Search Results (70)

The Beidou Global System (BDS-3) innovatively achieves autonomous navigation using inter-satellite links (ISL) across the entire constellation, but it still faces challenges such as the limitations of the prior constraint orbital accuracy and the overall constellation rotation. The gradual availability of satellite laser ranging (SLR) data, with advantages of high precision and no ambiguous parameters, can provide new ideas for solving the current problem. This work firstly deduces the mathematical model for orbit determination by combining inter-satellite links and the introduced satellite laser ranging observations, then designs orbit determination experiments with different prior orbit constraints and different observation data, and finally evaluates the impacts of the prior orbits and the introduction of SLR observations from two dimensions: orbit accuracy and constellation rotation. The experimental results using one month of measured data show the following: (1) There is good consistency among different days, and the accuracy of the prior orbits affects the performance of the orbit determination and the consistency. Compared with broadcast ephemerides, using precise ephemerides as prior constraints significantly improves the consistency, and the orbit accuracy can be increased by about 75%. (2) The type of observation data affects the performance of the orbit determination. Introducing SLR observations can improve the orbit accuracy by approximately 13% to 26%. (3) Regardless of whether broadcast ephemerides or precise ephemerides are used as prior constraints, the constellation translation and rotation still exist after introducing SLR observations. Among the translation parameters, TX is the largest, followed by TY, and TZ is the smallest; all three rotation parameters (RX, RY, and RZ) show relatively large values, which may be related to the limited number of available satellite laser ranging stations during this period. (4) After considering the constellation translation and rotation, the orbit accuracy under different prior constraints remains at the same level. The statistical root mean square error (RMSE) indicates that the orbit accuracy of inclined geosynchronous orbit (IGSO) satellites in three directions is better than 20 cm, while the accuracy of medium earth orbit (MEO) satellites in along-track, cross-track, and radial directions is better than 10 cm, 8 cm, and 5 cm, respectively. Full article

An accurate estimation of Differential Code Bias (DCB) is essential for high-precision applications of the Global Navigation Satellite System (GNSS) and for the precise determination of GNSS-derived total electron content (TEC). This study leverages BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS) dual-frequency observations of the China Seismo-electromagnetic Satellite (CSES) from day of the year (DOY) 201 to DOY 232 in 2018, we evaluate the quality of CSES onboard GNSS observations, improve the data preprocessing method, and use the least-squares to estimate DCBs for both GNSS satellites and CSES receivers. A comprehensive analysis of the estimation accuracy is presented, revealing that DCBs for BDS satellites, derived from joint BDS and GPS observations, exhibit superior consistency compared to those from single BDS observations. Notably, the stability of DCBs for the CSES BDS receiver as well as for BDS GEO, IGSO, and MEO satellites has been significantly enhanced by 70%, 14%, 22%, and 23%, respectively. Conversely, the consistency of GPS satellite DCBs estimated from joint observations shows a decline when compared to the DCB products from the Center for Orbit Determination in Europe (CODE) and the Chinese Academy of Sciences (CAS). When fewer than nine satellites are tracked daily and nighttime observations are under 25%, estimation errors increase. The optimal DCB estimation is achieved with a cutoff elevation angle set at 10°, with monthly mean DCB values for CSES GPS and BDS receivers determined to be −2.193 ns and −1.099 ns, respectively, accompanied by root mean square errors (RMSEs) of 0.10 ns and 0.31 ns. The highest accuracy of DCBs estimated by the single-GPS scheme is corroborated by examining the occurrence of negative vertical total electron content (VTEC) percentages. Full article

Broadcast ephemeris data are essential for the precision and reliability of the BeiDou Navigation Satellite System (BDS) but are highly susceptible to anomalies caused by various interference factors, such as ionospheric and tropospheric effects, solar radiation pressure, and satellite clock biases. Traditional threshold-based methods and manual review processes are often insufficient for detecting these complex anomalies, especially considering the distinct characteristics of different satellite types. To address these limitations, this study proposes an automated anomaly detection method using the IF-TEA-LSTM model. By transforming broadcast ephemeris data into multivariate time series and integrating anomaly score sequences, the model enhances detection robustness through data integrity assessments and stationarity tests. Evaluation results show that the IF-TEA-LSTM model reduces the RMSE by up to 20.80% for orbital parameters and improves clock deviation prediction accuracy for MEO satellites by 68.37% in short-term forecasts, outperforming baseline models. This method significantly enhances anomaly detection accuracy across GEO, IGSO, and MEO satellite orbits, demonstrating its superiority in long-term data processing and its capacity to improve the reliability of satellite operations within the BDS. Full article

