Beidou/GNSS Precise Positioning and Atmospheric Modeling

With the full operation of the global BeiDou navigation satellite system (BDS-3), positioning performance can be further enhanced by BDS-3 combined with the regional BeiDou navigation satellite system (BDS-2). However, due to satellite signals being out of lock and the limited visibility of satellites, the traditional multi-frequency BDS-2/3 precise point positioning (PPP) model is unable to maintain great positioning performance under urban environmental conditions. In this study, a mixed multi-frequency undifferenced and uncombined (UDUC) BDS-2/3 PPP model is presented to improve the positioning performance under urban environmental conditions by making full use of B1I, B1C, B2I, B2a, and B3I signals from all visible BDS satellites. In this model, BDS satellites with single-, dual-, triple- and quad-frequency observations all can participate in PPP. The static and kinematic experiments were carried out using the mixed multi-frequency UDUC BDS-2/3 PPP model to fully assess the positioning performance under urban environmental conditions with comparisons to the multi-frequency model. The static experiments indicated that the mixed multi-frequency UDUC BDS-2/3 PPP could continuously achieve decimeter-level positioning accuracy at a cut-off elevation angle of 40°, but part of the BDS-3 PPP would lose resolution due to limited visible satellites. Furthermore, the initial kinematic vehicle experiment showed that mixed multi-frequency UDUC BDS-2/3 PPP had better satellite geometry and more observation redundancy than the traditional multi-frequency model. Compared with the traditional multi-frequency BDS-2/3 model, the positioning accuracy of the mixed multi-frequency model was improved by 51.6, 35.5, and 39.1%, respectively, in east, north, and up directions. The convergence time was shortened by 40%. Full article

Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and computational burden increases in full ambiguity resolution. Therefore, an increasing number of partial ambiguity resolution (PAR) strategies have been proposed. The selection of the optimal subset of PAR is crucial in this method. The traditional optimal subset selection method of PAR commonly leads to a single judgment criterion and weakened geometric configuration strength because the satellites with low elevation angles are often easily eliminated during the optimal subset selection. In this paper, a multi-factor constrained optimal subset selection method for PAR was proposed, which incorporates the ambiguity variance, the ambiguity dilution of precision (ADOP), satellite position dilution of precision (PDOP) and ratio test values. In order to verify the feasibility of the proposed optimal subset selection method, PAR tests under two schemes were performed for GPS/Galileo based on the static observation data of 15 Multi-GNSS Experiment (MGEX) tracking stations. The results show that, compared with the ambiguity variance sorting method, the proposed subset selection method can further improve the accuracy of the coordinate solution and the strength of geometric figure positioning. The average root mean square of the coordinate residuals is found to decrease by about 12.90%, 6.83% and 9.39% in the eastern, northern and vertical directions, respectively. The increase in the fixed epoch rate ranged from 0.87% to 33.33%, with an average of about 8.71%. Full article

Currently, it is still challenging to detect earthquakes by using the measurements of Global Navigation Satellite System (GNSS), especially while only adopting single-frequency GNSS. To increase the accuracy of earthquake detection and warning, extra information and techniques are required that lead to high costs. Therefore, this work tries to find a low-cost method with high-accuracy performance. The contributions of our research are twofold: (1) an improved earthquake-displacement estimation approach by considering the relation between earthquake and ionospheric disturbance is presented. For this purpose, we propose an undifferenced uncombined Single-Frequency Precise Point Positioning (SF-PPP) approach, in which both the ionospheric delay of each observed satellite and receiver Differential Code Bias (DCB) are parameterized. When processing the 1 Hz GPS data collected during the 2013 Mw7.0 Lushan earthquake and the 2011 Mw9.0 Tohoku-Oki earthquake, the proposed SF-PPP method can provide coseismic deformation signals accurately. Compared to the results from GAMIT/TRACK, the accuracy of the proposed SF-PPP was not influenced by the common mode errors that exist in the GAMIT/TRACK solutions. (2) Vertical Total Electron Content (VTEC) anomalies before an earthquake are investigated by applying time-series analysis and spatial interpolation methods. Furthermore, on the long-term scale, it is revealed that significant positive/negative VTEC anomalies appeared around the earthquake epicenter on the day the earthquake occurred compared to about 4–5 days before the earthquake, whereas, on the short-term scale, positive/negative VTEC anomalies emerged several-hours before or after an earthquake. Full article

