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This study addresses the frequent convergence issues of satellite clocks within regional network, with a particular focus on the multifrequency advantages using data from 25 uniformly distributed reference stations across China. Experimental results demonstrate that incorporating the third frequency significantly enhances the accuracy of BDS-3 clock solutions, reducing the root mean square (RMS) by 44.5%. Additionally, employing a 2-min smoothing interval, multifrequency inclusion increases the wide-lane (WL) fixing rate by 30.4% at low elevation angles, which in turn leads to a marked improvement in narrow-lane (NL) ambiguity resolution. By leveraging phase-wide-lane observations, the stable wide-lane phase bias enables the continuous generation of inter-frequency clock bias (IFCB), ensuring reliable cyclic sequence construction even when satellites exit the observed region. The effectiveness of regional observable specific bias (OSB) on ambiguity resolution at the user level is highlighted, and over 95% of GPS, BDS-3, and Galileo NL fractional biases below 0.15 cycles could be achieved. Furthermore, the single-epoch convergence rates of multi-constellation precise point positioning (PPP) reach horizontal 91.9% and vertical 84.5% for multifrequency, a substantial improvement over the dual-frequency, which does not exceed 25%. [ABSTRACT FROM AUTHOR]

The least squares method is still commonly employed in traditional global navigation satellite system (GNSS) velocity estimation, but this method is easily biased by outliers from various sources. Random sample consensus (RANSAC) and solution separation (SS) algorithms have been employed in the domain of GNSS velocity estimation to identify and eliminate faults in the GNSS propagation process, yielding favorable outcomes. However, these algorithms are generally applied in single-epoch velocity estimation applications and use a single threshold for inspection and elimination, lacking adaptability to the observation environment. Therefore, a residual-based multithreshold constraint algorithm (RMCA) is proposed to improve the iterative results and obtain a time series solution of the GNSS velocity model. In the RMCA, the importance of residuals in the least squares approach is considered, and errors are directly expressed. Second, rather than employing a predetermined single threshold for exclusion, flexible threshold regulation is applied across various levels. Finally, the RMCA leverages the historically optimized velocity to establish sensible constraints on the current velocity estimation. Moreover, a mutual detection mechanism between GNSS velocity models is established. An experimental analysis of two groups of urban vehicles reveals that the velocity results obtained via the RMCA are more robust than those obtained via the traditional least squares algorithm and the SS scheme and are more continuous than those obtained via RANSAC. The RMCA is evidently well designed and efficient, demonstrating significant application value. [ABSTRACT FROM AUTHOR]

Multipath is a source of error that limits the Global Navigation Satellite System (GNSS) positioning precision in short baselines. The tightly combined model between systems increases the number of observations and enhances the strength of the mathematical model owing to the continuous improvement in GNSS. Multipath mitigation of the multi-GNSS tightly combined model can improve the positioning precision in complex environments. Interoperability of the multipath hemispherical map (MHM) models of different systems can enhance the performance of the MHM model due to the small multipath differences in single overlapping frequencies. The adoption of advanced sidereal filtering (ASF) to model the multipath for each satellite brings computational challenges owing to the characteristics of the multi-constellation heterogeneity of different systems; the balance efficiency and precision become the key issues affecting the performance of the MHM model owing to the sparse characteristics of the satellite distribution. Therefore, we propose a modified MHM method to mitigate the multipath for single-frequency multi-GNSS tightly combined positioning. The method divides the hemispherical map into 36 × 9 grids at 10° × 10° resolution and then searches with the elevation angle and azimuth angle as independent variables to obtain the multipath value of the nearest point. We used the k-d tree to improve the search efficiency without affecting precision. Experiments show that the proposed method improves the mean precision over ASF by 10.20%, 10.77%, and 9.29% for GPS, BDS, and Galileo satellite single-difference residuals, respectively. The precision improvements of the modified MHM in the E, N, and U directions were 32.82%, 40.65%, and 31.97%, respectively. The modified MHM exhibits greater performance and behaves more consistently. [ABSTRACT FROM AUTHOR]

Multipath effects can significantly reduce the accuracy of GNSS precise positioning. Traditional methods, such as sidereal filtering and grid-based approaches, attempt to model and mitigate these errors by leveraging the spatial autocorrelation of multipath based on residuals. However, these methods can only approximately handle spatial autocorrelation data, limiting their effectiveness. This study investigates the spatial cross-correlation of residuals between various GNSS frequency bands, analyzes their covariance function parameters, and evaluates the impact of constellation shifts on long-term multipath mitigation. Based on this, a simplified autocorrelation-based approach utilizing unified covariance parameters for multipath mitigation is proposed, with its efficacy assessed for both short- and long-term applications. The study demonstrates the correlation of multipath effects across various GPS and Galileo frequencies, including GPS L1/L2/L5 and Galileo E1/E5a/E5b/E5ab/E6, by analyzing correlation coefficients. A strong correlation (greater than 0.8) is observed between residuals of closely spaced frequencies, such as E5b and E5ab, despite their frequency differences. Additionally, the covariance parameters of the residuals are found to be consistent across all frequencies for a baseline, suggesting that unified parameters can be applied effectively for spatial autocorrelation-based multipath mitigation without sacrificing performance. The orbit shifts of certain GPS satellites, particularly G02, G20, and G21, result in significant changes in orbital parameters and satellite tracks, reducing the effectiveness of long-term multipath mitigation. However, the impact of GPS orbit shifts can be minimized through periodic model updates or by integrating GPS and Galileo modeling. In experiments, the LSC correction strategy based on a GPS/Galileo combination, utilizing unified parameters, outperforms the grid method based on the GPS/Galileo combination, improving the mean residual variance elimination rate by 11.3% for GPS L1 and 11.4% for Galileo E1. These improvements remain consistent, with rates of 11.3% and 15.7%, respectively, even on DOY 365, which is 327 days after the modeling data were collected. [ABSTRACT FROM AUTHOR]

Real-time time transfer is the basis for the time synchronization and establishment and maintenance of time scales. In this contribution, we present a regional multi-station real-time time transfer approach, in which observations from multi-global navigation satellite system (GNSS) received at regional multi-station are integrated to conduct an undifferenced network solution. Consequently, the simultaneous estimation of receiver clock offsets for multiple stations becomes possible, enabling the execution of real-time time transfer. One week of observation data from five multi-GNSS Experiment (MGEX) stations located in Europe are selected to generate four links (distances from 919.7 to 2153.4 km), and four schemes are designed, i.e., GPS-only, BDS-3-only, Galileo-only, and GPS/BDS-3/Galileo (GCE) solutions, respectively. Experiment results show that the mean number of observations, time dilution of precision (TDOP) values, and standard deviation (STD) of clock offset difference time series between the Center for Orbit Determination in Europe (CODE) and the estimated solutions for four time links are 90, 76, 72, 239 and 0.34, 0.38, 0.39, 0.21 and 0.039, 0.050, 0.043, 0.036 ns for GPS-only, BDS-3-only, Galileo-only, and GCE solutions, respectively. When the averaging time is shorter than 7680 s, the frequency stability of GCE solutions shows the best performance. The mean frequency stability of four time links at 7680 s is 6.59 × 10–15,7.25 × 10–15, 6.88 × 10–15 and 5.96 × 10–15 for GPS-only, BDS-3-only, Galileo-only, and GCE solutions, respectively. The GCE solution shows the best performance among the four schemes in terms of the number of observations, TDOP, STD, and frequency stability. The experiment results demonstrate that this approach is suitable for regional multi-station real-time time transfer. [ABSTRACT FROM AUTHOR]