The most commonly used real-time augmentation services in China are the International GNSS Service’s (IGS) real-time service (RTS), PPP-B2b service, and Double-Frequency Multi-Constellation (DFMC) service of the BeiDou Satellite-Based Augmentation System (BDSBAS) service. However, research on the performance evaluation, comparison, and application scope of these three products is still incomplete. This article introduces methods for obtaining real-time augmentation information and real-time orbit and clock offset recovery. Based on real-time orbit and clock offset accuracy, positioning accuracy, and positioning availability, this article systematically evaluates the performance and analyzes the application fields of Centre National d’Études Spatiales (CNES), PPP-B2b, and BDSBAS augmentation information. The results of the evaluation revealed that the radial accuracy of the CNES and PPP-B2b real-time orbit product is consistent, and the Root Mean Square (RMS) is better than 5 cm. The CNES real-time orbit product can achieve centimeter-level accuracy in both along-track and cross-track components, surpassing PPP-B2b’s decimeter-level accuracy. Both services demonstrate consistent accuracy in the real-time clock offset, with PPP-B2b showing similar standard deviations (STDs) of 0.16 ns for different satellites. However, for CNES, the STD of the real-time clock offset varies, with values of 0.10 ns, 0.19 ns, and 0.60 ns, respectively, for GPS, BDS-3 Medium Earth Orbit (MEO), and BDS-3 Inclined Geosynchronous Satellite Orbit (IGSO) satellites. Centimeter-level accuracy is achieved after convergence and positioning availability exceeds 99% for CNES and PPP-B2b services. Therefore, the difference between the two services in application areas depends on the acquisition of augmentation information. However, BDSBAS, which concentrates on code observations, demonstrates inferior performance in real-time orbit, clock offset, positioning accuracy, and positioning availability when compared to the other two services. Its primary application is in the aviation and maritime domains, where there is a greater need for service integrity, continuity, and reliability. Full article

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively. Full article

Earth rotation parameters (ERPs) are fundamental to geodetic and astronomical studies. With its high measurement accuracy and stability, the Very Long Baseline Interferometry (VLBI) plays an irreplaceable role in estimating the ERPs and maintaining the earth reference frame. However, the imperfect global station distribution, observation discontinuity, and vast cost of the VLBI make the GNSS a more attractive technique. In 2020, the third generation of the BeiDou Navigation System (BDS), namely BDS-3, was constructed completely. In this study, we conducted a series of experiments to estimate Earth’s rotation parameters based on the continuous BDS-3 observation data, the discontinuous VLBI observation data, and the combined BDS-3 and discontinuous VLBI observation data. We used two methods, namely the weighted averaging method and the normal equation combination method, to obtain ERP combination solutions. The results are compared with the International Earth Rotation and Reference Systems Service (IERS) EOP 20C04 at 00:00:00 UTC. Final results show that (a) the estimation accuracy becomes stable when the number of BDS-3 tracking stations is more than 40. At the same time, both the number of stations and the volume of polyhedrons formed by the observing stations affect the accuracy of the ERPs estimated by the BDS-3 or VLBI. (b) Results have also shown that the inclusion of the BDS-3 IGSO and GEO satellites contributes little to the ERP estimation. (c) For the BDS-3-only MEO satellites solution, the root mean square (RMS) was 113.2 µas, 102.8 µas, and 13.1 µs/day for X-pole coordinate, Y-pole coordinate, and length of day (LOD), respectively. For the VLBI solution, the RMSs of the X-pole, Y-pole, and LOD were 100.4 µas for the X-pole, 94.2 µas for the Y-pole, and 14.1 µs/day. The RMS was 82.6 µas, 70.3 µas, and 10.5 µs/day for the combined X-pole, Y-pole, and LOD using the weighted averaging method. It was 78.2 µas, 62.6 µas, and 8.6 µs/day when the normal equation combination method was applied. This demonstrates that by taking advantage of the BDS-3 and VLBI technique combinations, accuracy in estimating the ERPs can be improved over that using either of them, in addition to enhanced stability and reliability. Full article