As a frequently-occurred phenomenon in the high-latitude region, ionospheric scintillations affect the stable service of the positioning navigation and timing service of the Global Navigation Satellite System (GNSS), calling for an urgent need of monitoring the scintillations accurately. The monitoring of scintillations usually adopts a special type of receiver, called an ionospheric scintillation monitoring receiver (ISMR), which cannot cover the whole high-latitude region due to its loss distribution. Geodetic receivers are densely distributed, but set at a 30s-sampling-interval usually. It is a controversial issue, namely, the accuracy of the scintillation index extracted from 30s-sampling-interval observations. This paper evaluates the accuracy of two 30s-sampling-interval indices in monitoring scintillations from both the time and space aspects using observations collected in the whole year of 2020. The accuracy in the time aspect is assessed with the phase scintillation index from ISMR as the reference through the following three-pronged approaches, i.e., the accuracy of the daily scintillation occurrence rates in the year 2020, the correlation with space weather parameters, and the variation pattern of the scintillation occurrence rate with the local time and day of the year 2020. The accuracy in space is studied based on the scintillation grid model considering the following two aspects, i.e., the scintillation monitoring performance in a Swarm satellite observation arc, and the statistical scintillation occurrence rate in the whole research region throughout the year 2020. The results of this paper reveal the efficiency of the 30s-sampling-interval scintillation indices in monitoring scintillations and detecting the occurrence patterns in the high-latitude region. The outcome of this paper can provide a basic idea for introducing the widely distributed geodetic receivers to monitor and model the scintillations in the high-latitude region. Full article

Ionospheric delay is a critical error source in Global Navigation Satellite Systems (GNSSs) and a principal aspect of Satellite Based Augmentation System (SBAS) corrections. Grid Ionospheric Vertical Delays (GIVDs) are derived from the delays on Ionosphere Pierce Points (IPPs), which are observed by SBAS reference stations. SBAS master stations calculate ionospheric delay corrections by several methods, such as planar fit or Kriging. However, when there are not enough IPPs around an Ionosphere Grid Point (IGP) or the IPPs are unevenly distributed, the fitting accuracy of planar fit or Kriging is unsatisfactory. Moreover, the integrity bounds of Grid Ionospheric Vertical Errors (GIVEs) are overly conservative. Since Artificial Neural Networks (ANNs) are widely used in ionospheric research due to their self-adaptation, parallelism, non-linearity, robustness, and learnability, the ANN method for GIVD and GIVE derivation is proposed in this article. Networks are separately trained for IGPs, and five years of historical data are applied on network training. Principal Component Analysis (PCA) is applied for dimensionality reduction of geomagnetic and solar indices, which is employed as a network input feature. Furthermore, the GIVE algorithm of the ANN method is derived based on the distribution of the residual random variable. Finally, experiments are conducted on 12 IGPs over the East China region. Under normal ionospheric conditions, compared with the planar fit and Kriging methods, the residual reduction of the ANN method is approximately 15%. The ANN method fits the ionospheric delay residual error better. The percentage of GIVE availability under 2.7 m increases at least 25 points in comparison to Kriging. Under disturbed conditions, due to a lack of training samples, the ANN method is incompetent compared with planar fit or Kriging. Full article

