Search Results (69)

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. Full article

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent. Full article

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. Full article

The CNR (Carrier-to-Noise Ratio) of GPS (Global Positioning System) satellites is highly relevant to the multipath error. The multipath error is more serious in the flood environment since the reflection and diffraction coefficients of water are much higher compared to dry soil. Thus, the amplitude of CNR will decrease in the flood environment. In this study, the relationship between multipath error, flooding, and CNR is introduced in theory. Then, by using the characteristic of the orbital repetition period, the stability of CNR between 2 adjacent days in a static observation environment is demonstrated by 32 MGEX (Multi-GNSS Experiment) stations in different latitude and longitude regions of the world. The results show that the average RMS of different CNRs between two adjacent days is only about 0.62 dB-Hz. In addition, the correlation coefficient of CNRs between two adjacent days is analyzed. The correlation coefficient of the original signal CNR is 0.997. Moreover, after mitigating the influence of random noise and lower CNR, the correlation coefficients of the fitted CNRs larger than 40 dB-Hz can reach 0.999. Thus, based on the fluctuation in original CNR, fitted CNR, and seamless series characteristics of CNR, the whole flood process from occurrence to recession can be retrieved. A flood that occurred in Zhengzhou City, China, from DOY 200 to DOY 202, 2021 is used to demonstrate the process of retrieval. The experimental results indicate that the flood appeared at about 15:30 pm on DOY 200, reached a peak at approximately 8:30 am on DOY 202, and totally subsided at about 10:00 am on DOY 202. In conclusion, the CNR can be effectively used to retrieve the whole process of the flood, which lays a foundation for researching flood detection and warning based on GPS satellites. Full article

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

With the widespread application of GNSS, the delicate handling of biases among different systems and different frequencies is of critical importance, wherein the inter-frequency clock biases (IFCBs) and observable-specific signal biases (OSBs) should be carefully corrected. Usually, a serial approach is used to calculate these products. To accelerate the computation speed and reduce the time delay, a multicore parallel estimation strategy for IFCBs, code, and phase OSBs by utilizing task parallel library (TPL) is proposed, the parallel computations, including precise point positioning (PPP), IFCBs, and OSBs estimation, being carried out on the basis of data parallelisms and task-based asynchronous programming. Three weeks of observables from the multi-GNSS experiment campaign (MGEX) network is utilized. The result shows that the IFCB errors of GPS Block IIF and GLONASS M+ satellites are nonnegligible, in which the GLONASS M+ satellite R21 shows the largest IFCB of more than 0.60 m, while those of other systems and frequencies are marginal, and the code OSBs present excellent stability with a standard deviation (STD) of 0.10 ns for GPS and approximately 0.20 ns for other satellite systems. Besides, the phase OSBs of all systems show the stability of better than 0.10 ns, wherein the Galileo satellites show the best performance of 0.01 ns. Compared with the single-core serial computing method, the acceleration rates for IFCBs and OSBs estimation are 3.10, 5.53, 9.66, and 17.04 times higher using four, eight, sixteen, and thirty-two physical cores, respectively, through multi-core parallelized execution. Full article

Numerous organizations and Analysis Centers (AC) currently offer various Ambiguity Resolution (AR) products using various methodologies. However, there are no associated studies on their use for time-frequency transfer. This paper examines 16 Multi-GNSS Experiment (MGEX) stations with external high-precision atomic clocks to constitute 15 international time comparison links, and uses AR products data from CNES, SGG, CODE, and PRIDE laboratories, using three ambiguity-fixed strategies, to thoroughly evaluate the effects of various strategies and AR products for high-precision time-frequency transfer. We reach the following results by using the IGS final clock product as a reference and comparing it to ambiguity-float. With various ambiguity-fixed procedures, the time stability Standard Deviation (STD) of time transfer is increased for a single GPS, and the improvement ranges from 10 to 40%. The frequency stability has barely improved; up to 40%, the most notable improvement comes from FCB with GRM products. The time stability STD of combinations has improved after the addition of the Galileo system compared to the single GPS, and the improvement ranges from 2 to 9%. Most strategies have been improved, while a few techniques have been weakened with the GEC (GPS + Galileo + BDS) combination. We feel that the stability has not significantly increased with the systems’ increase in terms of short-term stability after comparing multiple groups of linkages. Full article