The inter-system-like bias between the regional (BDS-2) and global (BDS-3) constellation of the BeiDou Navigation Satellite System (BDS) has been identified on common B1I pseudo-range observations. In this study, its characteristics are investigated with tracking data from the International GNSS Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS) network. Firstly, the satellite-specific inter-system-like bias is calculated and the dependency on satellite is observed. Clearly noticeable discrepancies on BDS-2 and BDS-3 can be identified. Hence, the constellation-specific inter-system-like bias is estimated. Biases for all receivers are quite stable, with standard derivation (STDev) less than 0.2 m in average. The bias shows clear dependence on the receiver, while the firmware and antenna have limited but not negligible impacts, particularly for Trimble NetR9 and Alloy receivers. The Trimble NetR9 with TRM59800.00 antenna shows noticeable discrepancy up to about 1.5 m with different antenna, and the bias of the Trimble Alloy 5.37 jumps about 2.4 m with respect to later firmware. In addition, clear annual variations are observed for stations ABPO and MIZU with Septentrio POLARX5 5.3.2 and ASTERX4 4.4.2 receivers, respectively. Furthermore, the impacts of the biases on the BDS orbit and clock solutions are analyzed. Once BDS-2 and BDS-3 are treated as two independent systems, the root mean square (RMS) of code and carrier phase residuals can be reduced by around 9.3 cm and 0.23 mm, respectively, while the three-dimensional orbit consistency is improved by 6.8%, mainly in the tracking direction. Satellite laser ranging (SLR) shows marginal impacts on IGSO and MEO satellites. However, the SLR residual of C01 shifts −13.2 cm, resulting in a smaller RMS value. In addition, the RMS of linear clock fitting is reduced from 0.050 ns to 0.038 ns for BDS-3 MEO satellites in average. Full article

Differential code bias (DCB) of satellite is an error that cannot be ignored in precise positioning, timing, ionospheric modeling, satellite clock correction, and ambiguity resolution. The completion of the third generation of BeiDou Navigation Satellite System (BDS-3) has extended DCB to multichannel code bias observations and observable-specific signal bias (OSB). In this paper, the DCB and OSB products provided by the Chinese Academy of Sciences (CAS) are analyzed and compared. The DCB parameters for the BDS satellites are applied in both single- and dual-frequency single point positioning (SPP), and the results are intensively investigated. Based on the satellite DCB parameters of the BDS, the performance of precise point positioning (PPP) with different frequency combinations is also analyzed in terms of positioning accuracy and convergence time. The standard deviations (STDs) of DCBs at each signal pair fluctuate from 0.2 ns to 1.5 ns. The DCBs of BDS-2 are slightly more stable than those of BDS-3. The mean values and STDs of C2I and C7I OSBs for BDS-2 are at the same level and are numerically smaller than their counterparts for the C6I OSBs. The mean OSBs for each signal of the BDS-3, excluding C2I, fluctuate between 12.35 ns and 12.94 ns, and the STD fluctuates between 2.11 ns and 3.10 ns. The DCBs and OSBs of the BDS-3 of the IGSO satellites are more stable than those of the MEO satellites. The corrections for TGD and DCB are able to improve the accuracy of single-frequency SPP by 44.09% and 44.07%, respectively, and improve the accuracy of dual-frequency SPP by 6.44% and 12.85%, respectively. The most significant improvements from DCB correction are seen in single-frequency positioning with B1I and dual-frequency positioning with B2a+B3I. DCB correction can improve the horizontal and three-dimensional positioning accuracy of the dual-frequency PPP of different ionosphere-free combinations by 13.53% and 13.84% on average, respectively, although the convergence is slowed. Full article

Multipath error is an important factor restricting the relative positioning accuracy of the Beidou Navigation Satellite System (BDS). Because of the complexity of the reflection environment, the mathematical modeling of multipath errors is quite difficult. The sidereal filtering algorithm corrects multipath errors by using the feature of period repetition, which can greatly reduce its influence and improve the accuracy of positioning and attitude measurement. In view of the constellation heterogeneity of BDS, it is more complicated to apply sideral filtering. Based on the reconstructed single-difference residual of the carrier phase, the multipath repetition time of the Beidou satellite is estimated using the idea of segmentation. The Tikhonov regularization method and the classical wavelet method are used to extract the multipath of the single-difference residual of the carrier phase, and the “clean” sequence of the single-difference residual is obtained. The experimental results show that it is feasible to extract the multipath error correctly by Tikhonov regularization, and the multipath error is smoother than the original residual measurement. Furthermore, the estimation method of the regularization parameter is further optimized. After using the optimized Tikhonov regularization method with sidereal filtering, the mean RMS improvements of GEO, IGSO, and MEO satellites are 45.9%, 38.2%, and 37.5%, respectively. The positioning accuracy on E, N, and U components is improved by 24.8%, 26.3%, and 42.7%, respectively. The attitude resolution accuracy is improved by 22.9% in the yaw angle and 12.6% in the pitch angle. The proposed method can be an alternative BDS multipath error modeling and mitigation approach. Full article