BeiDou Global Navigation Satellite System (BDS-3) provides a regional Precise Point Positioning (PPP) service, called PPP-B2b, for users in China and surrounding areas through B2b signal transmitted from its three geostationary earth orbit (GEO) satellites. The information broadcasted by the B2b signal include satellite orbit corrections, satellite clock offset corrections, and differential code bias (DCB) corrections of BDS-3 satellites. In this study, the accuracies of PPP-B2b corrections along with real-time PPP performance are comprehensively evaluated referenced to precise orbit and clock products from GFZ and the precise DCB products from CAS. The result indicates that the accuracy of the BDS-3 broadcast orbit is similar to that of the PPP-B2b real-time orbit. The PPP-B2b clock offset correction improved the satellite clock offset precision of the BDS-3 broadcast ephemeris. The Signal-in-Space Range Error (SISRE) of broadcast ephemeris and PPP-B2b are calculated, which are 0.536 and 1.24 m, respectively. The large SISRE value of PPP-B2b is caused by the satellite-specified systematic bias to IGS final products. The positioning performance evaluation of real-time PPP with B2b service is carried out and compared with the real-time product provided by Wuhan University (WHU) based on the eight IGS MGEX stations in China and surrounding countries. The positioning accuracy of static positioning mode with PPP-B2b service achieved centimeter-level accuracy in the selected station, and that of kinematic positioning mode achieved decimeter-level accuracy. The availability rate of PPP-B2b corrections in the surrounding area of China, however, degrades from 88.76% to 60.91% in the selected stations. The accuracy of the PPP solution using PPP-B2b correction is better than that of using WHU real-time product within China. The positioning performance of stations located at the boundary of the PPP-B2b service area, however, is affected by the number of PPP-B2b available satellites. The positioning accuracy in kinematic positioning mode is worse than that of using WHU real-time precise product. Full article

Due to satellite signal deformations, there are different constant biases in the same satellite signal that are measured by different technical types of receivers and different satellite signals that are measured by the same type of receiver, which are named pseudorange biases. These biases cannot be transmitted to users with existing navigation parameters, such as satellite time group delay (TGD) and receiver differential code biases (DCB). With the improvement of the signal-in-space accuracy of the Global Navigation Satellite System (GNSS), the pseudorange bias has become one of the primary error sources affecting the accuracy of GNSS services. To ensure the accuracy for users under the wide area differential services (WADS), we extracted the pseudorange biases of Beidou Satellite Navigation System (BDS) B1I, B3I and B1I/B3I signals and analyzed the impact of those biases on users under the WADS. Finally, we tried to eliminate this influence. The results show that the pseudorange biases of the B3I signal are smaller than those of the B1I signal at the centimeter level, but the pseudorange biases of the B1I/B3I signal can reach the meter level. Due to the large pseudorange bias of the B1I/B3I signal, the average user equivalent ranging error (UERE) under the WADS is 1.19 m, which is no better than the average UERE under open services (OS). Influenced by the pseudorange biases, the average positioning accuracies of the B1I/B3I signal are 4.17 m and 4.24 m under the WADS and the OS. When the pseudorange biases are deducted, these accuracies are 3.03 m and 3.50 m, respectively. Full article

Satellite phase fractional cycle biases (FCBs) are crucial to precise point positioning with ambiguity resolution (PPP–AR), and they can improve the accuracy and reliability of a solution. Traditional methods need multiple iterations and need to keep the same reference when estimating satellite phase fractional cycle biases. In this paper, we propose an improved fast estimation of FCB, which does not need any iterations and can select any reference when estimating FCB. We compare the suitability and precision of a traditional and a proposed method by BDS-3 experiments. The results of the FCB experiments show that the calculated time of the proposed method is less than the traditional method and that computation efficiency is increased by 34.71%. These two methods have a similar rate of fixed epochs and ambiguities in the static and dynamic models. However, the time to first fix (TTFF) of the proposed method decreased by 19.69% and 28.83% for the static and dynamic models, respectively. The results show that the proposed method has a better convergence time in PPP–AR. Full article

China is promoting the construction of an integrated positioning, navigation, and timing (PNT) systems with the BeiDou Navigation Satellite System (BDS) as its core. To expand the positioning coverage area and improve the positioning performance by taking advantage of device-to-device (D2D) and self-organizing network (SON) technology, a BDS/SON integrated positioning system is proposed for the fifth-generation (5G) networking environment. This system relies on a combination of time-of-arrival (TOA) and BeiDou pseudo-range measurements to effectively supplement BeiDou signal blind spots, expand the positioning coverage area, and realize higher precision in continuous navigation and positioning. By establishing the system state model, and addressing the single-system positioning divergence and insufficient accuracy, a robust adaptive fading filtering (RAF) algorithm based on the prediction residual is proposed to suppress gross errors and filtering divergence in order to improve the stability and accuracy of the positioning results. Subsequently, a federated Kalman filtering (FKF) algorithm operating in fusion-feedback mode is developed to centrally process the positioning information of the combined system. Considering that the prediction error can reflect the magnitude of the model error, an adaptive information distribution coefficient is introduced to further improve the filtering performance. Actual measurement and significance test results show that by integrating BDS and SON positioning data, the proposed algorithm realizes robust, reliable, and continuous high precision location services with anti-interference capabilities and good universality. It is applicable in scenarios involving unmanned aerial vehicles (UAVs), autonomous driving, military, public safety and other contexts and can even realize indoor positioning and other regional positioning tasks. Full article