Global Navigation Satellite System (GNSS) signal quality, type of receiver equipment, and external environment can cause GNSS observations to be anomalous, and these anomalies are sometimes reflected in GNSS pseudorange observations rather than phase observations. To better detect blunders in pseudorange observations, this paper proposes three pseudorange blunder detection methods under the same frequency and different code types (case1), and the same code type and different frequencies (case2), of pseudorange observations, which are the Code Observation Difference Method (CODM), the Inter-satellite Code Observation Difference Method (ICODM), and the Inter-epoch and Inter-satellite Code Observation Difference Method (IICODM). The corresponding thresholds for the constructed test statistics of the three detection methods were derived based on the Bessel formula. Performance analysis of the three detection methods was performed under case1 based on C2 and P2 code observation data of Global Positioning System (GPS) at 137 Multi-GNSS Experiment (MGEX) stations, and case2 based on BDS B1I and B3I frequency observation data of BeiDou Navigation Satellite System (BDS) at 232 MGEX stations, on 29 July 2022. The results show that the statistical information value of the three methods in case1 was significantly smaller than that in case2. In the first case, the maximum values of test statistics, RMSE and threshold mean values were 0.526, 0.752 and 2.243 m, respectively, while the corresponding values in case2 were 7.066, 4.490 and 13.480 m respectively. The reason for this is that the data quality of global GPS is higher than that of BDS and the differential observation equation eliminates or weakens more errors with the same frequency and different types of code pseudorange observations. Under the same conditions, compared with ICODM and IICODM, CODM has high computational efficiency and a simple mathematical model. It is recommended to use CODM first for pseudorange blunder detection in the GNSS observation domain. According to the RMSE of 3 times as the limit, it is recommended that the threshold be set to 5 m under case1 for GPS and 15 m under case2 for BDS, which is half the existing reference value. Finally, the blunder detection methods proposed can improve positioning performance through actual data verification. Full article

The tropospheric model is the key model in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI). In this paper, we established the site-wise empirical Wuhan University Tropospheric Model (WTM) by using 10-year (2011–2020) monthly mean and 5-year (2016–2020) hourly ERA5 reanalysis data, where the Zenith Path Delay (ZPD), mapping function, and horizontal gradient as well as meteorological parameters are provided at 1583 specific space geodetic stations with additionally considering the diurnal and semi-diurnal variations. The mapping function and horizontal gradient from the WTM model were evaluated at 524 globally distributed GNSS stations during the year 2020 and compared with the latest grid-wise (1° × 1°) Global Pressure and Temperature 3 (GPT3) model. The significant improvements of the WTM model to the GPT3 model were found at the stations with terrain relief, and the maximal mapping function and horizontal gradient accuracy improvements reached 12.8 and 14.71 mm. The ZPD and mapping functions from the two models were also validated at 31 Multi-GNSS Experiment (MGEX) stations spanning the year 2020 by BeiDou Navigation Satellite System (BDS) Precise Point Positioning (PPP). The significant vertical coordinate and ZTD difference biases between the PPP schemes adopted by the two models were also found, and the largest biases reached −1.78 and 0.87 mm. 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