Understanding ionospheric irregularities and their dynamics is crucial, with the rate of change of the total electron content index (ROTI) serving as a significant metric for this purpose. However, inconsistencies in ROTI magnitudes have been noted when sampled at one‐second interval across various Global Navigation Satellite System (GNSS) receivers. This study presents a detailed statistical analysis to investigate inconsistencies in ROTI using multi‐GNSS observations in conjunction with four distinct GNSS receiver types. Various factors affecting the ROTI inconsistencies among receivers were examined, including differences in sampling rates (1, 5, 15, and 30 s), and varying time window widths (1, 2, and 5 min). By examination of data obtained from GNSS receivers with zero or short baselines on a global scale, the analysis uncovered substantial variations in multi‐GNSS ROTI values across the four assessed receiver types. The main findings suggest that reducing the sampling rate reduces the inconsistencies in the magnitude of ROTI, particularly at lower sampling rates. This reduction can be attributed to the exclusion of high‐frequency components in the ROTI spectrum. Interestingly, the width of the time window is found to have minimal impact on the ROTI magnitude. The study also shows a direct correlation between a larger magnitude of ROTI and the increased noise in the signals tracked by receivers. These results emphasize the importance of considering sampling rates and GNSS receiver types when utilizing ROTI to investigate ionospheric irregularities. Plain Language Summary: Studying the changes in the ionosphere is important, and the rate of change of total electron content index (ROTI) is a key measure used for this purpose. ROTI is calculated using data from Global Navigation Satellite Systems (GNSS). However, variations in ROTI values were seen when measured at one‐second interval using different types of GNSS receivers. This study looked at these variations by analyzing ROTI data from multiple GNSS systems (BeiDou, GPS, GLONASS, and Galileo) and different types of GNSS receivers (Septentrio, Javad, Trimble, and Leica). Factors like sampling rates (1, 5, 15, and 30 s) and time window widths (1, 2, and 5 min) were considered during the analysis. The research found notable differences in multi‐GNSS ROTI values among the receiver types, with the Septentrio and Trimble receiver showing the most significant variations. Lowering the sampling rate led to fewer inconsistencies at slower rates, which is caused by a decrease in the multi‐GNSS ROTI values due to missing high‐frequency components. It was interesting to discover that the duration of the time window had little impact on ROTI values. These results stress the importance of paying attention to sampling rates and the type of GNSS receiver when using ROTI to study ionospheric irregularities. Key Points: Differences in multi‐GNSS ROTI values were observed across various receiver types at zero/short‐baseline stations globallyLowering the sampling rate decreased inconsistencies in the multi‐GNSS ROTI values among diverse receiversTime window width had a minimal impact on both the consistency and magnitude of multi‐GNSS ROTI values [ABSTRACT FROM AUTHOR]

Broadcast ephemeris plays an important role in positioning, navigation, and timing (PNT) services. With the rise of new constellations of Galileo and BDS3, satellite services are moving towards multi-GNSS fusion. Therefore, systematic evaluation of the multi-GNSS broadcast ephemeris and determination of the impact of ranging errors of different constellations in the multi-GNSS standard single point positioning (SPP) are necessary. In the contribution, the 120-day broadcast ephemeris from 1 January 2022 to 30 April 2022 and precise ephemeris provided by three analysis centers (German Research Center for Geosciences (GFZ), European Centre for Orbital Determination (CODE), and Wuhan University (WHU)) are used to analyze the orbits, clock offsets, and signal-in-space ranging error (SISRE) for GPS, GLONASS, Galileo, BDS2, BDS3, and QZSS (G, R, E, C2, C3, and J). The ephemeris analysis shows that the assessments using the precise ephemeris from the three analysis centers are consistent. The average daily SISREs for different constellations evaluated by GFZ products are 0.16 ± 0.07 m (E), 0.38 ± 0.19 m (J), 0.46 ± 0.19 m (C3), 0.50 ± 0.17 m (G), 1.30 ± 0.27 m (C2), and 2.40 ± 0.73 m (R), respectively. In addition, we propose a weight determination method using joint weighting of SISREs and satellite elevation angle (Ele + SIS) based on the analysis. One consecutive week of observations tracked by 23 permanent reference stations is selected, and a comparison experiment is conducted using the classical elevation angle weighting scheme (Ele) and the Ele + SIS scheme in dynamic SPP to verify the feasibility. Compared to the classic Ele scheme, the positioning accuracy of GREC2C3J combined SPP using the Ele + SIS scheme is improved by 34.2 % in the 3D direction, and the 95th percentile of the positioning errors is reduced by 31.5 %. The same dynamic SPP test using data after one year of modeling the Ele + SIS weighting scheme shows that the enhancement of the positioning accuracy of the Ele + SIS scheme decreases by only 3.7 %, which demonstrates that the Ele + SIS scheme can be used in real-time application. [ABSTRACT FROM AUTHOR]

In the paper, the differences between position components obtained using the precise point positioning (PPP) technique with individual and type mean PCC models were investigated. Daily GNSS observations from ten selected European Permanent Network (EPN) stations were used in the study. Eight different combinations of GPS, Galileo, BeiDou and GLONASS systems observations were proposed for analyses. The observation processing was done using the open-source software package GAMP. The results show that differences in the calibration models propagate to the position domain. Position offsets, resulting from the use of individual calibrations instead of the type mean, reach up to 10 mm in the vertical component while are generally keeping below 2 mm in the horizontal ones. The analysis also shows that adapting GPS PCCs to other GNSS (e.g. Galileo or BeiDou) signals does not significantly increase achieved position component differences. [ABSTRACT FROM AUTHOR]

This study investigates ionospheric anomalies associated with the Mw 7.1 Wushi earthquake that occurred in Xinjiang, China, on January 22, 2024. We analyze multi-GNSS data, including GPS and BeiDou (BDS), from the Crustal Movement Observation Network of China (CMONOC) to detect pre-seismic ionospheric anomalies and co-seismic ionospheric disturbances (CIDs). A 27-day sliding interquartile range method is applied to BDS geostationary satellite data to identify pre-seismic anomalies while minimizing the influence of solar and geomagnetic activity. The results show that BDS geostationary satellites significantly improve the spatiotemporal resolution of ionospheric monitoring, and M_GIM outperforms CODE-TEC in regions with sparse IGS stations. Pre-seismic anomalies are observed on January 14, 15, 16, and 18, with those southeast of the epicenter possibly caused by additional electric fields generated in the seismic preparation zone. CIDs are detected within 400 km of the epicenter using the Butterworth filtering technique, revealing a propagation speed of approximately 1 km/s, likely caused by acoustic-gravity waves generated by the earthquake. This study demonstrates the importance of multi-GNSS observations and high-resolution regional modeling for detecting and understanding seismo-ionospheric anomalies, providing insights into the earthquake preparation process and ionospheric disturbance propagation characteristics.

