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Keywords = BDS-3 MEO

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19 pages, 3553 KiB  
Article
Research on the Autonomous Orbit Determination of Beidou-3 Assisted by Satellite Laser Ranging Technology
by Wei Xiao, Zhengcheng Wu, Zongnan Li, Lei Fan, Shiwei Guo and Yilun Chen
Remote Sens. 2025, 17(14), 2342; https://doi.org/10.3390/rs17142342 - 8 Jul 2025
Viewed by 347
Abstract
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 [...] Read more.
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
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17 pages, 3801 KiB  
Article
Solar Radiation Pressure Modeling and Validation for BDS-3 MEO Satellites
by Qiuli Chen, Xu Zhang, Chen Wang, Haihong Wang, Chen Ren, Fujian Ma and Xinglong Zhao
Remote Sens. 2025, 17(6), 1068; https://doi.org/10.3390/rs17061068 - 18 Mar 2025
Viewed by 589
Abstract
The solar radiation pressure (SRP) model, as a key factor affecting the precise orbit determination (POD) accuracy of navigation satellites, is related to the state and optical properties of the satellite surface. This study establishes a high-precision SRP model for BDS-3 medium earth [...] Read more.
The solar radiation pressure (SRP) model, as a key factor affecting the precise orbit determination (POD) accuracy of navigation satellites, is related to the state and optical properties of the satellite surface. This study establishes a high-precision SRP model for BDS-3 medium earth orbit (MEO) satellites manufactured by the China Academy of Space Technology based on the satellite engineering parameters, which comprises the satellites’ size and optical properties measured before launch. Then, the physical-based SRP model is re-constructed into the body-fixed coordinate as the function of the Sun elongation angle. The use of the hybrid SRP model, combining the reconstructed SRP model and the 5-parameter ECOM, results in a better POD performance. The orbit results, validated using satellite laser ranging (SLR) observations, show that the radial precision of approximately 3–4 cm can be achieved, with a reduction of the bias by up to 38% and a removal of the systematic error related to the Sun elongation angle in SLR residuals. Considering the possible degradation of the reconstructed SRP model with the engineering parameters, the evolution of SRP accelerations along with orbit quality based on a time series from over 5 years was studied. The results indicate that a variation of the total SRP acceleration for the BDS-3 satellites is minor and there is no apparent degradation in validations of 2019–2023, which proved the reliability and usability of the proposed SRP model for the BDS-3 MEO satellites. Full article
(This article belongs to the Special Issue BDS/GNSS for Earth Observation: Part II)
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20 pages, 4377 KiB  
Article
Improving BeiDou Global Navigation Satellite System (BDS-3)-Derived Station Coordinates Using Calibrated Satellite Antennas and Station Inter-System Translation Parameters
by Tao Zhang, Shiwei Guo, Lei Fan and Chuang Shi
Remote Sens. 2025, 17(3), 510; https://doi.org/10.3390/rs17030510 - 31 Jan 2025
Viewed by 835
Abstract
The BeiDou global navigation satellite system (BDS-3) has been widely applied in various geodetic applications since its full operation. However, the estimated station coordinates using BDS-3 are less precise compared to GPS results. It contains systematic errors caused by scale bias with respect [...] Read more.
The BeiDou global navigation satellite system (BDS-3) has been widely applied in various geodetic applications since its full operation. However, the estimated station coordinates using BDS-3 are less precise compared to GPS results. It contains systematic errors caused by scale bias with respect to International GNSS Service (IGS) 2020 frame and Inter-System Translation Parameters (ISTPs). In order to improve the consistency of BDS-3-derived station coordinates with respect to IGS20 products, we firstly estimated the satellite antenna Phase Center Offsets (PCOs) for BDS-3 Medium Earth Orbit (MEO) constellation, and then estimated station-specific ISTPs from GPS to BDS-3 systems. The results indicate that the PCO-Z estimates show large differences among satellites from different manufacturers and orbit planes. The estimated BDS-3 satellite PCOs exhibit a systematic bias of −9.3 cm in the Z-direction compared to ground calibrations. The maximum mean station-specific ISTPs can reach up to 3 mm, highlighting significant variability and the need for refinement in positioning. When using the estimated PCOs instead of igs20.atx values, the estimated scale bias with respect to the IGS20 frame is reduced from 0.38 ppb to −0.12 ppb, indicating that the refined BDS-3 satellite PCOs are well compatible with IGS20. Regarding the Up component that is correlated with the scale factor, the station coordinate differences with respect to the IGS20 frame is reduced from 7.0 mm to 6.2 mm in terms of the root mean square (RMS), which is improved by 11.4%. Considering the additional ISTP corrections, a further improvement of 17% was obtained in station coordinates. The RMS of station coordinate differences with respect to the IGS20 frame is 2.3 mm, 2.7 mm, and 5.2 mm for the North, East, and Up components, respectively. Full article
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19 pages, 8948 KiB  
Article
Differential Code Bias Estimation and Accuracy Analysis Based on CSES Onboard GPS and BDS Observations
by Jiawen Pang, Fuying Zhu and Shang Wu
Remote Sens. 2025, 17(3), 374; https://doi.org/10.3390/rs17030374 - 23 Jan 2025
Viewed by 959
Abstract
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 [...] Read more.