Single-frequency (SF) receivers are much cheaper than that of dual-frequency (DF). Even though DF precise point positioning (PPP) is nowadays applied in the time community, the cost of equipment is one of the key considerations for time users. Furthermore, the hardware delay calibration of single-frequency devices is simpler than that of dual-frequency devices. In addition, there is no literature to study real-time SF PPP time transfer. In this contribution, the possibility of time transfer using SF PPP was studied. The Un-combined SF PPP was employed for time transfer with ionospheric-constraint using real-time precise products. In this case, 18 multi-GNSS experiment (MGEX) stations and one time lab station were used to study real-time SF PPP time transfer using GPS, Galileo and BDS-2/3 satellites with 20-day. The results suggested that real-time single-frequency PPP can meet time transfer. the standard deviation (STD) of the clock difference obtained from GPS-only, Galileo-only and BDS-2/3 single-frequency PPP are about (0.51, 0.54, 0.91) ns, respectively. The frequency stability of real-time single-frequency PPP can achieve (1E-12, 1E-13, 1E-13) level at short-term and (1E-13, 1E-13, 1E-14) level at long-term, respectively, for BDS-2/3, Galileo-only and GPS-only based. Full article

Soil moisture is an important geophysical parameter for studying terrestrial water and energy cycles. It has been proven that Global Navigation Satellite System Interferometry Reflectometry (GNSS-IR) can be applied to monitor soil moisture. Unlike the Global Positioning System (GPS) that has only medium earth orbit (MEO) satellites, the Beidou Navigation Satellite System (BDS) also has geosynchronous earth orbit (GEO) satellites and inclined geosynchronous satellite orbit (IGSO) satellites. Benefiting from the distribution of three different orbits, the BDS has better coverage in Asia than other satellite systems. Previous retrieval methods that have been confirmed on GPS cannot be directly applied to BDS MEO satellites due to different satellite orbits. The contribution of this study is a proposed multi-satellite soil moisture retrieval method for BDS MEO and IGSO satellites based on signal-to-noise ratio (SNR) observations. The method weakened the influence of environmental differences in different directions by considering satellite repeat period. A 30-day observation experiment was conducted in Fengqiu County, China and was used for verification. The satellite data collected were divided according to the satellite repeat period, and ensured the response data moved in the same direction. The experimental results showed that the BDS IGSO and MEO soil moisture estimation results had good correlations with the in situ soil moisture fluctuations. The BDS MEO B1I estimation results had the best performance; the estimation accuracy in terms of correlation coefficient was 0.9824, root mean square error (RMSE) was 0.0056 cm³cm⁻³, and mean absolute error (MAE) was 0.0040 cm³cm⁻³. The estimations of the BDS MEO B1I, MEO B2I, and IGSO B2I performed better than the GPS L1 and L2 estimations. For the BDS IGSO satellites, the B1I signal was more suitable for soil moisture retrieval than the B2I signal; the correlation coefficient was increased by 19.84%, RMSE was decreased by 42.64%, and MAE was decreased by 43.93%. In addition, the BDS MEO satellites could effectively capture sudden rainfall events. Full article