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]

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]

The satellite hardware differential code biases (SDCBs) are one of the important factors affecting the accuracy of GNSS-based ionospheric total electron content (TEC) estimation. The accuracy of SDCB estimates is directly influenced by the data processing methodology. To analyze the impact of various factors on multi-GNSS SDCB estimation, we conducted a comprehensive analysis of the number of contributed stations, the data sampling rate, the contributed satellite systems, and the cut-off elevation angle. Two sets of GNSS data obtained from the International GNSS Service (IGS) multi-GNSS experiment (MGEX) network, covering both high and low solar activities during the ascending phase of solar cycle 25, were processed to estimate multi-GNSS SDCBs. The results indicate that the number of contributed stations is the primary factor that influences multi-GNSS SDCB estimation. To achieve a balance between computational efficiency and accuracy, a data sampling rate of 540 s is recommended, which results in a multi-GNSS SDCB root-mean-square (RMS) error of less than 0.01 ns compared to a 60-second sampling rate. The stability of SDCBs is hardly affected by incorporating observations from multiple GNSS systems, and the differences of the standard deviations of SDCBs for quad-, triple- and dual-system solutions are below 0.002 ns. Additionally, the results indicate that the optimal cutoff elevation angle for multi-GNSS SDCB estimation is between 20° and 30°, which ensures the best stability in the estimated multi-GNSS SDCBs. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) data preprocessing is crucial for achieving high-precision navigation, positioning, and timing applications to convert the data format, edit the data content, and analyze the data quality. However, existing preprocessing tools are not yet user-friendly enough to handle multi-frequency and multi-system GNSS data due to extra costs, strong professionalism, and complex operations. In this paper, we present an open-source GNSS Data Preprocessing Software (GDPS) written by Python. It compiles and runs on both Windows and Linux operating systems, supports processing Receiver Independent Exchange Format (RINEX) 2.11 to 4.01 format data, and implements four functional modules: format translation, data editing, quality checking, and auxiliary tools. In addition, it also offers a user-friendly graphical user interface (GUI) that enables users to customize and select different processing setting parameters and then analyze the corresponding results through drawing tools. This paper takes the WUH2 station derived from the International GNSS Service (IGS) as an example to evaluate software performance. The results indicate that GDPS software can meet multi-frequency and multi-GNSS data preprocessing requirements and is expected to provide an open-source, convenient, and integrated GNSS data preprocessing solution for relevant researchers. [ABSTRACT FROM AUTHOR]

The national Beidou Navigation Satellite System (BDS) ground-based augmentation network (BGAN) of China is constructed with the existing GNSS observation resources of industrial sectors and local governments, based on the concept of joint building and sharing with sustainable development. This study provides a detailed introduction to the design, construction and operation of a meteorological application system based on BGAN, and validation of its water vapor products. BDS and GPS real-time observation of atmospheric water vapor is achieved nationwide in China and multi-GNSS applications. Through the application of multi-GNSS data and validation of the water vapor products from 2018 to 2020, the accuracy of precipitable water vapor (PWV) derived from BDS only is equivalent to that from GPS only. The root mean square error (RMSE) between them is about 2 mm with high correlation coefficient. Based on radiosonde data, the validation is conducted with the products of BDS-PWV, GPS-PWV, and Combined-PWV derived with multi-GNSS of BDS and GPS. The error characteristics of the three products show a consistent trend over the months. The bias is relatively small. The RMSE of the three products is in the range of 2.18–2.73 mm. The BDS-PWV has the largest RMSE, followed by GPS-PWV, and Combined-PWV has the smallest RMSE. [ABSTRACT FROM AUTHOR]

Abstract Integer Ambiguity Resolution (IAR) can significantly improve the accuracy of GNSS Precise Orbit Determination (POD). Traditionally, the IAR in POD is achieved at the Double Differenced (DD) level. In this contribution, we develop an Un-Differenced (UD) IAR method for Global Positioning System (GPS)+ BeiDou Navigation Satellite System (BDS) + Galileo navigation satellite system (Galileo)+ Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range. Based on this method, we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center (IAC) of the International GNSS Monitoring and Assessment System (iGMAS). One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products. Notably, the UD Ambiguity Resolution (AR) yields more resolved integer ambiguities than the traditional DD AR, scaling up to 9%, attributable to its avoidance of station baseline formation. Benefiting from the removal of ambiguity parameters, the computational efficiency of parameter estimation undergoes a substantial 70% improvement. Compared with the float solution, the orbit consistencies of UD AR solution achieve the accuracy of 1.9, 5.2, 2.8, 2.1, and 2.7 cm for GPS, BeiDou-2 Navigation Satellite System (BDS-2), BeiDou-3 Navigation Satellite System (BDS-3), Galileo, and GLONASS satellites respectively, reflecting enhancements of 40%, 24%, 54%, 34%, and 42%. Moreover, the standard deviations of Satellite Laser Ranging (SLR) residuals are spanning 2.5–3.5 cm, underscoring a comparable accuracy to the DD AR solution, with discrepancies below 5%. A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock (IRC), facilitating Precise Point Positioning (PPP) AR without requiring additional Uncalibrated Phase Delay (UPD) products. To assess the performance of quad-system kinematic PPP based on IRC, a network comprising 120 stations is utilized. In comparison to the float solution, the IRC-based PPP AR accelerates convergence time by 31% and enhance positioning accuracy in the east component by 54%.