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
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27 pages, 36855 KiB  
Article
Evaluation and Anomaly Detection Methods for Broadcast Ephemeris Time Series in the BeiDou Navigation Satellite System
by Jiawei Cai, Jianwen Li, Shengda Xie and Hao Jin
Sensors 2024, 24(24), 8003; https://doi.org/10.3390/s24248003 - 14 Dec 2024
Cited by 1 | Viewed by 1635
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation)
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18 pages, 9065 KiB  
Article
Modeling of Solar Radiation Pressure for BDS-3 MEO Satellites with Inter-Satellite Link Measurements
by Yifei Lv, Zihao Liu, Rui Jiang and Xin Xie
Remote Sens. 2024, 16(20), 3900; https://doi.org/10.3390/rs16203900 - 20 Oct 2024
Cited by 2 | Viewed by 1430
Abstract
As the largest non-gravitational force, solar radiation pressure (SRP) causes significant errors in precise orbit determination (POD) of the BeiDou global navigation satellite system (BDS-3) medium Earth orbit (MEO) satellite. This is mainly due to the imperfect modeling of the satellite’s cuboid body. [...] Read more.
As the largest non-gravitational force, solar radiation pressure (SRP) causes significant errors in precise orbit determination (POD) of the BeiDou global navigation satellite system (BDS-3) medium Earth orbit (MEO) satellite. This is mainly due to the imperfect modeling of the satellite’s cuboid body. Since the BDS-3’s inter-satellite link (ISL) can enhance the orbit estimation of BDS-3 satellites, the aim of this study is to establish an a priori SRP model for the satellite body using 281-day ISL observations to reduce the systematic errors in the final orbits. The adjustable box wind (ABW) model is employed to refine the optical parameters for the satellite buses. The self-shadow effect caused by the search and rescue (SAR) antenna is considered. Satellite laser ranging (SLR), day-boundary discontinuity (DBD), and overlapping Allan deviation (OADEV) are utilized as indicators to assess the performance of the a priori model. With the a priori model developed by both ISL and ground observation, the slopes of SLR residual for the China Academy of Space Technology (CAST) and Shanghai Engineering Center for Microsatellites (SECM) satellites decrease from −0.097 cm/deg and 0.067 cm/deg to −0.004 cm/deg and −0.009 cm/deg, respectively. The standard deviation decreased by 21.8% and 26.6%, respectively. There are slight enhancements in the average values of DBD and OADEV, and a reduced β-dependent variation is observed in the OADEV of the corresponding clock offset. We also found that considering the SAR antenna only slightly improves the orbit accuracy. These results demonstrate that an a priori model established for the BDS-3 MEO satellite body can reduce the systematic errors in orbits, and the parameters estimated using both ISL and ground observation are superior to those estimated using only ground observation. Full article
(This article belongs to the Special Issue GNSS Positioning and Navigation in Remote Sensing Applications)
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17 pages, 5448 KiB  
Article
Orbit Determination Method for BDS-3 MEO Satellites Based on Multi-Source Observation Links
by Jie Xin and Kai Li
Remote Sens. 2024, 16(19), 3702; https://doi.org/10.3390/rs16193702 - 4 Oct 2024
Cited by 1 | Viewed by 1303
Abstract
Research on augmentation and supplement systems for navigation systems has become a significant aspect in comprehensive positioning, navigation and timing (PNT) studies. The BeiDou-3 navigation satellite system (BDS-3) has constructed a dynamic inter-satellite network to gain more observation data than ground monitoring stations. [...] Read more.