Precipitable water vapor (PWV) plays a vital role in climate research, especially for Antarctica in which meteorological observations are insufficient due to the adverse climate and topography therein. Reanalysis data sets provide a great opportunity for Antarctic water vapor research. This study investigates the climatological PWV means, variability and trends over Antarctica from four reanalyses, including the fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA5), the Second Modern-Era Retrospective analysis for Research and Applications (MERRA-2), Japanese 55-year Reanalysis (JRA-55) and National Centers for Environmental Prediction/Department of Energy (NCEP/DOE), in the period of 2001–2018 based on radiosonde and GNSS observations. PWV data from the ERA5, MERRA-2, JRA-55 and NCEP/DOE have been evaluated by radiosonde and GNSS observations, showing that ERA5 and MERRA-2 perform better than JRA-55 and NCEP/DOE with mean root mean square (RMS) errors below 1.2 mm. The climatological PWV mean distribution over Antarctica roughly shows a decreasing trend from west to east, with the highest content in summer and the lowest content in winter. The PWV variability is generally small over Antarctica, showing a seasonal dependence that is larger in the cold season and smaller in the warm season. PWV trends for all reanalyses at most Antarctic regions are insignificant and most reanalyses present overall drying trends from 2001 to 2018, except for ERA5 exhibiting a moistening trend. PWV trends also show seasonal and regional dependence. All reanalyses are generally consistent with radiosonde and GNSS observations in reproducing the PWV means (mean differences within 1.1 mm), variability (mean differences within 3%) and trends (mean differences within 6.4% decade⁻¹) over Antarctica, except for NCEP/DOE showing spurious variability and trends in East Antarctica. Results can help us further understand these four reanalysis PWV products and promote climate research in Antarctica. Full article

This study investigates methods of deriving meteorological parameters needed in space geodetic applications, from the surface data of the numerical weather model (NWM). It is more efficient than pressure level data in terms of storage and transmission. Based on more realistic assumptions for the structure of the troposphere, formulas for accurate vertical reduction of pressure (P) and precipitable water vapor (PWV) are deduced, and they are applied with the gridded lapse rate data provided by the GPT2w model. The new method achieves better accuracy especially when a large height difference between the grid point and station exists. Validation with global radiosonde observations shows that the RMS errors of P, temperature (T), and water vapor pressure (e) derived from 2.5° × 2.5° ERA surface data are 1.16 hPa, 1.95 K, and 1.76 hPa respectively; zenith tropospheric delays (ZTDs) calculated from derived P, T, and e values have a mean RMS error of 3.26 cm, comparable to that obtained from in situ measurements; adding PWV will increase ZTD estimation accuracy to 1.52 cm, comparable to that obtained from NWM pressure level data. Validations with Global Navigation Satellite System estimated ZTDs from global and regional station networks display similar results on the globe, as well as features for localized regions. Using higher spatial resolution NWM seems to have little effect on the accuracy of ZTDs calculated from P, T, and e, while it apparently improves the accuracy of ZTDs calculated from P, T, e, and PWV. Full article

For the development of a global navigation satellite system (GNSS), the third generation of BeiDou Navigation Satellite System (BDS-3) achieved full constellation for worldwide service on 23 June 2020. The new signals, B1C and B2a of BDS-3, further enhance the compatibility and interoperability between different GNSSs. In this study, we first assessed the quality of all the signals in BDS-3/GPS/Galileo. Then, to achieve the interoperability among BDS-3/GPS/Galileo, the inter-system bias (ISB), which appears if an inter-system difference exists between two GNSSs, was estimated at overlapping frequencies. Finally, we used the estimated ISBs in real-time kinematic (RTK) positioning. The results show the higher quality of the overlapping frequency B2a/L5/E5a than B1C/L1/E1 in terms of pseudo range multipath. The ISBs are stable both in the short term for one day and in the long term for over a year, which fit a zero-mean normal distribution well when the identical type of receiver is applied. Thus, it is reasonable to ignore the ISBs in the inter-system differences. With the estimated ISBs, the inter-system double-difference RTK can be achieved, which is called a tightly combined model (TCM) RTK. Compared with the traditional intra-system double-difference RTK, which is called a loosely combined model (LCM) RTK, the TCM RTK can achieve a higher success rate (SR) in terms of ambiguity resolution and higher positioning accuracy. In addition, the higher the cutoff elevation angle set, the greater the promotion can be obtained in SR. Even with a cutoff elevation angle of 50°, the SR of TCM is over 80%. Thus, it is important to apply TCM RTK when the observation conditions are limited, such as in dense jungles or the urban canyons. Full article