Integer Ambiguity Resolution (IAR) can significantly improve the accuracy of GNSS Precise Orbit Determination (POD). Traditionally, the IAR in POD is achieved at the Double Differenced (DD) level. In this contribution, we develop an Un-Differenced (UD) IAR method for Global Positioning System (GPS)+ BeiDou Navigation Satellite System (BDS) + Galileo navigation satellite system (Galileo)+ Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range. Based on this method, we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center (IAC) of the International GNSS Monitoring and Assessment System (iGMAS). One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products. Notably, the UD Ambiguity Resolution (AR) yields more resolved integer ambiguities than the traditional DD AR, scaling up to 9%, attributable to its avoidance of station baseline formation. Benefiting from the removal of ambiguity parameters, the computational efficiency of parameter estimation undergoes a substantial 70% improvement. Compared with the float solution, the orbit consistencies of UD AR solution achieve the accuracy of 1.9, 5.2, 2.8, 2.1, and 2.7 cm for GPS, BeiDou-2 Navigation Satellite System (BDS-2), BeiDou-3 Navigation Satellite System (BDS-3), Galileo, and GLONASS satellites respectively, reflecting enhancements of 40%, 24%, 54%, 34%, and 42%. Moreover, the standard deviations of Satellite Laser Ranging (SLR) residuals are spanning 2.5–3.5 cm, underscoring a comparable accuracy to the DD AR solution, with discrepancies below 5%. A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock (IRC), facilitating Precise Point Positioning (PPP) AR without requiring additional Uncalibrated Phase Delay (UPD) products. To assess the performance of quad-system kinematic PPP based on IRC, a network comprising 120 stations is utilized. In comparison to the float solution, the IRC-based PPP AR accelerates convergence time by 31% and enhance positioning accuracy in the east component by 54%. [ABSTRACT FROM AUTHOR]

For real-time (RT) precise point positioning (PPP), the state space representation (SSR) information is often delayed due to possible communication delays and specific broadcast intervals. In this case, the positioning results will diverge and re-converge due to the increase of SSR products extrapolation errors. In addition, RT orbit and clock offset accuracy, as well as their extrapolation errors, will vary in different systems and satellites. We propose a PPP with ambiguity resolution (PPP-AR) method that combines a time-differenced carrier phase (TDCP) model, in which the characteristics of the orbit and clock are considered. Under normal communication, the PPP-AR solution is obtained by fixing satellites with small SSR product errors. When the communication is abnormal, the TDCP model is utilized to extrapolate user coordinates by considering different extrapolation error characteristics of satellites. The experimental results show that GPS and Galileo SSR products have better accuracy than BDS, with signal-in-space user ranger errors (SISREs) of 2.7, 2.2, and 8.6 cm, respectively. Optimizing the PPP stochastic model based on SISREs can effectively reduce the convergence time. Under 5 min SSR delay, SISREs caused by clock and orbit extrapolation for GPS/Galileo/BDS are 3.5, 1.4, and 2.6 cm, respectively. After optimizing the TDCP stochastic model based on extrapolation errors, the horizontal and vertical positioning accuracies can be maintained at 0.7 cm and 5.0 cm. For multi-GNSS, the combination of the TDCP and PPP-AR can overcome the influence of short delay. After optimizing the stochastic model, the GPS/Galileo/BDS positioning accuracy can be maintained at about 2.4 cm under 3 min delay, showing an accuracy improvement rate of 59.3% compared with the traditional method using only PPP. Additionally, the rapid PPP convergence results can be obtained by inheriting previous filter state information when the communication recovers normally. [ABSTRACT FROM AUTHOR]

PPP_Mansoura is a new software that can process multi-GNSS data work on MATLAB environment and linked with C# in the preprocessing stage. It gives highly accurate results and provides a results file for each epoch, and the users can choose the GNSS system they want to run with the primary systems (GPS or GLONASS) and all this with simple MATLAB Code. For testing the software, we processed the raw data (RINEX 3) from 17 MGEX stations for 24 h data during 1-week with a 30-s interval time and submitted it to the new software and PPPH software. The averaged positioning errors obtained from PPP_Mansoura and PPPH were 5.14 mm and 6.9 mm respectively, for the East direction, 11.6 mm and 14 mm for the North direction, and 14.56 mm and 20.4 mm respectively for the Up direction, the averaged convergence time obtained from PPP_Mansoura and PPPH were 35.3 min and 54.47 min, so the results show that PPP_Mansoura give results with high accuracy can be comparable with PPP standards results and PPP software results. [ABSTRACT FROM AUTHOR]

The International GNSS Service (IGS) provides combined satellite and station clock products, which are generated from the individual clock solutions produced by the analysis centers (ACs). Combinations for GPS and GLONASS are currently available, but there is still a lack of combined products for the new constellations such as Galileo, BeiDou, and QZSS. This study presents a combination framework based on least squares variance component estimation using the ACs' aligned clock solutions. We present the various alignments required to harmonize the solutions from the ACs, namely the radial correction derived from the differences of the associated orbits, the alignment of the AC clocks to compensate for different reference clocks within each AC solution, and the inter-system bias (ISB) alignment to correct for different AC ISB definitions when multiple constellations are used. The combination scheme is tested with IGS MGEX and repro3 products. The RMS computed between the combined product and the aligned ACs' solutions differ for each constellation, where the lowest values are obtained for Galileo and GPS with on average below 45 psec (13 mm) and reaching more than 150 psec (45 mm) for QZSS. The same behavior is repeated when the process is performed with the repro3 products. A clock and orbit combination validation is done using precise point positioning (PPP) that shows ionosphere-free phase residuals below 10 mm for all constellations, comparable with the AC solutions that are in the same level. [ABSTRACT FROM AUTHOR]

For GNSS Real-Time Kinematic (RTK), the reference Base receiver operating at a precise location together with the wirelessly connected Rover receiver(s) provide(s) high-quality real-time position solutions. This work shows the potential of compact, low-cost, single-frequency (CLS) GNSS modules as the RTK Rover up to large baseline distances. A combination of the uBLOX M8T CLS module and the Tallysman TW2710 patch antenna is used in single and hybrid GNSS combinations for short-to-long single-baseline lengths with the open-source RTKLib as the processing software. The results show that, for up to 288 km baseline distance, GPS, GLONASS and Galileo standalone operation provides below 1, 3 and 2 m precisions, respectively and sub-0.5 m precision is achieved for GPS+GLONASS+Galileo and GPS+Galileo+QZSS operations. The work shows the advantages of CLS modules as Rover those exploits the multi-constellation signal availability from India using open-source RTK processing software for reduction of the overall RTK infrastructure cost. [ABSTRACT FROM AUTHOR]

For high spatiotemporal resolution global navigation satellite system interferometric reflectometry (GNSS-IR) snow depth monitoring, addressing terrain effects and multi-GNSS data fusion together is essential due to their coupling. Analyzed multi-GNSS spatiotemporal availability to ensure coverage and revisit rate. Improved data usage and inversion accuracy through complete ensemble empirical mode decomposition. Corrected anisotropic terrain errors using digital elevation model to account for varied reflection footprints. A grid was established for data partitioning and fusion. Considering intersystem errors, the proposed signal peak ratio weighting (PRW) fusion of single-system inversions is based on signal quality. Then, by using inverse distance weighting, the multi-GNSS results were fused, achieving high-accuracy, hourly snow depth inversions with high spatial resolution. With terrain correction, the correlation coefficient (R) reached 0.984, root mean square error (RMSE) 0.136 m, and mean error (ME) –0.060 m, reduced by 9.05% and 24.84%. PRW further enhanced accuracy, increasing R to 0.985, reducing RMSE 14.6% to 0.128 m, improving ME 40.57% to –0.047 m. Grid fusion effectively integrated multi-GNSS data, showing daily R 0.865, RMSE 0.102 m, ME –0.050 m. Across season, R 0.984, RMSE 0.134 m, ME –0.065 m. Compared to equal weighting, R improved 4.72% and 3.05%, RMSE reduced 26.09% and 14.10%, ME decreased 28.57% and 16.44%. Hourly results achieved 94.44% coverage, averaging 5.19 usable tracks, demonstrating effectiveness. Overall, this article presents an end-to-end solution for high spatiotemporal resolution snow depth inversion using GNSS-IR, and the methodology can be extended to other geophysical parameter retrievals.

