BDS-3 PPP simulation experiments. The results show that after adding S1 and S2 constellations to BDS-3, respectively, the convergence times of the nine stations are reduced by 35.5%∼96.5% and 43.7%∼96.2%, and the positioning accuracy is improved by 5.7%∼71.9% and 24.2%∼69.5%, respectively. Overall, each S1 and S2 constellations can significantly improve the global service performance and PPP performance of BDS-3. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

For many years, the navigation team at the French Space Agency (CNES) has been developing its Precise Point Positioning project. The goal was initially to promote a technique called undifferenced ambiguity resolution. One of the main characteristics of this technique is the capability for a user receiver to perform centimeter-level accuracy in real time. To do so, a demonstrator has been built. Its architecture is composed of three main elements: a correction processing software called the server part, a means to transmit the corrections using standardized messages, and a user software capable of handling the corrections to compute an accurate positioning at the user level. In this paper, we present the recent advances in the CNES precise point positioning demonstrator. They are composed of some evolution of the network of stations and server software, the implementation of the new state space representation standard, a new method for instantaneous ambiguity resolution using uncombined four-frequency signals, its implementation in real-time at the server and the user level, and the use of high-rate Doppler measurements to improve the accuracy of the solution in harsh urban environments. On top of that, the computation of high-accuracy post-processed phase biases with the majority of current GNSS signals supported, compatible with the uncombined method and a new online positioning service to demonstrate the capacity of the user software, is demonstrated. [ABSTRACT FROM AUTHOR]

Real-time GNSS PPP is commonly used for high-precision positioning, but its utility is constrained by factors that necessitate extended convergence periods for a dependable accuracy. Multipath, as an unmodeled error, significantly curtails PPP performance in time-constrained scenarios. Approximately 31 consecutive days of multi-GNSS data from the satellite positioning service of the German national survey (SAPOS) network were collected to evaluate the effectiveness of multipath correction for real-time PPP ambiguity resolution (AR). Using principal component analysis (PCA) to extract the common-mode error (CME) from observation residuals prior to multipath modeling, a multipath hemispherical map (MHM) and sidereal filtering (SF) approach were employed to alleviate the effects of multipath and assess the efficacy of multipath correction in real-time PPP-AR. The average RMS reductions of the carrier-phase and pseudorange residual of multi-GNSS were 25.5% and 20.1% with MHM 0.5 , while being 24.4% and 18.3% using SF. With MHM 0.5 correction, the TTFF reductions were approximately 7.0%, 17.7%, 37.5%, and 23.7% for G/GE/GC/GEC kinematic PPP-AR, respectively; and the convergence times for G/GE/GC PPP-AR were reduced to 18.2, 11.7, and 8.6 min, while GEC achieved an average convergence time of 7.1 min; a remarkable improvement compared to the multipath-uncorrected result (18 min). Moreover, 80% of the stations achieved convergence within 10 min, while 40% achieved convergence within 5 min. The kinematic positioning accuracy for the GEC solution improved from 0.97, 0.88, and 2.07 cm, to 0.94, 0.70, and 1.72 cm. In the static results, the TTFF shortened by 30.1%, 19.1%, and 20.1% for G/GE/GC, and the GEC decreased from 10.5 to 9.7 min; the average convergence time for G/GE/GC shortened to 13.0, 10.0, and 11.3 min, and for GEC shortened from 12.5 to 8.3 min. For the GPS-only solution, 78.3% of stations achieved convergence within 15 min. Similarly, for the GE scheme, the convergence time was primarily concentrated within 10 min, and for GC and GEC, with the application of enhanced multipath error correction, some of the stations even achieved convergence of PPP-AR within 5 min. The static positioning accuracy for GEC PPP was 0.50, 0.30, and 0.71 cm for the east, north, and up components. [ABSTRACT FROM AUTHOR]

This study presents the contribution of multi-GNSS (Global Navigation Satellite System) observations to the kinematic single-frequency precise point positioning (SF-PPP) technique and examines the effect of twenty-one different global ionosphere maps (GIMs), which are relied on 1/2 day predicted, broadcast, rapid, and final observations, provided to the GNSS-users by eight different Ionosphere Associate Analysis Centers (IAACs) on the SF-PPP technique. Two different experimental data were used in this contribution. First, thirty International GNSS Service (IGS) station observation data from the IGS network were evaluated, and then a kinematic vehicle experiment was performed. Both the contribution of multi-GNSS observations to the SF-PPP technique and the effect of GIMs on the SF-PPP were investigated employing these two experimental data. The outcomes clearly demonstrate that the quad combination improves the position accuracy of the SF-PPP technique in the horizontal component by an average of 39%, 24%, and 11%, respectively, compared to those obtained from single, dual, and triple constellations. Moreover, the results clearly indicate that the GIMs considerably shorten the convergence time of the SF-PPP technique, while among the GIMs, CARG, CASG, CODG, and IGSG provide more position accuracy improvements than others for horizontal and vertical components. Finally, the findings clearly show that the C1PG and C2PG, which are 1/2 day predicted GIMs, are quite promising, although the CKMG and GPSG products based on broadcast observations are not yet at the required accuracy. [ABSTRACT FROM AUTHOR]