Research on augmentation and supplement systems for navigation systems has become a significant aspect in comprehensive positioning, navigation and timing (PNT) studies. The BeiDou-3 navigation satellite system (BDS-3) has constructed a dynamic inter-satellite network to gain more observation data than ground monitoring stations. Low Earth orbit (LEO) satellites have advantages in their kinematic velocity and information carrying rate and can be used as satellite-based monitoring stations for navigation satellites to make up for the distribution limitation of ground monitoring stations. This study constructs multi-source observation links with satellite-to-ground, inter-satellite and satellite-based observation data, proposes an orbit synchronization method for navigation satellites and LEO satellites and verifies the influence thereof on orbit accuracy with different observation data. The experimental results under conditions of real and simulated observation data showed the following: (1) With the support of satellite-based observation links, the orbit accuracy of the BDS-3 MEO satellites could be improved significantly, with a 78% improvement with the simulation data and a 76% improvement with the real data. When the navigation satellites leave the monitoring area of the ground monitoring stations, the accuracy reduction tendency of the orbit prediction could also be slowed down with the support of the LEO satellites and the accuracy could be maintained within centimeters. (2) Comparing the orbit accuracy with the support of the satellite-to-ground observation links, the orbit accuracy of the MEO satellites could be improved by 65.5%, 73.7% and 79.4% with the support of the 6, 12 and 60 LEO satellites, respectively. When the observation geometry and the covering multiplicity meet the basic requirement of orbit determination, the improvements to the orbit accuracy decrease with the growth of LEO satellite numbers. (3) The accuracy of orbit determination with the support of the LEO satellites or the inter-satellite links was at the centimeter level for both, verifying that inter-satellite links and satellite-based links can be used as each other’s backups for navigation satellites. (4) The accuracy of orbit determination with the multi-source observation links was also at the centimeter level, which was not better than the results with the support of the satellite-to-ground and inter-satellite links or the satellite-to-ground and satellite-based links. Full article
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20 pages, 3230 KiB  
Article
SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits
by Ran Li, Chen Wang, Hongyang Ma, Yu Zhou, Chengpan Tang, Ziqian Wu, Guang Yang and Xiaolin Zhang
Remote Sens. 2024, 16(11), 2016; https://doi.org/10.3390/rs16112016 - 4 Jun 2024
Cited by 3 | Viewed by 1228
Abstract
Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing [...] Read more.
Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing a basis for comprehensive evaluation of the BDS-3 satellite orbit. We utilized the SLR data from February to May 2023 to comprehensively evaluate the orbits of BDS-3 MEO satellites from different analysis centers (ACs). The results show that, whether during the eclipse season or the yaw maneuver season, the accuracy was not significantly decreased in the BDS-3 MEO orbit products released from the Center for Orbit Determination in Europe (CODE), Wuhan University (WHU), and the Deutsches GeoForschungsZentrum (GFZ) ACs, and the STD (Standard Deviation) of SLR residuals of those three ACs are all less than 5 cm. Among these, CODE had the smallest SLR residuals, with 9% and 12% improvement over WHU and GFZ, respectively. Moreover, the WHU precise orbits exhibit the smallest systematic biases, whether during non-eclipse seasons, eclipse seasons, or satellite yaw maneuver seasons. Additionally, we found some BDS-3 satellites (C32, C33, C34, C35, C45, and C46) exhibit orbit errors related to the Sun elongation angle, which indicates that continued effort for the refinement of the non-conservative force model further to improve the orbit accuracy of BDS-3 MEO satellites are in need. Full article
(This article belongs to the Special Issue Space-Geodetic Techniques (Third Edition))
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18 pages, 11941 KiB  
Article
Performance Evaluation and Application Field Analysis of Precise Point Positioning Based on Different Real-Time Augmentation Information
by Mengjun Wu, Le Wang, Wei Xie, Fan Yue and Bobin Cui
Remote Sens. 2024, 16(8), 1349; https://doi.org/10.3390/rs16081349 - 11 Apr 2024
Cited by 6 | Viewed by 1522
Abstract
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 [...] Read more.