Precise Point Positioning (PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring. As atmospheric reanalysis data products' accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay (ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts (ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System (GNSS) PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service (IGS) stations for 2016–2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm, respectively. Further, GNSS observations for one week in each of the four seasons (spring: DOY 92–98; summer: DOY 199–205; autumn: DOY 275–281; and winter: DOY 22–28) from 34 multi-GNSS experiments (MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes (without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern (E) and Northern (N) directions, while the average convergence time over four weeks in the vertical (U) direction improved by 53.3% and 52.7%, respectively (in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively. Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

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]

• The contribution of the BDS-3 in multi-GNSS SF PPP is verified. • The contribution of BDGIM in SF PPP is investigated. • The performance of Klobuchar, CNES VTEC, GIM, BDIM in SF PPP is compared. • The performance of ionosphere-corrected, ionosphere-free and ionosphere-weighted model in SF PPP is compared. Due to the advantages of low-cost and high precision, single-frequency precise point positioning (SF-PPP) plays a vital role in the booming market of the SF global navigation satellite system (GNSS) receivers. With the full completion of the BeiDou global navigation satellite system (BDS-3), its contribution to single-GNSS SF-PPP is worthy of comprehensive exploration. In this study, three SF-PPP models including ionosphere-corrected (IC), ionosphere-free (IF), and ionosphere-weighted (IW) strategies are analyzed, and four ionospheric models including the GPS Klobuchar, BDGIM (BeiDou global ionospheric delay correction model), CNES real-time VTEC (vertical total electron content) and GIM (global ionospheric maps) are used for conducting SF-PPP. As to GPS/GLONASS/Galileo-only IC SF-PPP, its 3D positioning accuracy can be improved by 6.9–11.6 % with the adoption of BDS-3 observations. Similarly, for the IF SF-PPP solution, the corresponding positioning accuracy and convergence time can be improved by at least 17.3 and 38.3 %, respectively. In IW SF-PPP, the convergence performance of the CNES-VTEC-constrained SF-PPP is much better than that of both GPS Klobuchar- and BDGIM-constrained solutions. When using the BDGIM constraints, the horizontal/vertical convergence time of GPS/Galileo + BDS-3 solutions can be shortened by at least 16.5/27.9 % in comparison with GPS/Galileo-only solutions. While for GIM-constrained SF-PPP, the convergence improvement is only shown in the vertical component. In summary, the GIM-constrained SF-PPP with quad-system observations has the best performance, compared to IF solution, its convergence time can be shortened by 82.8 % to 5.5 min in horizontal and 29.7 % to 26.0 min in vertical when converging to 0.3 m. Note that the corresponding improvements in the BDGIM-constrained solution are relatively limited with only 5 %. At present, the quad-system IW SF-PPP has the ability to achieve cm-level fast positioning, with an RMS of 0.06 m in horizontal, showing promising applications in engineering and scientific fields. [ABSTRACT FROM AUTHOR]

Variometric approach (VA) technique has been introduced as an alternative to real-time kinematics and real-time precise point positioning techniques. As the ability of the variometric approach to detect short-term dynamic behaviors in real-time mode in applications such as Global Navigation Satellite Systems (GNSS)-seismology and structural health monitoring is demonstrated, the demand for open-source VA software is increasing. However, open-source software that is capable of VA processing in real-time mode based on single- and dual-frequency multi-GNSS observations is scarce. In view of this fact, we have developed an open-source VA processing software called PPPH-VA that can evaluate single- and dual-frequency multi-GNSS observations in real-time mode. PPPH-VA is developed in the MATLAB environment, and it can simultaneously process GPS, GLONASS, Galileo, BeiDou-2, and BeiDou-3 data with the VA technique in real-time mode, employing both single- and dual-frequency observations. We evaluated PPPH-VA using shake table experiments based on real data, and the results demonstrate that it provides high accuracy in terms of detection of dynamic displacements. Toolbox can successfully detect the dominant frequencies of short-term dynamic behaviors and is capable of determining the amplitude values corresponding to the peak frequency at the sub-mm level. Moreover, in the time domain, it can obtain dynamic behaviors with an accuracy of millimeters. [ABSTRACT FROM AUTHOR]

In Precise Point Positioning (PPP), the receiver clock parameter is typically estimated independently in each observation epoch, which increases the noise of the estimated station coordinates and troposphere parameters due to correlations. Applying stochastic modeling to the receiver clock parameter stabilizes PPP solutions and reduces clock noise for the time transfer. However, the receiver clock modeling is possible only for the GNSS receivers connected to the utmost stable atomic clocks. We propose receiver clock modeling that involves the Markov stochastic process in the form of a random walk. We test different levels of random walk constraints for GNSS stations equipped with different types of clocks for Galileo-only and multi-GNSS solutions in kinematic and static PPP. In multi-GNSS solutions, the common clock parameter is derived with inter-system biases (ISBs). This raises the question of the constraints that should be imposed on the common clock only or also on the ISBs. We found that similar results can be achieved by imposing constraints on the common clock parameter and estimating ISB as a constant parameter and when constraining the common clock parameter and ISBs with a ratio of 1:100. Other ratios of clock-to-ISB constraints, such as 1:1 and 1:10, give inferior results. In the kinematic PPP, stochastic clock modeling has a marginal impact on the North and East coordinate components, whereas the Up component is substantially improved for GNSS receivers equipped with hydrogen masers. In the static PPP, the clock modeling improves the time transfer, due to the reduced noise of the clocks. [ABSTRACT FROM AUTHOR]

Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution. [ABSTRACT FROM AUTHOR]

High-precision Global Navigation Satellite Systems (GNSS) orbits are critical for real-time clock estimation and precise positioning service; however, the prediction error grows gradually with the increasing prediction session. In this study, we present a new efficient precise orbit determination (POD) strategy referred to as the epoch-parallel processing to reduce the orbit update latency, in which a 24-h processing job is split into several sub-sessions that are processed in parallel and then stacked to solve and recover parameters subsequently. With a delicate handling of parameters crossing different sub-sessions, such as ambiguities, the method is rigorously equivalent to the one-session batch solution, but is much more efficient, halving the time-consuming roughly. Together with paralleling other procedures such as orbit integration and using open multi-processing (openMP), the multi-GNSS POD of 120 satellites using 90 stations can be fulfilled within 30 min. The lower update latency enables users to access orbits closer to the estimation part, that is, 30–60-min prediction with a 30-min update latency, which significantly improves the orbit quality. Compared to the hourly updated orbit, the averaged 1D RMS values of predicted orbit in terms of overlap for GPS, GLONASS, Galileo, and BDS MEO are improved by 39%, 35%, 41%, and 37%, respectively, and that of BDS GEO and IGSO satellites is improved by 47%. We also demonstrate that the boundary discontinuities of half-hourly orbit are within 2 cm for the GPS, GLONASS, and Galileo satellites, and for BDS the values are 2.6, 15.5, and 9.8 cm for MEO, GEO, and IGSO satellites, respectively. This method can also be implemented for any batch-based GNSS processing to improve the efficiency. [ABSTRACT FROM AUTHOR]