Tropospheric delay (TD) parameter estimation is a critical issue underlying high-precision data processing for global navigation satellite systems (GNSSs). The most widely used TD parameter estimation methods are the random walk (RW) and piece-wise constant (PWC). The RW method can effectively track rapid variations of tropospheric delay, but it may introduce excessive noise. In contrast, the PWC method introduces less noise, but it is less adaptable to cases of large variations of tropospheric delay. To address the problem of how to choose the optimal TD parameter estimation method, this paper investigates the variation patterns of international GNSS service zenith tropospheric delay (IGS ZTD) products and proposes a combined strategy model for TD parameter estimation. Firstly, this paper avoids the day-boundary jumps problem of IGS ZTD products by grouping based on single-day data. Secondly, this paper introduces discrete point areas (DPAs) to measure the magnitude of the ZTD values and uses comprehensive indicators to reflect the variation of ZTD. Next, based on the Köppen-Geiger climate classification, this study selected five different climate classifications with a total of 20 IGS stations as experimental data. The data assessed span from day of year (DOY) 001 to DOY 365 in 2022. This paper then applied 26 different parameter estimation strategies for static precise point positioning (PPP) data processing, and the parameter estimation strategies that were used include the RW and PWC (with the piece-wise constant ranging from twenty minutes to five hundred minutes at twenty-minute intervals). Finally, ZTD and positioning results were obtained using various parameter estimation methods, and a combined strategy model was established. We selected five different climate classifications of IGS stations as validation data and designed three sets of comparative experiments: RW, PWC120, and the combined strategy model, to verify the effectiveness of the combined strategy model. The experimental results revealed that: RW and the combined strategy model have a comparable ZTD accuracy and both are superior to PWC120. The combined strategy model improves the positioning accuracy in the U direction compared to RW and PWC120. In arid (B) and polar (E) regions with a small variation of TD, the PWC120 strategy displayed a better positioning accuracy than the RW strategy; in equatorial (A) and warm-temperate (C) regions, where there are large variations of TD, the RW strategy exhibited a better positioning accuracy than the PWC120 strategy. The combined strategy model can flexibly select the optimal parameter estimation method according to the comprehensive indicator while ensuring ZTD estimation accuracy; it enhances positioning accuracy. [ABSTRACT FROM AUTHOR]

In addition to the legacy B1I and B3I signals, the BeiDou global navigation satellite system (Beidou-3) are capable of transmitting B1C/B2a/B2b/B2 several new navigation signals. The multi-frequency signals of Beidou-3 are expected to benefit precise point positioning with ambiguity resolution (PPP AR). Currently, most international GNSS service (IGS) analysis center adopt the Beidou-3 B1I/B3I ionosphere-free (IF) combination to estimate the satellite orbit and clock products, the Beidou-3 B1C/B2a/B2b/B2 phase biases should be aligned with satellite B1I/B3I clocks. Therefore, in this paper, the multi-frequency phase observable-specific phase biases (OSB) estimation method is developed for Beidou-3 system, which is compatible with satellite B1I/B3I legacy clock. Experimenting on the Beidou-3 multi-frequency observations over 30 days from the globally distributed stations, the characteristics of the estimated Beidou-3 multi-frequency phase OSB and the positioning performance of the IF kinematic PPP AR with different frequency combination are assessed. After the OSB are used in the raw observations, the results demonstrate that the wide-lane ambiguities residuals within ± 0.25 cycle are approximately 97%, 94%, 97% and 93% for Beidou-3 B1I/B3I, B1C/B2b, B1C/B3I and B1C/B2a combinations, respectively. When the OSB and satellite B1I/B3I legacy clock are used in different dual-frequency combination PPP AR tests, over 94% of the corresponding narrow-lane ambiguities are within ± 0.25 cycle. In addition, owing to the low noise of the B1C/B2a combination, the positioning performance of B1C/B2a PPP AR outperforms that of the other frequency combinations. More specifically, in case of B1I/B3I PPP AR, almost 22.7 min is required to successfully achieve 10 cm for east, north and up components, while only 18.8 min is needed for B1C/B2a PPP AR. The results show that such phase OSB, along with Beidou-3 satellite B1I/B3I legacy clock, can fully recover the PPP ambiguities based on all available frequency choices and observable combinations. [ABSTRACT FROM AUTHOR]