The asymmetric delay has a considerable impact on Global Navigation Satellite Systems (GNSS) Positioning, Navigation and Timing (PNT) applications. In GNSS analyses, the impacts of the asymmetric delay are commonly compensated by using the classical methods with considering the north-south and east-west horizontal gradients. In this paper, we have initiatively proposed an extended method where the north-south and east-west horizontal gradients as well as the second-order horizontal gradients are included to better fit the asymmetric delay. The modeling accuracy of the extended method was evaluated at globally distributed 905 GNSS stations during 40 days in 2020. Significant performance of the extended method respect to the classical method was found, where the hydrostatic and wet modeling accuracy at 4° elevation angle was improved from 5.3 and 10.6 mm to 1.6 and 4.9 mm by 70% and 54%, respectively. The GNSS Precise Point Positioning (PPP) performance using the extended method was also validated at 107 Multi-GNSS Experiment (MGEX) stations. The superior performance on the coordinate repeatability and significant effectiveness on the coordinate and Zenith Total Delay (ZTD) estimations were also found, and the maximal vertical (U) coordinate and ZTD difference biases reached 8.6 and −4.5 mm. The extended method is therefore recommended to substitute the classical methods in the GNSS analyses, especially under severe atmospheric conditions. Full article

The broadcast ionospheric model is one of the main methods for eliminating ionospheric delay errors for the Global Navigation Satellite Systems (GNSS) single-frequency users. GPS Klobuchar model (GPSK8) is the widely used broadcast ionospheric model for GPS, while BDS usually implements the BDS Klobuchar model (BDSK8) and BeiDou Global Broadcast Ionospheric Delay Correction Model (BDGIM). Geomagnetic storms may cause interference within the ionosphere and near-Earth space, compromising the accuracy of ionospheric models and adversely affecting the navigation satellite systems. This paper analyzes the static Standard Point Positioning (SPP) accuracy of GPS and BDS by implementing the broadcast ionospheric models and then investigates the impact of strong geomagnetic storms occurring in 2021 on positioning accuracy. The results show that the global 3D positioning accuracy (95%) of GPS + GPSK8, BDS + BDSK8, and BDS + BDGIM are 3.92 m, 4.63 m, and 3.50 m respectively. BDS has a better positioning accuracy in the northern hemisphere than that of the southern hemisphere, while the opposite is valid for GPS. In the mid-latitude region of the northern hemisphere, BDS + BDSK8 and BDS + BDGIM have similar positioning accuracy and are both better than GPS + GPSK8. The positioning accuracy after applying those three broadcast ionospheric models shows the superior performances of winter and summer over spring and autumn (based on the northern hemisphere seasons). With the exception of during winter, nighttime accuracy is better than that of daytime. The strong geomagnetic storm that occurred on the day of year (DOY) 132, 2021 has an impact on the positioning accuracy for only a small number of stations; however, the global average positioning accuracy is not significantly affected. The strong geomagnetic storms that occurred in DOY 307 and DOY 308 have a significant impact on the positioning accuracy of dozens of stations, and the global average positioning accuracy is affected to a certain extent, with some stations experiencing a serious loss of accuracy. Decreased degrees in positioning accuracy is proportional to the intensity of the geomagnetic storm. Of the 33 IGS Multi-GNSS Experiment (MGEX) stations worldwide, those located in the low and mid-latitudes are more significantly affected by the geomagnetic storms compared with higher latitudes. Evident fluctuations of the positioning errors existed during the strong geomagnetic storms, with an increase in extreme values, particularly in the up direction. Full article

With the completion of the BeiDou Global Navigation Satellite System (BDS-3), the multi-system precise point positioning ambiguity resolution (PPP-AR) has been realized. The satellite phase fractional cycle bias (FCB) is a key to the PPP-AR. Compared to the combined ionosphere-free (IF) model, the undifferenced and uncombined (UDUC) model retains all the information from the observations and can be easily extended to arbitrary frequencies. However, the FCB is difficult to apply directly to the UDUC model. An observable-specific signal bias (OSB) can interact directly with the original observations, providing complete flexibility for PPP-AR for multi-frequency multi-GNSS. In this study, the OSB product generation for the GPS (G), Galileo (E), and BDS-3 (C) systems is performed using 117 globally distributed multi-GNSS experiment (MGEX) stations, and their performances are evaluated. Then, the PPP-AR comparison and analysis of the two positioning models of the UDUC and IF are conducted. The results show that the stability of OSB products of the three systems is better than 0.05 ns. For the precise point positioning (PPP) ambiguity fixed solution, with comparable positioning accuracy and convergence time to the products of both the Wuhan University (WUM) and the Centre National d’Etudes Spatials (CNES) institutions, an average fixed-ambiguity rate is over 90%. Compared to the PPP float solution, the PPP-AR has the most significant improvement in positioning accuracy in the E-direction. The average improvements in the positioning accuracy under the IF and UDUC models in the static and kinematic modes are higher than 45% and 40%, respectively. The convergence times of the IF and UDUC models are improved on average by 48% and 60% in the static mode and by 40% and 55% in the kinematic mode, respectively. Among the IF and UDUC positioning models, the former has slightly better positioning accuracy and convergence time than the latter for the PPP float solution. However, both models have comparable positioning accuracy and convergence time after the PPP-AR. The GCE multi-system combination is superior to other system combinations. The average convergence time for the static PPP fixed solution is 8.5 min, and the average convergence time for the kinematic PPP fixed solution is 16.4 min. Full article