Inter-system bias (ISB) parameters are usually introduced in multi-GNSS processing. However, the differences in correlation processing within GNSS receivers can introduce signal distortion bias (SDB) into pseudorange observations. SDB differences of these satellites from the same constellation, similar to the GLONASS inter-frequency bias (IFB) related to individual frequencies, can cause intra-system biases. Based on multi-GNSS observations that consider intra-system bias, the relationship between intra-system and inter-system biases and their impacts on the multi-GNSS undifferenced (UD) model are analyzed in this article. Then, empirical calibration strategies are proposed. Ten receiver types from four manufacturers are selected to analyze the intra-system bias characteristics of code division multiple access (CDMA) and frequency division multiple access (FDMA), and the calibrations and improvements of the multi-GNSS solution are also analyzed. The results show that the intra-system biases of GPS and Galileo remain at the centimeter–decimeter level with 10-cm stability, while bias of BDS can reach several meters with worse stability. The intra-system biases of CDMA signals have stronger consistency among the same types of receivers than those of FDMA. One month of data verified the centimeter-level differences between ISB parameters that were independently estimated based on multi-GNSS precise products with unified datum and inter-constellation differences in intra-system biases. The pre-estimated intra-system bias can be used to calibrate pseudorange residuals and further promote the convergence speed of single or multi-GNSS precise point positioning (PPP), especially for BDS and GLONASS. Comparative experiments show that intra-system bias calibration can decrease the residual RMS of BDS by 22 cm on average and that of GLONASS by 41 cm, with 15% and 23% improvement rates, respectively. The convergence time of BDS PPP in the horizontal and vertical directions can be reduced by 10 min to half an hour with approximately 20–60% improvement rates. For GLONASS PPP, the convergence time can also be reduced by more than 40 min with a 50–90% improvement. [ABSTRACT FROM AUTHOR]

Recently, the factor graph-based global navigation satellite systems (GNSS) positioning methods have attracted much attention for more robust positioning performance in urban canyons compared with the traditional filter-based method. In the existing factor graph optimization (FGO)-based GNSS positioning methods, the pseudorange and Doppler measurements are mainly utilized to construct factors among consecutive GNSS epochs for outlier resisting and robust localization. However, the potential of high-precision positioning by using carrier phase observations is not fully explored. A factor graph optimization-based multi-GNSS real-time kinematic (FGO-RTK) framework is proposed to fill this gap, aiming to realize robust and precise positioning in urban canyons. In our method, a sliding window-based FGO estimator is designed, in which the continuously tracked double difference ambiguities are used to establish the ambiguity constraints of position states that have common-view satellites within the window. A marginalization-based carrier phase ambiguity propagation (AP) method is developed to fully use the information of carrier phase observations for achieving more reliable and continuous ambiguity resolution. Experiments in both medium urban and deep urban environments verified the effectiveness of the proposed method. Results show that FGO-RTK (with or without the AP) can achieve centimeter-level positioning accuracy in medium urban situations, showing comparable performance with the traditional extended Kalman filter (EKF)-based RTK. With the GNSS observation conditions deteriorating in deep urban environments, FGO-RTK without AP cannot outperform EKF-RTK. By contrast, the proposed FGO-RTK, considering the AP, achieves significant improvements in centimeter- to decimeter-level positioning availability, and the 3D positioning accuracy is improved by 69.6%, compared with the EKF-RTK. Furthermore, by analyzing the impact of the window size against the performance of FGO-RTK, we found that in comparison to the FGO-RTK only using the carrier phase observations inside a fixed-size window, the proposed AP method can significantly reduce the dependence on window size, and the optimal window size can be reduced from 10 to 4 epochs with more than 50% optimization time decreasing. [ABSTRACT FROM AUTHOR]

The quality control of multi-global navigation satellite system (multi-GNSS) real-time satellite clock estimation is time-consuming since mutual influence exists between multidimensional outliers, and the ambiguity calculation burden for multiple updates is heavy. Thus, we propose a computationally efficient prior quality control method for multi-GNSS real-time clock estimation that can delete outliers and adjust the weight of low-quality observations in advance. The weights of pseudorange and carrier phase observations are determined by robustly estimating the clock with only pseudoranges and the clock variation by time-differenced carrier phases, respectively. The calculation time of quality control can be significantly reduced owing to eliminating the ambiguity parameters. The multi-GNSS real-time satellite clock estimation shows that observation weight ratios were better in the updated weight model than in the original model. The prior quality control method significantly improved the clock standard deviation (STD) and the root-mean-square (RMS) accuracy. Especially for the GPS/BeiDou global satellite navigation system (BDS-3), the STD was improved by 14.8% and 36.8% in the proposed approach, respectively, and the RMS was improved by 24.2% and 67.8%, respectively. The calculation time of the updated weight model was only 0.3 s, accounting for 8.4% of the total time. Thus, the proposed quality control method can significantly improve the accuracy of clock estimation and complete the calculation in less time. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP) has proven to be a powerful GNSS positioning method used for various scientific and commercial applications nowadays. We present a flexible and user-friendly software package named raPPPid suitable for processing single to triple-frequency GNSS observations in various PPP approaches (e.g., ionospheric-free linear combination, uncombined model), available under https://github.com/TUW-VieVS/raPPPid. To tune the PPP procedure, the user can select from many satellite products, models, options, and parameters. This way, the software raPPPid can handle high-to-low quality observation data ranging from geodetic equipment to smartphones. Despite significant improvements, the convergence time of PPP is still a major topic in scientific research. raPPPid is specially designed to reduce the convergence period with diverse implemented approaches, such as PPP-AR or ionospheric pseudo-observations, and to offer the user multiple plots and statistics to analyze this critical period. Typically, raPPPid achieves coordinate convergence times of around 1 min or below with high-quality observations and ambiguity fixing. With smartphone data and a simplified PPP approach, a 2D position accuracy at the one-meter level or below is accomplished after two to three minutes. [ABSTRACT FROM AUTHOR]