Objectives: In October 2019, the International GNSS Service(IGS) began the third data reprocessing campaign(repro3). To enable more robust ambiguity resolution(AR) in precise point positioning (PPP), one of IGS important tasks is to combine satellite clock and code/phase bias products. Methods: We elaborated the precise satellite clock product model, code/phase bias product model, as well as prior corrections and specific processes for the combination of global navigation satellite system(GNSS) satellite clock and code/phase bias products. What􀆳s more, entrusted by the IGS Analysis Center Coordinator, we combined the clock/bias products of repro3 from 2000 to 2020 successfully. Results: Through the statistics of the combination, it is concluded that the integrity rate of combined clock can reach more than 95% after stabilization, which is superior to most of the products of IGS Analysis Centers. The average root mean square error of GPS and Galileo satellite navigation system satellite clock reach 6.13 ps and 5.63 ps respectively, which prove that the correction models in the combination can significantly improve the consistency. The average weight of Graz University of Technology participating in the combination reaches 21.83%, which has better precision than that of other analysis centers. The weight of phase/integer clock is higher than that of legacy clock, with better stability and precision. Furthermore, 103 stations with uniform global distribution were selected for the static PPP-AR solution to validate the positioning precision of the combined products. The results showed that the average fixed rates of GPS wide and narrow-lane ambiguity based on combined products are 90.16% and 86.72% respectively, and those of Galileo are 97.11% and 93.77% respectively, which are about 1-5 percentage points higher than those based on Center for Orbit Determination in Europe (COD) repro3 products. The average positioning precision based on combined products in the east, north and high directions is 0.154, 0.178 and 0.542 centimeters respectively, which is 20% to 30% higher than COD. Conclusions: The multi-GNSS satellite clock and code/phase combination method can effectively solve the problems of the consistency among products of analysis centers,and enable more robust ambiguity resolution in PPP-AR. Moreover, the combined products have been officially downloaded (IGSMAIL-8248:https://cddis.nasa.gov/archive/gnss/products/repro3/). [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) in precision agriculture (PA) represent a cornerstone for field mapping, machinery guidance, and variable rate technology. However, recent improvements in GNSS components (GPS, GLONASS, Galileo, and BeiDou) and novel remote sensing and computer processing-based solutions in PA have not been comprehensively analyzed in scientific reviews. Therefore, this study aims to explore novelties in GNSS components with an interest in PA based on the analysis of scientific papers indexed in the Web of Science Core Collection (WoSCC). The novel solutions in PA using GNSS were determined and ranked based on the citation topic micro criteria in the WoSCC. The most represented citation topics micro based on remote sensing were "NDVI", "LiDAR", "Harvesting robot", and "Unmanned aerial vehicles" while the computer processing-based novelties included "Geostatistics", "Precise point positioning", "Simultaneous localization and mapping", "Internet of things", and "Deep learning". Precise point positioning, simultaneous localization and mapping, and geostatistics were the topics that most directly relied on GNSS in 93.6%, 60.0%, and 44.7% of the studies indexed in the WoSCC, respectively. Meanwhile, harvesting robot research has grown rapidly in the past few years and includes several state-of-the-art sensors, which can be expected to improve further in the near future. [ABSTRACT FROM AUTHOR]

The fast motion of low Earth orbit (LEO) satellites provides rapid geometric changes in a short time, which can accelerate the initialization of precise point positioning (PPP). The rapid convergence of ambiguity parameters is conducive to the rapid success of ambiguity fixing. This paper presents the performance of single- and four-system combined PPP Ambiguity Resolution (AR), enhanced with an ambiguity-float solution LEO. Two LEO constellations were designed: L was a typical polar orbit constellation, with a higher number of visible satellites at high latitudes than at low and middle latitudes; and M was designed to compensate for the lack of visible satellites at low and middle latitudes. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because the global navigation satellite systems (GNSSs) were fully operational, the GNSS data were real observation data from the MGEX stations. Based on the daily observation datasets collected at 258 stations in the global MGEX observation network over three days (from 1 January to 3 January 2022), in addition to the LEO simulation data, we evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP ambiguity resolution and compared it with LEO-enhanced PPP. The L+M mixed constellation was able to reduce the time to first fix (TTFF) of the four-system combined PPP-AR to 5 min, and four LEO satellites were sufficient to achieve this. L+M mixed constellation was able to reduce the convergence time of the four-system combined PPP to 2 min. Unlike PPP-AR, PPP required more LEO satellites for augmentation to saturate. [ABSTRACT FROM AUTHOR]