Global Navigation Satellite System (GNSS) ultra-rapid orbit is critical for geoscience and real-time engineering applications. To improve the computational efficiency and the accuracy of predicted orbit, a parallel approach for multi-GNSS ultra-rapid orbit determination is proposed based on Message Passing Interface (MPI)/Open Multi Processing (OpenMP). This approach, compared with earlier efficient methods, can improve the efficiency of multi-GNSS ultra-rapid orbit solution without changing the original observation data and retaining the continuity and consistency of the original parameters to be estimated. To obtain high efficiency, three steps are involved in the approach. First and foremost, the normal equation construction is optimized in parallel based on MPI. Second, equivalent reduction of the estimated parameters is optimized using OpenMP parallel method. Third, multithreading is used for parallel orbit extrapolation. Thus, GNSS ultra-rapid orbit determination is comprehensively optimized in parallel, and the computation efficiency is greatly improved. Based on the data from MGEX and IGS stations, experiments are carried out to analyze the performance of the proposed approach in computational efficiency, accuracy and stability. The results show that the approach greatly improves the efficiency of satellite orbit determination. It can realize 1-h update frequency for the multi-GNSS ultra-rapid orbit determination using 88 stations with four-system observations. The accuracy of the GPS, GLONASS, Galileo and BDS ultra-rapid orbit with 1-h update frequency using the parallel approach is approximately 33.4%,31.4%,40.1% and 32.8% higher than that of the original orbit, respectively. The root mean squares (RMS) of GPS, GLONASS, Galileo and BDS predicted orbit are about 3.2 cm, 5.1 cm, 5.6 cm and 11.8 cm. Moreover, the orbit provided by the proposed method has a better stability. The precision loss of all parallel optimization can be negligible and the original correlation between the parameters is fully preserved. Full article

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms. Full article

Observable-specific bias (OSB) parameterization allows observation biases belonging to various signal types to be flexibly addressed in the estimation of ionosphere and global navigation satellite system (GNSS) clock products. In this contribution, multi-GNSS OSBs are generated by two different methods. With regard to the first method, geometry-free (GF) linear combinations of the pseudorange and carrier-phase observations of a global multi-GNSS receiver network are formed for the extraction of OSB observables, and global ionospheric maps (GIMs) are employed to correct ionospheric path delays. Concerning the second method, satellite and receiver OSBs are converted directly from external differential code bias (DCB) products. Two assumptions are employed in the two methods to distinguish satellite- and receiver-specific OSB parameters. The first assumption is a zero-mean condition for each satellite OSB type and GNSS signal. The second assumption involves ionosphere-free (IF) linear combination signal constraints for satellites and receivers between two signals, which are compatible with the International GNSS Service (IGS) clock product. Agreement between the multi-GNSS satellite OSBs estimated by the two methods and those from the Chinese Academy of Sciences (CAS) is shown at levels of 0.15 ns and 0.1 ns, respectively. The results from observations spanning 6 months show that the multi-GNSS OSB estimates for signals in the same frequency bands may have very similar code bias characteristics, and the receiver OSB estimates present larger standard deviations (STDs) than the satellite OSB estimates. Additionally, the variations in the receiver OSB estimates are shown to be related to the types of receivers and antennas and the firmware version. The results also indicate that the root mean square (RMS) of the differences between the OSBs estimated based on the CAS- and German Aerospace Center (DLR)-provided DCB products are 0.32 ns for the global positioning system (GPS), 0.45 ns for the BeiDou navigation satellite system (BDS), 0.39 ns for GLONASS and 0.22 ns for Galileo. Full article

This study evaluates the EUREF Permanent Network (EPN) station position time series of approximately 200 GNSS stations subject to the Repro 2 reprocessing campaign in order to characterize the dominant types of noise and amplitude and their impact on estimated velocity values and associated uncertainties. The visual inspection on how different noise model represents the analysed data was done using the power spectral density of the residuals and the estimated noise model and it is coherent with the calculated Allan deviation (ADEV)-white and flicker noise. The velocities resulted from the dominant noise model are compared to the velocity obtained by using the Median Interannual Difference Adjusted for Skewness (MIDAS). The results show that only 3 stations present a dominant random walk noise model compared to flicker and powerlaw noise model for the horizontal and vertical components. We concluded that the velocities for the horizontal and vertical component show similar values in the case of MIDAS and maximum likelihood estimation (MLE), but we also found that the associated uncertainties from MIDAS are higher compared to the uncertainties from MLE. Additionally, we concluded that there is a spatial correlation in noise amplitude, and also regarding the differences in velocity uncertainties for the Up component. Full article