BDSBAS refers to the DFMC protocol to broadcast long-term corrections and integrity messages in real-time to meet the high integrity requirements of civil aviation users. Based on the measured data of the BDSBAS monitoring station, the long-term corrections and integrity messages of BDS/GPS/GAL are calculated, and from the user's perspective verifies the service capability of the above information which mainly including positioning accuracy, pseudorange bias and Protection Level (PL). The test results show that the accuracy of multi-GNSS long-term corrections is better than 0.14 m; when the user uses the long-term corrections, the positioning accuracy can be improved by 27% in the horizontal direction and 31% in the vertical direction compared with the level of the single BDS. In addition, the results show that the BDSBAS DFMC service can satisfy the LPV-200 availability contour in Mainland China except western China and satisfy the Cat-I availability contour only in the central region of China depend on only BDS constellation. When all the messages of BDSBAS DFMC service based on BDS/GPS/GAL constellations are used, it can reach the availability of 100% which satisfy the LPV-200 index in China and surrounding areas, and the availability of 99.4% which satisfy the Cat-I index in Mainland China. Finally, the effect of pseudorange bias errors on positioning accuracy of different types of receivers are analyzed. Results show that pesudorange bias of BDS and GPS is about 0.2 m ∼ 0.3 m, and for Galileo is about 0.05 m. With multi-GNSS corrections and integrity information, the level of service availability and coverage for LPV-200 and CAT-I of BDSBAS DFMC service could be effectively improved. [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]

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]

Abstract Integrity monitoring for precise point positioning is critical for safety-related applications. With the increasing demands of high-accuracy autonomous navigation for unmanned ground and aerial vehicles, the integrity monitoring method of high-precision positioning has become an essential requirement. While high precision Global Navigation Satellite Systems (GNSS) positioning is widely used in such applications, there are still many difficulties in the integrity monitoring method for the multi-frequency multi-GNSS undifferenced and uncombined Precise Point Positioning (PPP). The main difficulties are caused by using the measurements of multiple epochs in PPP. Based on the baseline Multiple Hypothesis Solution Separation (MHSS) Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm, this paper discusses the feasibility of the pseudorange-based baseline ARAIM method on the single-epoch PPP based on Real-Time Kinematic (RTK) networks (PPP-RTK) framework to overcome these difficulties. In addition, a new scheme is proposed to transfer the conventional PPP process into the single-epoch PPP-RTK framework. The simulation results using the proposed model are analyzed in this study. The Protection Levels (PLs) estimated by PPP Wide-lane Ambiguity Resolution (PPP-WAR) model with regional corrections can reach the meter level and the PLs estimated by PPP Ambiguity Resolution (PPP-AR) and PPP-RTK models are usually the sub-meter level. Given a horizontal Alert Limit (AL) of 1.5 m, the global coverage of availability above 99.9% for PPP-WAR, PPP-AR, and PPP-RTK can reach 92.6%, 99.4%, and 99.7% respectively. The results using real kinematic data also show that tight PLs can be achieved when the observation conditions are good.

Abstract We have developed a new multi-GNSS data pre-processing software “RINGO” that provides various features including editing, quality checking, clock jump correction, higher order ionosphere correction, conversion of BINEX and RTCM files, and an interactive viewer for RINEX files. The recent increase in number of GNSS satellites has made GNSS data more complex; however, the software available to pre-process them is very limited. RINGO is a command line tool capable of handling multi-GNSS data, including GPS, QZSS, GLONASS, Galileo, and other systems in RINEX 2.xx, 3.0x, and 4.00 formats, which allows users to easily manage the multi-GNSS data observed at continuously operating reference stations. We present algorithms and applications for each RINGO feature. The results of the quality check feature were compared with results estimated by other existing software packages. Our results agreed well with those of the TEQC software. With RINGO, users can easily pre-process multi-GNSS data without combining multiple tools, and the software will contribute to the popularization of the latest RINEX format. Graphical Abstract

Abstract The PPP–RTK method, which combines the concepts of Precise of Point Positioning (PPP) and Real-Time Kinematic (RTK), is proposed to provide a centimeter-accuracy positioning service for an unlimited number of users. Recently, the PPP–RTK technique is becoming a promising tool for emerging applications such as autonomous vehicles and unmanned logistics as it has several advantages including high precision, full flexibility, and good privacy. This paper gives a detailed review of PPP–RTK focusing on its implementation methods, recent achievements as well as challenges and opportunities. Firstly, the fundamental approach to implement PPP–RTK is described and an overview of the research on key techniques, such as Uncalibrated Phase Delay (UPD) estimation, precise atmospheric correction retrieval and modeling, and fast PPP ambiguity resolution, is given. Then, the recent efforts and progress are addressed, such as improving the performance of PPP–RTK by combining multi-GNSS and multi-frequency observations, single-frequency PPP–RTK for low-cost devices, and PPP–RTK for vehicle navigation. Also, the system construction and applications based on the PPP–RTK method are summarized. Moreover, the main issues that impact PPP–RTK performance are highlighted, including signal occlusion in complex urban areas and atmosphere modeling in extreme weather events. The new opportunities brought by the rapid development of low-cost markets, multiple sensors, and new-generation Low Earth Orbit (LEO) navigation constellation are also discussed. Finally, the paper concludes with some comments and the prospects for future research.

Multi-GNSS PPP partial ambiguity resolution (PAR) can improve the fixing success rate and shorten the time to first fix (TTFF). Ambiguity subset selection based on the bootstrapping success rate sorting criterion (BSSC) is widely used in PPP PAR due to its ease of computation and comprehensive evaluation of the global quality of ambiguity solutions. However, due to the influence of unmodeled errors, such as atmospheric residuals and gross errors, ambiguity parameter estimation will inevitably introduce bias. For ambiguity parameters with bias, their variance will converge incorrectly and will not accurately reflect the estimation accuracy. As a result, the selected ambiguity subset based on the BSSC becomes inaccurate, affecting the fixing success rate and TTFF. Therefore, we proposed an improved multi-GNSS PPP PAR method based on a two-step sorting criterion (TSSC). This method aims to address the influence of inaccurate variance of ambiguity parameters, particularly those with low observation quality, on the ambiguity subset selection based on the BSSC. The ambiguity subset satisfying the preset success rate threshold is selected to reduce the influence of unconverged ambiguity on the TSSC. In the first step of the sorting process, the observations whose elevation angle is below 30° or whose posterior residual falls into the IGG3 model reduction domain are clustered together. The posterior observation weight criterion (POWC) instead of the BSSC is adopted to sort ambiguities to overcome the false convergence of variance of ambiguity parameters. In the second step of the sorting process, the remaining ambiguities with reasonable variances are sorted based on the BSSC. Finally, the bottom ambiguity is removed one by one from the ambiguity subset sorted based on the two-step sorting criterion (TSSC) until the requirements of the ratio test for LAMBDA are met. The static data from 10 MGEX stations over a period of 30 days, along with urban kinematic data, were collected to validate the proposed method. Compared with the PAR based on the BSSC, the static experiments demonstrated a reduction of 8.7% and 16.8% in the TTFF and convergence time, respectively. Additionally, the positioning accuracy in the east, north, and up directions was improved by 20.1%, 17.1%, and 4.67%, respectively. Furthermore, the kinematic experiment revealed that the TTFF and convergence time decreased from 1.65 min and 10.5 min to 1.3 min and 1.8 min, respectively, with higher positioning accuracy. [ABSTRACT FROM AUTHOR]