The official launch of the Chinese BeiDou Navigation Satellite System with global coverage (BDS-3) presents significant opportunities for various applications, including precision agriculture and autonomous driving, among others. With its global spatial coverage and hybrid space constellation comprising geosynchronous Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO) satellites, BDS can significantly contribute to various GNSS remote sensing applications that require real-time, precise water surface height measurements with high temporal and spatial resolution, such as in tidal monitoring. In this paper, we propose a carrier-phase-based method for BDS Reflectometry (BDS-R) to precisely retrieve real-time water surface height. Firstly, the BDS-R altimetry method is introduced, along with a detailed explanation of the data processing procedures. Secondly, a quality control method tailored to the characteristics of low-cost BDS devices is developed. Thirdly, a land altimetry experiment is conducted to evaluate the precision of BDS-R and analyze the specific contribution of the BDS hybrid constellation. Finally, a water surface altimetry experiment validates the real-time monitoring capabilities for low-cost BDS-R. The results indicate that low-cost BDS-R can achieve real-time centimeter-level water level monitoring with a temporal resolution of 1 s in lakefront environments. The performance of BDS-R can be significantly improved by the BDS hybrid constellation, particularly IGSOs. It is concluded that low-cost BDS-R has great potential for promoting ground-based GNSS remote sensing applications. Full article

As an essential infrastructure that provides positioning, navigation, and timing services, China constructed the BeiDou Navigation Satellite System (BDS). The last BDS satellite was launched in June 2020, which represents the completion of BDS. BDS’s constellation consists of Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and Geostationary Orbit satellites. The precise modeling of non-conservative forces for BDS satellites is a challenging task. As an independent observation, Satellite Laser Ranging (SLR) is an important validation method of GNSS orbit modeling. In this paper, we validated the precise orbit products of different Analysis Centers (ACs) by using SLR observations, focusing on the BDS orbit modeling. By comparing BDS precise orbit products generated by four ACs with respect to SLR observations for the period of February 2017 to March 2021, we proved that an obvious satellite signature effect exists in the SLR residuals of BDS observed by multi-photon stations. The result indicates that multi-photon stations have a root mean square (RMS) of SLR residuals about 5 mm lower than that of single-photon detectors. The slope of SLR residuals with regard to nadir angle of IGSO satellites for single-photon and multi-photon stations is −2.0 and −2.5 mm/deg, respectively, while the slope of MEO satellites for these stations is about −0.6 to −0.3 and −1.0 to −0.4 mm/deg, respectively. To assess the effect of non-conservative force modeling, we selected seven high-performing stations, including five single-photon and two multi-photon stations. By comparing the SLR residuals of four ACs’ orbits, we analyzed the effect of the solutions of orbit processing, especially solar radiation pressure (SRP) models. We found that some centers may have modeling defects, including BDS-3 orbits of the Deutsches GeoForschungsZentrum and BDS-2 orbits of the European Space Agency, inferred from the large RMS of SLR residuals. Modeling the SRP of BDS satellites is challenging, while an appropriate prior box-wing model can improve the accuracy of SRP modeling and provide a more stable performance. Full article

The orbit maneuver detection is crucial in Global Navigation Satellite System (GNSS) precise orbit determination, which is necessary for adjusting data processing strategies. The frequency of orbit maneuvers for the BeiDou Navigation System is significantly higher than that of other navigation systems, especially for geosynchronous orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. We propose a novel real-time and postprocessing method for detecting orbit maneuvers for BeiDou satellites based on the orbit differences between the epoch-updated orbit estimated using square root information (SRIF) and the predicted orbit according to the precise orbit estimated during non-maneuver period, as well as the orbital state difference during maneuver and non-maneuver periods. This method has significant advantages over using observation residuals and it is not affected by observation outliers, thus improving the accuracy and timeliness of orbit maneuver detection. We demonstrated that 32 orbit maneuver events of BeiDou satellites were successfully detected in 2022, of which 1 was for medium Earth orbit (MEO), 7 were for IGSO with an average detected maneuvering time of 7–8 min, and 24 were for GEO satellites with an average detected time of 4–5 min. Moreover, our method can be easily integrated into current real-time filter-based precise orbit determination (POD) processing without any extra task line, which simplifies the overall data processing. The data used in this method can be accessed easily, including GNSS observation data, broadcast ephemeris, and other open-source information files. Full article