In this work, quad-frequency precise point positioning (PPP) time and frequency transfer methods using Galileo E1/E5a/E5b/E5 and BDS-3 B1I/B3I/B1C/B2a observations were proposed with corresponding mathematical models. In addition, the traditional dual-frequency (BDS-3 B1I/B3I and Galileo E1/E5a) ionospheric-free (IF) model was also described and tested for comparison. To assess the proposed method for time transfer, datasets selected from timing labs were utilized and tested. Moreover, the number of Galileo or BDS-3 satellites, pseudorange residuals, positioning accuracy and tropospheric delay at receiver end were all analyzed. The results showed that the proposed quad-frequency BDS-3 or Galileo PPP models could be used to time transfer, due to stability and accuracy identical to that of dual-frequency IF model. Furthermore, the quad-frequency models can provide potential for enhancing the reliability and redundancy compared to the dual-frequency time transfer method. Full article

On 31 July 2020, the Beidou global navigation satellite system (BDS-3) was officially announced as being commissioned. In addition to offering global positioning, navigation, and timing (PNT) services, BDS-3 also provides precise point positioning (PPP) augmentation services. The satellite orbit correction, clock correction and code bias correction of BDS-3 and other global navigation satellite systems (GNSS) are broadcast by the BDS-3 geostationary earth orbit (GEO) satellites through the PPP-B2b signal. The PPP-B2b service is available for users in China and the surrounding area. In this study, an initial assessment of the PPP-B2b service is presented, with collected 3-day PPP-B2b messages. Based on broadcast ephemeris and PPP-B2b messages, the precise satellite orbits and clock offsets can be recovered. This precision is evaluated with the precise ephemeris from the GeoForschungsZentrum Potsdam (GFZ) analysis center as references. The results indicate that the accuracy of BDS-3 satellite orbits in the direction of radial, along-track, and cross-track is 0.138, 0.131, and 0.145 m, respectively, and for GPS a corresponding accuracy of 0.104, 0.160, and 0.134 m, respectively, could be obtained. The precision of clock offsets can reach a level of several centimeters for both GPS and BDS-3. Both the performance of static PPP and kinematic PPP are evaluated using the observations from four international GNSS monitoring assessment service (iGMAS) stations. Regarding static PPP, the average convergence time is 17.7 min to achieve a horizontal positioning accuracy of better than 0.3 m, and a vertical positioning accuracy of better than 0.6 m. The average positioning accuracy in the direction of east, north, and up-directions are 2.4, 1.6, and 2.3 cm. As to kinematic PPP, the average RMS values of positioning errors in the direction of east, north, and up are 8.1 cm, 3.6 cm, and 8.0 cm after full convergence. Full article

The BeiDou Navigation Satellite System (BDS) has completed third phase construction and currently provides global services, with a mixed constellation of BDS-2 and BDS-3. The newly launched BDS-3 satellites are equipped with rubidium and passive hydrogen maser (PHM) atomic clocks. The performance of atomic clocks is one of the cores of satellite navigation system, which will affect the performance of positioning, navigation and timing (PNT). In this paper, we systematically analyze the characteristics of BDS-2 and BDS-3 atomic clocks, based on more than one year of precise satellite clock products and broadcast ephemeris. Firstly, the results of overlapping Allan variations demonstrate that BDS-3 Rb and PHM clocks improve better in stability than BDS-2 Rb clock and are comparable to GPS IIF Rb and Galileo PHM clocks. Accordingly, the STDs of BDS-3 broadcast satellite clock are better than GPS and BDS-2, which are at the same level with that of Galileo. Secondly, the inter-system bias (ISB) between BDS-2 and BDS-3 is analyzed by satellite clock datum comparison and precise point positioning (PPP). Surprisingly, the discrepancy between BDS-2 and BDS-3 satellite clock datum has a great difference between products that could reach up to about 10 ns for WHU satellite clock products and broadcast ephemeris. Moreover, the ISBs between BDS-2 and BDS-3 satellite clocks are quite stable over one-year periods. Thirdly, due to the improved stability of BDS-3 atomic clock, the 68% positioning accuracy is better than 0.65 m at 10 min for BDS-3 PPP, based on broadcast ephemeris. Besides, the non-negligible bias between BDS-2 and BDS-3 will greatly affect the BDS precise data processing. The accuracy of positioning is greatly improved when considering the ISB. Full article