In this study, positioning quality is tested with the use of low-cost in-house developed receivers. The analyzes consider the practical use of low-cost devices in surveying works. In the network solution, the accuracy of the GNSS positioning based on low-cost receivers can be characterized by the repeatability of the baseline length of 1 and 6 mm in 24 h and 10 min observation sessions, respectively. The field experiment of 4 GNSS receivers and 3 GNSS low-cost receivers allowed for establishing a precise geodetic control network. The accuracy of the control point coordinates determined with low-cost GNSS receivers equals a maximum of 17 and 40 mm for the horizontal and height components, respectively. Therefore, low-cost GNSS receivers can provide positioning accuracy at the some centimeter level and can support land surveying and geodetic monitoring activities. [ABSTRACT FROM AUTHOR]

Estimating inter-system biases (ISBs) is important in multi-constellation Global Navigation Satellite System (GNSS) processing. The present study aims to evaluate and screen out an optimal estimation strategy of ISB for multi-GNSS kinematic precise point positioning (PPP). The candidate strategies considered for ISB estimation are white noise process (ISB-WN), random walk process (ISB-RW), constant (ISB-CT) and eliminated by between-satellite single-differenced observations (ISB-SD). We first present the mathematical model of ISB derived from the observation combination among different GNSSs, and we demonstrate the equivalence between ISB-WN and ISB-SD in the Kalman filter. In order to evaluate the performance of these four ISB solution strategies, we implement kinematic PPP with 1-month static data from 112 International GNSS service stations and two-hour dynamic vehicular data collected in an urban case. For comparison, precise orbit and clock products from the Center for Orbit Determination in Europe (CODE), GeoForschungsZentrum in Germany (GFZ) and Wuhan University (WHU) are employed in our experiments. The results of static tests show that the positioning accuracy is comparable among the four strategies, but ISB-CT performs slightly better in convergence time. In the kinematic test, there are more cycle slips than static test, and the ISB-CT improves the positioning accuracy by 15.7%, 38.9% and 63.2% in east, north and up components, and reduces the convergence time by 60.1% comparing with the other strategies. Moreover, both the static and kinematic tests prove the consistence among CODE, GFZ and WHU precise products and the equivalence between ISB-WN and ISB-SD strategies. Finally, more, i.e., the same amount of cycle slips as for the dynamic data, are artificially added to the static data to conduct the pseudo-kinematic test. The result shows that ISB-CT improves the positioning accuracy and convergence time by 19.2% and 24.4%, respectively. [ABSTRACT FROM AUTHOR]

In the classic Precise Point Positioning (PPP) approach, observations of Global Navigation Satellite Systems (GNSS) are processed at the network level to generate satellite clocks and positions. This information can be used to enable accurate point positioning for a single GNSS receiver. In the PPP Real-Time Kinematic (PPP-RTK) approach, satellite phase biases are considered as well, enabling ambiguity resolution at the network and user levels. In this research, 30 s multi-frequency raw GPS, Galileo, and BDS-2/3 observations are processed at the network and user levels in a sequential Kalman filter. PPP-RTK enabling products are generated for up to five frequencies, and ambiguity resolution is performed at the network and user levels using a flexible ambiguity reparameterization approach, comparable to wide- and narrow-laning, which has shown to yield a significantly improved single epoch coordinate solution when multi-frequency observations are available. Different assumptions regarding the time stability of receiver and satellite phase biases have been made and compared. The availability of a precise user coordinate solution when multi-frequency and dual-frequency observations are processed is assessed and compared. A precise ambiguity-fixed solution is available in three epochs or fewer in 77% of all cases with an average of 24 visible satellites for static and kinematic receivers when multi-frequency observations are processed. When only dual-frequency observations are considered, a fixed solution is available in seven epochs or fewer in 71% of all cases. The fastest fixed solution was found in two epochs with multi-frequency observations and in six epochs with dual-frequency observations. Estimating a reference phase clock did not lead to an improvement in the coordinate solution. The findings indicate that a fixed solution can potentially be found faster than often suggested, with potential for further improvement when more satellites or regional atmospheric corrections are considered. [ABSTRACT FROM AUTHOR]

Relative to single Global Navigation Satellite System (GNSS) measurements, i.e., the measurements from a single GNSS system, a single GNSS code, and a single GNSS receiver, multi-GNSS measurements for time transfer could improve reliability and provide better short-term stability. Previous studies applied equal weighting to different GNSS systems or different GNSS time transfer receivers, which, to some extent, revealed the improvement in the additional short-term stability from the combination of two or more kinds of GNSS measurements. In this study, the effects of the different weight allocation for multi-measurements of GNSS time transfer were analyzed, and a federated Kalman filter was designed and applied to fuse multi-GNSS measurements combined with the standard-deviation-allocated weight. Tests with real data showed that the proposed approach can reduce the noise level to well below about 250 ps for short averaging times. [ABSTRACT FROM AUTHOR]

The monitoring of bridges is a crucial operation for their structural health examination and maintenance. GNSS technology is one of the methods which are applied with the main advantage that the direct measurement of the bridge displacement is conducted in an independent global coordinate system. However, the high cost of the GNSS stations, which are consisted of dual-frequency receivers and geodetic GNSS antennas, is the main reason of the limited application of GNSS for bridge monitoring. In this study, we assessed the performance of low-cost multi-GNSS receivers in monitoring dynamic motion, similar to that of bridge response. The performance of the low-cost GNSS receivers was assessed based on controlled experiments of horizontal and vertical motion. For the horizontal motion, controlled experiments of circular motion of various predefined radius between 5 and 50 cm were executed where the low-cost GNSS receivers were assessed against dual-frequency geodetic receivers. For the vertical motion, manually controlled experiments of vertical oscillations of amplitude 8 and 15 mm were executed where the low-cost GNSS receivers were assessed against the Robotic Total Station (RTS). Finally, a low-cost monitoring system formed by two closely spaced low-cost GNSS receivers was applied in dynamic displacement monitoring of the Wilford Suspension Bridge. The analysis of the low-cost GNSS data revealed the beneficial contribution of (i) the multi-constellation on the accuracy and precision of the GNSS solution and (ii) the combination of closely spaced low-cost GNSS receivers, to limit potential cycle slips and the low-cost GNSS noise level and reach accuracy and precision similar to that of geodetic-grade GNSS receivers. This was confirmed in the bridge monitoring application, where the main modal frequency and the response amplitude of the bridge were identified successfully by the low-cost GNSS receivers' data analysis. [ABSTRACT FROM AUTHOR]