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
(This article belongs to the Section Engineering Remote Sensing)
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21 pages, 12261 KiB  
Article
Earth Rotation Parameters Derived from BDS-3 New Signals B1C/B2a Dual-Frequency Combination Observations
by Zhenlong Fang, Tianhe Xu, Wenfeng Nie, Yuguo Yang and Min Li
Remote Sens. 2024, 16(8), 1322; https://doi.org/10.3390/rs16081322 - 9 Apr 2024
Viewed by 1555
Abstract
The Earth rotation parameters (ERP) play a crucial role in defining the global reference frame and the Global Navigation Satellite System (GNSS) is one of the important tools used to obtain ERP, including polar motion (PM), its rates, and length of day (LOD). [...] Read more.
The Earth rotation parameters (ERP) play a crucial role in defining the global reference frame and the Global Navigation Satellite System (GNSS) is one of the important tools used to obtain ERP, including polar motion (PM), its rates, and length of day (LOD). The latest IGS Repro3 ERP products, which provided the IGS contribution to the latest ITRF2020, were generated without consideration of the Beidou Navigation Satellite System (BDS) observations. The global BDS, namely the BDS-3 constellation, has been completely constructed from July 2020 and the observing stations are evenly distributed globally now. Two couple dual-frequency combinations, including the B1I/B3I and B1C/B2a combinations, are commonly used for BDS-3 ionosphere-free combination usage. With the goal of identifying the optimal dual-frequency combination for BDS-3 ERP estimates for the future ITRF definition with a consideration of BDS-3, this research evaluated the performance of ERP estimation using B1I/B3I and B1C/B2a combinations. Firstly, we conducted a comparison of the ambiguity resolutions. The mean percentage of successfully resolved ambiguities for the BDS-3 B1C/B2a combination is 86.5%, surpassing that of B1I/B3I. The GNSS satellite orbits and ERP were estimated simultaneously, thus the accuracy of orbits could also reflect the performance of the ERP estimates. Subsequently, we validated the orbits of 22 BDS-3 Medium Earth Orbit (MEO) satellites using Satellite Laser Ranging (SLR), and the root mean square error (RMS) of the SLR residuals for the 3-day arc orbit with B1C/B2a signals was 5.72 cm, indicating superior accuracy compared with the B1I/B3I combination. Finally, we compared the performance of ERP estimation, considering both internal and external accuracy. For the internal accuracy, B1C/B2a-based solutions demonstrated a reduction in mean formal errors of approximately 17% for PM, 22% for LOD, and 21% for PM rates compared with B1I/B3I-based solutions. In terms of external accuracy, we compared BDS-3-derived ERP estimates with the IERS 20C04 products. The B1C/B2a combination exhibited a slightly better standard deviation performance and a significant reduction in mean bias by 56%, 54%, 39%, 64%, and 23% for X, Y polar motion, X, Y polar motion rates, and LOD, respectively, compared with B1I/B3I solutions. In conclusion, the results highlight the excellent signal quality for BDS-3 B1C/B2a and its superiority in ERP estimation when compared with the B1I/B3I combination. Full article
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21 pages, 2810 KiB  
Article
Investigating the Global Performance of the BDS-2 and BDS-3 Joint Real-Time Undifferenced and Uncombined Precise Point Positioning Using RTS Products from Different Analysis Centers
by Ahao Wang, Yize Zhang, Junping Chen, Hu Wang, Tianning Luo, Mingyou Gong and Quanpeng Liu
Remote Sens. 2024, 16(5), 788; https://doi.org/10.3390/rs16050788 - 24 Feb 2024
Cited by 1 | Viewed by 1227
Abstract
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 [...] Read more.
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
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24 pages, 1819 KiB  
Article
Improved SSA-Based GRU Neural Network for BDS-3 Satellite Clock Bias Forecasting
by Hongjie Liu, Feng Liu, Yao Kong and Chaozhong Yang
Sensors 2024, 24(4), 1178; https://doi.org/10.3390/s24041178 - 11 Feb 2024
Cited by 6 | Viewed by 1820
Abstract
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. [...] Read more.
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
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12 pages, 5013 KiB  
Communication
SISRE of BDS-3 MEO: Evolution as Well as Comparison between D1 and B-CNAV (B-CNAV1, B-CNAV2) Navigation Messages
by Zhenghua Dong and Songlin Zhang
Remote Sens. 2024, 16(3), 484; https://doi.org/10.3390/rs16030484 - 26 Jan 2024
Cited by 3 | Viewed by 1754
Abstract
The signal-in-space range error (SISRE) has a direct impact on the performance of global navigation satellite systems (GNSSs). It is an important indicator of navigation satellite space server performance. The new B-CNAV navigation messages (B-CNAV1 and B-CNAV2) are broadcast on the satellites of [...] Read more.