From August to October 2020, a serious wildfire occurred in California, USA, which produced a large number of particulate matter and harmful gases, resulting in huge economic losses and environmental pollution. Particulate matter delays the GNSS signal, which affects the like precipitable water vapor (LPWV) derived by the GNSS non-hydrostatic delay. Most of the information of GNSS-derived LPWV is caused by water vapor, and a small part of the information is caused by particulate matter. A new method based on the difference (ΔPWV) between the PWV of virtual radiosonde stations network and GNSS-derived LPWV is proposed to detect the changes of particulate matter in the atmosphere during the 2020 California wildfires. There are few radiosonde stations in the experimental area and they are far away from the GNSS station. In order to solve this problem, we propose to use the multilayer perceptron (MLP) neural network method to establish the virtual radiosonde network in the experimental area. The PWV derived by the fifth-generation European center for medium-range weather forecasts reanalysis model (PWV_ERA5) is used as the input data of machine learning. The PWV derived by radiosonde data (PWV_RAD) is used as the training target data of machine learning. The ΔPWV is obtained based on PWV derived by the virtual radiosonde station network and GNSS in the experimental area. In order to further reduce the influence of noise and other factors on ΔPWV, this paper attempts to decompose ΔPWV time series by using the singular spectrum analysis method, and obtain its principal components, subsequently, analyzing the relationship between the principal components of ΔPWV with particulate matter. The results indicate that the accuracy of PWV predicted by the virtual radiosonde network is significantly better than the fifth-generation European center for the medium-range weather forecast reanalysis model, and the change trend of ΔPWV is basically consistent with the change law of particulate matter in which the value of ΔPWV in the case of fire is significantly higher than that before and after the fire. The mean of correlation coefficients between ΔPWV and PM10 at each GNSS station before, during and after wildfires are 0.068, 0.397 and 0.065, respectively, which show the evident enhancement of the correlation between ΔPWV and particulate matter during wildfires. It is concluded that because of the high sensitiveness of ΔPWV to the change of particulate matter, the GNSS technique can be used as an effective new approach to detect the change of particulate matter and, then, to detect wildfires effectively. Full article

The modernized GPS, Galileo, and BeiDou global navigation satellite system (BDS3) offers new potential for time transfer using overlap-frequency (L1/E1/B1, L5/E5a/B2a) observations. To assess the performance of time and frequency transfer with overlap-frequency observations for GPS, Galileo, and BDS3, the mathematical models of single- and dual-frequency using the carrier-phase (CP) technique are discussed and presented. For the single-frequency CP model, the three-day average RMS values of the L5/E5a/B2a clock difference series were 0.218 ns for Galileo and 0.263 ns for BDS3, of which the improvements were 36.2% for Galileo and 43.9% for BDS3 when compared with the L1/E1/B1 solution at BRUX–PTBB. For the hydrogen–cesium time link BRUX–KIRU, the RMS values of the L5/E5a/B2a solution were 0.490 ns for Galileo and 0.608 ns for BDS3, improving Galileo by 6.4% and BDS3 by 12.5% when compared with the L1/E1/B1 solution. For the dual-frequency CP model, the average stability values of the L5/E5a/B2a solution at the BRUX–PTBB time link were 3.54 × 10⁻¹² for GPS, 2.20 × 10⁻¹² for Galileo, and 2.69 × 10⁻¹² for BDS3, of which the improvements were 21.0%, 45.1%, and 52.3%, respectively, when compared with the L1/E1/B1 solution. For the BRUX–KIRU time link, the improvements were 4.2%, 30.5%, and 36.1%, respectively. Full article