Search Results (96)

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

Conducting surveys and the timely acquisition of satellite status, especially for high-value geostationary orbit (GEO) targets, is of great significance for space traffic management. This article proposes an approach for patrolling inclined geosynchronous orbit (IGSO) targets based on crossing points and spiral rings. The method involves six steps: (1) calculate the crossing position and crossing time of the IGSO targets; (2) design a spiral trajectory that satisfies the desired patrol time; (3) divide IGSO targets into regions using a dichotomy approach; (4) calculate the bidirectional longitude drift rate within each region; (5) determine the starting position of patrol for each region; and (6) determine the transfer trajectory for each region. By selecting a class of IGSO satellites as the target set, the proposed approach is analyzed and validated in detail. The results show that the patrol orbit can effectively achieve patrol all of IGSO targets, with a period of no more than 40 days and less than 13.5 kg fuel consumption. The total fuel consumption of a single patrol cycle in all regions does not exceed 91.82 kg. 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 geostationary earth orbit (GEO) represents a distinctive geosynchronous orbit situated in the Earth’s equatorial plane, providing an excellent platform for long-term monitoring of ionospheric total electron content (TEC) at a quasi-invariant ionospheric pierce point (IPP). With GEO satellites having limited dual-frequency coverage, the inclined geosynchronous orbit (IGSO) emerges as a valuable resource for ionospheric modeling across a broad range of latitudes. This article evaluates satellite differential code biases (DCB) of BDS high-orbit satellites (GEO and IGSO) and assesses regional ionospheric modeling utilizing data from international GNSS services through a refined polynomial method. Results from a 48-day observation period show a stability of approximately 2.0 ns in BDS satellite DCBs across various frequency signals, correlating with the available GNSS stations and satellites. A comparative analysis between GEO and IGSO satellites in BDS2 and BDS3 reveals no significant systematic bias in satellite DCB estimations. Furthermore, high-orbit BDS satellites exhibit considerable potential for promptly detecting high-resolution fluctuations in vertical TECs compared to conventional geomagnetic activity indicators like Kp or Dst. This research also offers valuable insights into ionospheric responses over mid-latitude regions during the March 2024 geomagnetic storm, utilizing TEC estimates derived from BDS GEO and IGSO satellites. Full article

Equatorial plasma bubbles (EPBs) occur frequently in low-latitude areas and have a non-negligible impact on navigation satellite signals. To systematically analyze the effects of a single EPB event on multi-frequency signals of GPS, Galileo, GLONASS, and BDS, all-sky airglow images over South China are jointly used to visually determine the EPB structure and depletion degree. The results reveal that scintillations, or GNSS signal fluctuations, are directly linked to EPBs and that the intensity of scintillation is positively correlated with the airglow depletion intensity. The center of the airglow depletion often corresponds to stronger GNSS scintillation, while the edge of the bubble, which is considered to have the largest density gradient, corresponds to relatively smaller scintillation instead. This work also systematically analyzes the responses of multi-constellation and multi-frequency signals to EPBs. The results show that the L2 and L5 frequencies are more susceptible than the L1 frequency is. For different constellations, Galileo’s signal has the best tracking stability during an EPB event compared with GPS, GLONASS, and BDS. The results provide a reference for dual-frequency signal selection in precise positioning or TEC calculation, that is, L1C and L2L for GPS, L1C and L5Q for Galileo, L1P and L2C for GLONASS, and L1P and L5P for BDS. Notably, BDS-2 is significantly weaker than BDS-3. And inclined geosynchronous orbit (IGSO) satellites have abnormal data error rates, which should be related to the special signal path trajectory of the IGSO satellite. 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

Satellite clock error is a key factor affecting the positioning accuracy of a global navigation satellite system (GNSS). In this paper, we use a gated recurrent unit (GRU) neural network to construct a satellite clock bias forecasting model for the BDS-3 navigation system. In order to further improve the prediction accuracy and stability of the GRU, this paper proposes a satellite clock bias forecasting model, termed ITSSA-GRU, which combines the improved sparrow search algorithm (SSA) and the GRU, avoiding the problems of GRU’s sensitivity to hyperparameters and its tendency to fall into local optimal solutions. The model improves the initialization population phase of the SSA by introducing iterative chaotic mapping and adopts an iterative update strategy based on t-step optimization to enhance the optimization ability of the SSA. Five models, namely, ITSSA-GRU, SSA-GRU, GRU, LSTM, and GM(1,1), are used to forecast the satellite clock bias data in three different types of orbits of the BDS-3 system: MEO, IGSO, and GEO. The experimental results show that, as compared with the other four models, the ITSSA-GRU model has a stronger generalization ability and forecasting effect in the clock bias forecasting of all three types of satellites. Therefore, the ITSSA-GRU model can provide a new means of improving the accuracy of navigation satellite clock bias forecasting to meet the needs of high-precision positioning. 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

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

Positioning services based on GNSS (Global Navigation Satellite Systems) have been using MEO satellites designed to guarantee Earth global coverage for decades. This satellite distribution is sometimes complemented with satellites in Inclined Geosynchronous (IGSO) and Geostationary (GEO) Orbits to improve satellite visibility in particular service areas. During recent years, with the advancements and reduction in costs in the deployment of LEO (Low Earth Orbit) constellations, the opportunity of using LEO satellites for PNT (Positioning, Navigation, and Timing) solutions is being studied. This concept opens the possibility to provide high accuracy positioning overcoming the typical drawbacks of RTK (Real-Time Kinematics) or PPP (Precise Point Positioning), such as the need for ground infrastructure or long convergence times. The high velocity dynamics of the low orbits can help to cancel the effect of the ionosphere in the signals to be processed at the user level. Therefore, the introduction of LEO satellites together with the classical MEO GNSS constellations could be a solution to reduce the dependency on dense station networks. The size of the LEO constellations and the design of their orbits are key factors to improve the PPP solution. Moreover, both the accuracy and the convergence time of the PPP solution depend also on the quality of the on-board equipment of the satellite, especially on the quality of the atomic clock in terms of stability and noise, and on the quality of the orbit and clock corrections sent to the PPP users. GMV has decades of experience in both GNSS and LEO precise orbit determination (POD) fields and in high-accuracy GNSS applications for different market domains. With this experience, several analyses have been carried out to assess the achievable performance when introducing the processing of LEO signals for high accuracy positioning solutions, contributing to the overall GNSS community. The objective of this paper is to describe the analysis run by GMV with the use of synthetic data simulating GNSS and LEO signals, showing results and the associated assessment of the achievable performance. 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

The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by applying the double difference observation model. In the actual monitoring environment, due to the complexity of the BDS constellation, it is difficult for existing algorithms to consider GEO, IGSO, MEO and other different orbital types of satellites for real-time and efficient multipath error reduction. Therefore, we propose a novel BDS dual-frequency multipath error reduction method for real deformation monitoring for BDS considering various satellite orbit types. This method extracts the single error residual of each satellite based on the assumption of “zero mean” and divides the appropriate grid density of GEO and IGSO/MEO, respectively, to construct a dual-frequency multipath hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multipath error elimination of the observed values of different orbits and different frequencies. The results of simulation experiments and real deformation monitoring data demonstrate that this method can effectively eliminate low-frequency multipath delay errors in the observation domain and coordinate domain. After multipath correction, the precision of the horizontal coordinates and height coordinates are 1.7 mm and 4.6 mm. The precision of the horizontal coordinate and height coordinate is increased by 50% and 60%, respectively. The fixed rate of ambiguity increased by 5–7%. Full article