Regional navigation system Quasi-Zenith Satellite System (QZSS) play an important role in positioning, time and frequency transfer for the Asia-Pacific region under high cut-off angle. This paper combines QZSS and the major navigation systems for Precise Point Positioning (PPP) positioning and time–frequency transfer. The time–frequency transfer experimental results show that with the addition of QZSS, the clock difference accuracy and the frequency stability of the corresponding time link are significantly improved for the case of cut-off above 15°. The corresponding range is between 5% and 30% of accuracy, and between 1% and 90% of frequency stability. [ABSTRACT FROM AUTHOR]

Currently, the space segment of all the five satellite systems capable of providing precise time transfer services, namely BDS (including BDS-3 and BDS-2), GPS, GLONASS, Galileo, and Quasi-Zenith Satellite System (QZSS), has almost been fully deployed, which will definitely benefit the precise time transfer with satellite-based precise point positioning (PPP) technology. This study focuses on the latest performance of the BDS/GPS/GLONASS/Galileo/QZSS five-system combined PPP time transfer. The time transfer accuracy of the five-system integrated PPP was 0.061 ns, and the frequency stability was 1.24 × 10−13, 2.28 × 10−14, and 8.74 × 10−15 at an average time of 102, 103, and 104 s, respectively, which significantly outperforms the single-system cases. We also verified the outstanding time transfer performance of the five-system integrated PPP at locations with limited sky view. In addition, a method is proposed to mitigate the day-boundary jumps of inter-system bias (ISB) estimates by considering the difference in the satellite clock datums between two adjacent days. After applying a priori ISB constraints, the time transfer accuracy of the five-system integrated PPP can be improved by 37.9–51.6%, and the frequency stability can be improved by 14.8–21.6%, 5.3–7.6% and 20.0–29.6% at the three average times, respectively. [ABSTRACT FROM AUTHOR]

The service of the Global Satellite Navigation System (GNSS) satellite clock correction should be provided to achieve a high-precision user positioning. To explore new method for improving the real-time service capability of the Galileo satellite clock correction, its positioning performances of modeling and extrapolation with the polynomial and harmonics-based function are tested. The single point positioning result of the strategy, which employs the 1-h satellite clock correction series to fit the 4-h extrapolation coefficients of 1st order polynomial, is comparable to the current broadcast ephemeris of 10-min age. This shows that the age of the Galileo broadcast ephemeris can be extended. The precise point positioning (PPP) performances of the different extrapolation strategies are analyzed to establish an optimal Galileo real-time service (RTS) strategy, which supports a longer update interval of the transmitted coefficients. The PPP results show that the 6th order polynomial is suitable to establish the RTS of 1- and 2- min update intervals, while that of 2nd order polynomial has the best performance in 5- min interval RTS and the 1st order polynomial is the best one in the 10-min interval RTS. In these RTS strategies, the 1-h satellite clock correction series is optimal to fit the transmitted coefficients. [ABSTRACT FROM AUTHOR]

Multi Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) has become the mainstream of PPP technology. Due to the differences in the coordinates and time references of each GNSS, multi-GNSS PPP must include additional Inter-System Bias (ISB) parameters to ensure compatibility between different GNSSs. Therefore, research on the characteristics of ISB is also essential. To analyze the short- and long-term time characteristics of multi-GNSS ISBs, as well as their relationship with receiver type and receiver antenna type, the Undifferenced and Uncombined (UDUC) PPP model of Global Positioning System (GPS), BeiDou navigation satellite system (BDS), and Galileo satellite navigation system (Galileo) was rigorously derived, and the physical of ISBs was elaborated in depth. ISB parameters were estimated and analyzed using 31 days of data from the 31 Multi-GNSS Experimental stations (MGEX). The results indicate that: (1) the ISB value is dependent on the station receiver type, receiver antenna type, analysis center product utilized, and GNSS system. (2) The short-term time characteristics of ISB-COM, ISB-WUM, and ISB-GBM are similar for the same station but not for the long term. In addition, ISBs are more stable in the short term. (3) There is little correlation between the ISB time characteristics, the receiver type, and the receiver antenna type, and the day-boundary discontinuity(DBD) on the ISB can be ignored for the concussive days' process. [ABSTRACT FROM AUTHOR]