The signal-in-space range error (SISRE) has a direct impact on the performance of global navigation satellite systems (GNSSs). It is an important indicator of navigation satellite space server performance. The new B-CNAV navigation messages (B-CNAV1 and B-CNAV2) are broadcast on the satellites of the Beidou Global Navigation Satellite System (BDS-3), and they are different from D1 navigation messages in satellite orbit parameters. The orbit accuracy of B-CNAV navigation messages lacks analyses and comparisons with D1. The accuracy and stability of the new hydrogen and rubidium clocks on BDS-3 satellites need annual analyses of long time series, which will affect the service quality of this system. Based on precise ephemeris products from the Center for Orbit Determination in Europe (COD), the orbit error, clock error, and SISRE of 24 medium Earth orbit (MEO) satellite D1 and B-CNAV navigation messages of BDS-3 were computed, analyzed, and compared. Their annual evolution processes for the entire year of 2022 were studied. Thanks to the use of inter-satellite links (ISLs) adopted by BDS-3 MEO satellites, the ages of the ephemeris are accurate and the percent of ages of data, ephemerides (AODEs), and ages of data and clocks (AODCs) shorter than 12 h were 99.95% and 99.96%, respectively. In addition, the broadcast orbit performance was also improved by ISLs. The root mean square (RMS) values of the BDS-3 MEO broadcast ephemeris orbit error were 0.067 m, 0.273 m, and 0.297 m in the radial, cross, and along directions, respectively. Moreover, the 3D RMS value was 0.450 m. Thanks to the use of new orbit parameters in the B-CNAV navigation messages of BDS-3 MEO, its satellite orbit accuracy was obviously better than that of D1 in the radial direction. Its improved accuracy can reach up to about 1.2 cm, and the percentage of its accuracy improvement was about 19.06%. With respect to clock errors, the timescale differences between the two clock products were eliminated to assess the accuracy of broadcasting ephemeris clock errors. A standard deviation value of 0.256 m shows good performances as a result of the use of the two new types of atomic clocks, although the RMS value was 0.541 m due to a nonzero mean bias. Overall, the accuracy of atomic clocks was good. For the new hydrogen and rubidium atomic clocks, their RMS and standard deviation were 0.563 m and 0.231 m and 0.519 m and 0.281 m, respectively. The stability of the former was better than that of the latter. However, due to the nonzero mean bias the latter was better than the former in accuracy. The RMS value of the SISRE of BDS-3 MEO’s broadcast ephemeris was 0.556 m, and the value was 0.920 m when it had a 95% confidence level. In contrast, after deducting the influence of the clock error, the value of SISRE_ORB was 0.092 m. Since the satellite clock error was substantially larger than the orbit radial error, the SISRE was mainly affected by the clock error, and their annual evolutions were consistent. Because of the improvement to the B-CNAV’s navigation message with respect to orbit radial accuracy, SISRE_ORB has improved in accuracy. Compared to D1, it had a significant effect on improving the accuracy of SISRE_ORB, and the percentage of the accuracy improvement was 8.40%. Full article
(This article belongs to the Special Issue Remote Sensing in Space Geodesy and Cartography Methods II)
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20 pages, 4355 KiB  
Article
Estimation of Earth Rotation Parameters Based on BDS-3 and Discontinuous VLBI Observations
by Chenxiang Wang, Jizhang Sang, Xingxing Li and Pengfei Zhang
Remote Sens. 2024, 16(2), 333; https://doi.org/10.3390/rs16020333 - 14 Jan 2024
Cited by 2 | Viewed by 1802
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Space-Geodetic Techniques II)
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19 pages, 6515 KiB  
Article
Characteristics of Inter-System Bias between BDS-2 and BDS-3 and Its Impact on BDS Orbit and Clock Solutions
by Xiaolong Xu and Zhan Cai
Remote Sens. 2023, 15(24), 5659; https://doi.org/10.3390/rs15245659 - 7 Dec 2023
Cited by 1 | Viewed by 1428
Abstract
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 [...] Read more.
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
(This article belongs to the Section Engineering Remote Sensing)
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