Inclined Geosynchronous Satellite Orbit Research Articles

Effects of Equatorial Plasma Bubbles on Multi-GNSS Signals: A Case Study over South China

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.

Performance Evaluation and Application Field Analysis of Precise Point Positioning Based on Different Real-Time Augmentation Information

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.

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

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.

Enhanced precise orbit determination for GPS and BDS-2/3 with real LEO onboard and ground observations

Due to the current geographical situation in China that it is difficult to achieve globally well distributed ground monitoring stations for Chinese BeiDou Navigation System (BDS), the BDS Medium Earth Orbit (MEO) satellite orbital accuracy can be seriously affected by the insufficient length of continuous observation arc based on regional ground network. What is more, the highly static characteristics of BDS Geosynchronous Orbiting (GEO) satellites resulting in meter-level orbit determination accuracy is far from satisfactory for precise positioning services. In order to overcome these problems, the low Earth orbit (LEO) satellites serving as fast-moving space monitoring stations can be used as a good supplement for the current BDS ground monitoring stations layout. In this study, real measured spaceborne data from two LEO satellites, namely Fengyun-3D (FY-3D) and Tianjin University No. 1 (TJU-01), are collected and studied for the augmentation of BDS precise orbit determination (POD). The multipath errors of spaceborne code observations are comprehensively analyzed. It is found that not only BDS-2 relevant satellite-induced code bias but also near-field multipath errors, especially distinct in GPS, exist in a spaceborne environment. The piece-wise linear model is therefore established and applied to correct the code observations to reduce the multipath errors in the integrated POD processing. The GPS and BDS-2/3 POD solutions are compared with orbital overlapping differences and Satellite Laser Ranging (SLR) residuals validation. It is demonstrated that including the two LEO satellites can improve the orbit determination accuracy of GPS and BDS-2/3 significantly under a regional ground network, especially in the along component. The average overlapping orbital Root Mean Square (RMS) is decreased by 18.4 %, 34.3 %, 24.9 %, 21.4 %, and 7.8 % for the GPS, GEO, Inclined Geosynchronous Orbit (IGSO), BDS-2 MEO, and BDS-3 MEO satellites, respectively, in the along component. The RMS of SLR residuals is decreased from 37.1 cm to 17.8 cm for the GEO satellites, and the overall improvement is about 8 %-12 % for the BDS MEO satellites. There has also been a slight improvement under a global network, with an average improvement of 2–3 cm in the SLR residuals RMS. However, significant systematic errors are also observed in the SLR residuals in BDS GEO, IGSO, and MEO satellites, and are expected to be improved with refined observation models based on more LEO satellites, i.e., the phase center variation (PCV).

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

Determination of Earth rotation parameters by Beidou navigation satellite system

Earth Rotation Parameters (ERP) play an important role in astrometry, geophysics, and space geodesy. Beidou Navigation Satellite System (BDS) has three orbital types of satellites, i.e., Geostationary orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites. The orbital diversity of BDS constellation provides the opportunity to study the influence of system-specific satellite constellation with different orbital characteristic on ERP. In this article, different strategies of ERP estimation are conducted in terms of different solar radiation pressure (SRP) models and different orbital types of satellites. For ERP derived from BDS MEO observations, compared with C04 products from International Earth Rotation and Reference System Service, the results show that the accuracy of ERP with extended Empirical CODE Orbit Model (ECOM) with 9 parameters (ECOM2) outperforms other SRP models (e.g., ECOM with 5 parameters (ECOM1) and ECOM1 with an empirical prior model (EMP + ECOM1)). In EMP + ECOM1 solutions, the application of a prior EMP model would intensify the influence of draconitic year in pole coordinates spectrum, while the visible signal of a period close to 7.4 days with ECOM1 solution can be mitigated. Moreover, the bias of B0 parameter in EMP + ECOM1 would cause a mean offset in Length Of Day (LOD). The accuracy of ERP is also affected by the BDS constellation characteristic. For pole coordinate, MEO-only solution with ECOM2 model shows the best accuracy, while the LOD achieves the best solution when 3 orbital types are employed. Additionally, using the combined constellation of MEO, IGSO, and GEO satellites can decorrelate some of the systematic signals, e.g., the spurious signals of LOD at 2.35-day and 3.5-day in MEO-only solutions are reduced. Likewise, the increase of orbital planes can reduce the amplitude of 3 cycles per draconitic year (close to 121 days) in the pole coordinate spectrum, which is the main error source in pole coordinates estimated from BDS MEO constellation. However, some signals around 10 ∼ 24, 33– and 50-day are found in the Y-pole coordinate and its rate.