As the first hybrid-constellation global navigation system, China’s BeiDou navigation satellite system (BDS) has been fully constructed since July 2020 and provides open services for worldwide users. Due to the natural sensitivity of satellite tracking techniques to geocenter motion, BDS has the capability to determine the geocenter coordinates (GCC). This study aims to improve the precision of geocenter coordinates derived from BDS. To that end, 3-year sets of daily geocenter coordinates have been determined with BDS observations. Different solar radiation pressure (SRP) models, including the empirical CODE orbit model (ECOM), the extended ECOM model (ECOM2), and the a priori box-wing along with the ECOM model (BW + ECOM), have been applied for the BDS geocenter estimation. We show that the BW + ECOM model is beneficial in recovering the geocenter motion. Compared to the ECOM, the BW + ECOM model appears to mitigate the draconitic signal of BDS, which reduces the annual amplitude of the GCC-Z by a factor of 2.9. On the other hand, the amplitude of the 3 cpy signal is also reduced by a factor of 2.9. Furthermore, we studied the impact of BDS constellation configuration on the geocenter estimation. The results indicate that the inclusion of IGSO satellites significantly mitigates the spurious signals in the spectra of the GCC-Z. The amplitudes of the annual signal and 3 cpy signal are reduced by (28%, 14%), (33%, 61%), and (31%, 9%) for ECOM, ECOM2, and BW + ECOM cases, respectively. Meanwhile, the amplitude of the 7-day signal related to the orbital period of MEO satellites is also reduced by 32–45%. Thus, the BW + ECOM model and the MEO+IGSO hybrid configuration are recommended for BDS to determine the geocenter coordinates. However, despite these improvements, a significant annual signal with an amplitude of 20.2 mm and a visible 3 cpy signal with an amplitude of 6.1 mm still exist when compared to the Satellite Laser Ranging (SLR) solution. Full article

The precise point positioning service on B2b signal (PPP-B2b) is a real-time decimeter-level positioning service provided by the BeiDou-3 Global Navigation Satellite System (BDS-3). The service provides users with high-precision orbit and clock corrections through geostationary orbit (GEO) satellites, which means that the PPP-B2b service would be unusable if GEO satellites were blocked. In this study, the performance of PPP-B2b corrections and real-time positioning results during outages of the PPP-B2b service are comprehensively investigated. The results showed that PPP can achieve satisfactory accuracy during outages of the PPP-B2b service by extending the nominal validity of the received PPP-B2b corrections. After extending the PPP-B2b corrections for 10 min, for BDS-3 medium earth orbit (MEO) satellites, the mean root-mean-square error (RMSE) values of the extended orbit were 0.16 m, 0.26 m, and 0.23 m in the radial, along-, and cross-track directions, respectively. The accuracy of the BDS-3 inclined geostationary orbit (IGSO) satellites was slightly worse than that of the BDS-3 MEO satellites; for Global Positioning System (GPS) satellites, the mean RMSE values of the extended orbit were 0.11 m, 0.45 m, and 0.33 m in the radial, along-, and cross-track directions, respectively. In terms of the extended clock, the mean standard deviation (STD) reached 0.17 ns, 0.20 ns, and 0.22 ns after 10 min for the BDS-3 MEO, BDS-3 IGSO, and GPS satellites, respectively. The positioning performance maintained with the extended corrections during the PPP-B2b service outage was evaluated based on five stations in and around China. Our experiments showed that, as long as the interruption time does not exceed 10 min, the real-time positioning with extended PPP-B2b corrections can achieve a comparable accuracy with that obtained following PPP-B2b correction. Full article

The BeiDou Global Satellite Navigation System (BDS-3) broadcast newly developed B1C and B2a signals. To provide a better service for global users, the vertical phase center offset (PCO) and phase center variation (PCV) are estimated for the B1C/B2a ionospheric-free linear combination of the BDS-3 inclined geostationary orbit (IGSO) and medium earth orbit (MEO) satellites in this study. And considering the traditional PCC estimation method needs two Precise orbit determination (POD) processing, based on the correlation between PCO z-offset and PCV, the theoretical analysis and experimental comparison have been made to discuss whether the POD procedure for the PCO estimation can be omitted. The estimated z-offset time series revealed the inadequacy of the solar radiation pressure (SRP) model for the IGSO satellites and the MEO satellites with Pseudo Random Noise code (PRN) C45 and C46. The PCVraws estimated by the traditional method and the PCO estimation omitted method have the same characteristic. The final PCO z-offsets and PCVs calculated by the two schemes agreed very well with differences can be harmlessly ignored, which confirmed that the PCO estimation can be safely omitted to save computation time. The PCC model proposed in this study has been compared with the Test and Assessment Research Center of China Satellite Navigation Office (TARC/CSNO) released model, the qualities of the orbits and BDS-only precise point positioning (PPP) solutions of the new model both show improvements, except for the IGSO orbits. The analysis of the IGSO orbits further verifies the SRP model is not suitable for the IGSO satellites. Full article