The Hunga Tonga Volcano eruption launched a myriad of atmospheric waves that have been observed to travel around the world several times. These waves generated traveling ionospheric disturbances (TIDs) in the ionosphere, which are known to adversely impact radio applications such as Global Navigation Satellite Systems (GNSS). One such GNSS application is Precise Point Positioning (PPP), which can achieve cm‐level accuracy using a single receiver, following a typical convergence time of 30 min to 1 hr. A network of ionosondes located throughout the Australian region were used in combination with GNSS receivers to explore the impacts of the Hunga Tonga Volcano eruption on the ionosphere and what subsequent impacts they had on PPP. It is shown that PPP accuracy was not significantly impacted by the arrival of the TIDs and Spread‐F, provided that PPP convergence had already been achieved. However, when the PPP algorithm was initiated from a cold start either shortly before or after the TID arrivals, the convergence times were significantly longer. GNSS stations in northeastern Australia experienced increases in convergence time of more than 5 hr. Further analysis reveals increased convergence times to be caused by a super equatorial plasma bubble (EPB), the largest observed over Australia to date. The EPB structure was found to be ∼42 TECU deep and ∼300 km across, traveling eastwards at 30 m/s. The Hunga Tonga Volcano eruption serves as an excellent example of how ionospheric variability can impact real‐world applications and the challenges associated with modeling the ionosphere to support GNSS. Plain Language Summary: Global Navigation Satellite System (GNSS) applications permeate modern society, with many industry sectors heavily relying on precision satellite positioning, navigation and timing. Precise Point Positioning (PPP) is an advanced positioning technique that can achieve cm‐level accuracy without the need for nearby reference stations. However, the time that it takes for the PPP solution to "converge" is typically in the range of 10s of mins to hours, limiting the widespread uptake of PPP. There are numerous previous reports of waves and disturbances in the ionosphere, which are known to adversely impact GNSS applications. In this study, the impact of the disturbances in the ionosphere caused by the 2022 Hunga Tonga‐Hunga Ha'pai Volcano eruption on PPP across the Australian region is investigated. It is found that convergence times increased by more than 5 hr across northern Australia due to small‐scale ionospheric turbulence. The source of the turbulence was also found in this analysis to be due to a "super Equatorial Plasma Bubble" (a localized region of depleted plasma) that persisted above northern Australia for several hours. This event serves as an excellent example of how ionospheric disturbances can impact relied upon GNSS applications. Key Points: Precise Point Positioning (PPP) convergence times across northern Australia were significantly impacted in the hours after the eruptionExtended periods of enhanced rate of TEC index were the cause of convergence time increasesA super equatorial plasma bubble, the largest observed over Australia, was responsible for PPP convergence time increases after the eruption [ABSTRACT FROM AUTHOR]

BeiDou Global Navigation Satellite System (BDS-3) broadcasts multifrequency signals that offer more choices of frequencies and more signal combinations for positioning. This paper analyzes the effect of timing group delay (TGD) and differential code bias (DCB) of BDS-3 on the corresponding triple-frequency positioning. The triple-frequency observation models of BDS-3 are summarized and the DCB correction models are derived for the four different frequency combinations of triple-frequency ionospheric-free (IF) combination (IF123), two dual-frequency IF combinations (IF1213) and triple-frequency uncombined (UC123) positioning modes. Standard point positioning (SPP) and precise point positioning (PPP) experiments were conducted using 30 days of observations from 25 multi-GNSS experiment (MGEX) stations. The results show that the TGD/DCB correction has a significant impact on the accuracy of SPP. The positioning accuracy using IF123 and IF1213 models improved by about 73~90% after TGD correction, in comparison to a 27~30% improvement achieved using the UC123 model. In addition, the correction effect of DCB is slightly better than TGD. The DCB correction significantly improves accuracy in the initial epoch of the PPP, which helps the convergence of the filtering and reduces the convergence time. The average convergence times of IF123, IF1213 and UC123 are 26.1, 26.9 and 38.3 min, respectively, which are reduced by 6.79, 2.54 and 8.59% with DCB correction. The pseudorange residuals are closer to zero-mean random noise after DCB correction. Furthermore, the DCB affects the evaluation of the inter-frequency bias (IFB), ionospheric delay and floating ambiguity parameters. However, the tropospheric delay is almost unaffected by DCB. [ABSTRACT FROM AUTHOR]