The time-varying biases within carrier phase observations are integrated into satellite clock offset parameters for precise clock estimation. Consequently, when the precise satellite clock bias is applied to the third frequency observation for precise point positioning (PPP), a new type of inter-frequency clock bias (IFCB) with satellite dependence should be noticed. If the IFCB is estimated together with the receiver coordinates, tropospheric wet delay, ambiguity and other parameters, it will increase the computational burden and lead to more time consumption. In order to solve this problem, the IFCB of GPS Block IIF satellites were estimated using 162 global uniformly distributed Multi-GNSS Experiment (MGEX) stations. By analyzing the time-varying characteristic of each satellite IFCB and combining the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function is proposed. The feasibility of this method was verified through the Student’s t-distribution, comparison with the measured IFCB, the posteriori residual of the third frequency carrier phase and the kinematic/static PPP solutions. The results showed that since the IFCB period was not a complete 24 h, the difference in the IFCBs time series on different days was increasingly significant with the passage of lag time, and the correlation constantly decreased. The peak-to-peak amplitudes of the IFCB difference reached 1.13, 3.44, 6.86 and 11.25 cm when the lag time was 1, 9, 19 and 29 days, respectively. In addition, based on the lag characteristic of final precise ephemerides released by the International GNSS Service (IGS) analysis centers, the prediction accuracy of the IFCB was evaluated with a time lag of 7 days. The root mean square of the posteriori residuals at the third-frequency observation decreased by approximately 51.3% compared to that without considering for IFCB correction. The triple-frequency uncombined PPP in the horizontal and vertical directions improved by approximately 33.2% and 17.2% for the static PPP solutions and 50.2% and 39.7% for the kinematic PPP solutions, respectively. In general, the accuracy and convergence time of the triple-frequency uncombined PPP were equivalently improved when the predicted IFCB and the measured IFCB were used. Full article

The third generation of the Beidou navigation satellite system (BDS-3) broadcasts navigation signals of five frequencies. Focusing on the deep integration of five-frequency signals, we applied the joint BDS-3 five-frequency undifferenced and uncombined precise point positioning (UC-PPP) to analyze the receiver inter-frequency biases (IFB). Firstly, 12 Multi-GNSS Experiment tracking (MGEX) stations are selected to investigate the time-varying characteristics of receiver IFB and, according to random characteristics, three random modeling schemes are proposed. Secondly, the effects of three stochastic modeling methods on zenith tropospheric delay, ionospheric delay, floating ambiguity, and quality control are analyzed. Finally, the effects of three IFB stochastic modeling methods on positioning performance are evaluated. The results showed that the amplitude in the IFB for B2b is 5.139 m, B2a is 1.964 m, and B1C is 0.950 m by measuring one week’s observation data. The IFB stochastic modeling method based on random walks can shorten the PPP convergence time by 4~12%, diminish the false alarm of quality control, and improve the positioning accuracy. The random walk model is recommended to simulate the variation of IFB, which can not only overcome the disadvantage of the time constant model being unable to accurately describe the time-varying characteristics of the IFB, but also avoid reducing the strength of the kinematic PPP positioning model due to the large process noise of the white noise model. Full article