A two-step method to detect broadcast ephemeris unavailable periods caused by BeiDou satellite orbital maneuvers

The space constellation of the BeiDou navigation satellite system (BDS) is a hybrid constellation containing medium earth orbit (MEO) satellites, geostationary earth orbit (GEO) satellites, and inclined geosynchronous orbit (IGSO) satellites. Due to the geosynchronous characteristics of GEO and IGSO, GEO satellites and IGSO satellites often need to perform orbital maneuvers, which can affect the signal-in-space (SIS) availability performance of BeiDou satellites. A two-step detection method for BeiDou satellite orbital maneuvers has been proposed in this paper. The first step is to identify orbital maneuvers based on time series analysis of broadcast ephemeris, and the second step is to verify orbital maneuvers based on bidirectional orbit prediction. The two-step detection method was used to detect the orbital maneuvers of BeiDou satellites in 2019. Through the double guarantees of identification and verification, the detection accuracy of BeiDou satellite orbital maneuvers has been effectively improved. And the orbital maneuver detection results are continued to be used to assess the SIS availability of BeiDou satellites. The results show that the availability loss of GEO satellite orbital maneuvers is about 0.45%–1.07%, and the availability loss of IGSO satellite orbital maneuvers is about 0.12%–0.19%.

Signal-in-Space Range Error of the Global BeiDou Navigation Satellite System and Comparison with GPS, GLONASS, Galileo, and QZSS

Based on the standard of precise multisystem orbit and clock offset, the evaluation methods of satellite orbit, satellite clock offset and the signal-in-space range error (SISRE) from broadcast ephemeris were given in this study. The SISRE was used as a key performance index to compare the global BeiDou navigation satellite system (BDS-3) with the regional navigation satellite system (BDS-2), Global Positioning System (GPS), Galileo, Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS), and Quasi-Zenith Satellite System (QZSS). Through the combination of domestic tracking stations and inter satellite links, the orbit determination accuracy of BDS-3 has been significantly improved. The radial (R), tangential (T) and normal (N) direction orbit accuracies of BDS-3 medium Earth orbit (MEO) satellites were 0.08, 0.37, and 0.34 m, respectively, which were considerably better than those of other satellite navigation systems. The R-, T-, and N-direction orbit accuracies of BDS-3 inclined geosynchronous orbit (IGSO) satellites were 0.17, 0.59, and 0.56 m, respectively, which were better than those of QZSS IGSO satellites. The R-, T-, and N-direction orbit accuracies of BDS-3 geostationary earth orbit (GEO) satellites were 0.27, 3.42, and 1.29 m, respectively, revealing considerable accuracy advantages in the R and N directions compared with QZSS GEO, although performance in the T direction was inferior. For the clock offset, the BDS-3 MEO satellites had an accuracy of 1.83 ns, which was noticeably superior, similar, slightly inferior, and superior to those of BDS-2, GPS, Galileo, and GLONASS. The clock offset accuracies of BDS-3 IGSO and GEO satellites were 3.13 and 3.17 ns, respectively, which were slightly better than those of QZSS IGSO and GEO satellites but did not have an obvious advantage over BDS-2. The primary reason could be that the launch time of the two types of BDS-3 satellites was close to the analysis period, and therefore, the clocks may be still in the aging process. Considering only orbit error, the average SISRE (orb) of BDS-3 MEO, Galileo, GPS, and GLONASS was 0.10, 0.28, 0.57, and 1.03 m, respectively. The SISRE (orb) of BDS-3 IGSO was 0.19 m, which was marginally greater than that of BDS-3 MEO but smaller than those of the other systems and considerably smaller than that (0.90 m) of QZSS IGSO. The SISRE (orb) of BDS-3 GEO was 0.60 m, which was comparable to that of GPS (0.59 m) and considerably smaller than that of QZSS GEO (0.91 m) satellites. Considering both orbit and clock offset error, the SISRE of BDS-3 MEO satellites was 0.52 m, which was slightly greater than that of Galileo (0.40 m), marginally smaller than that of GPS (0.59 m), and considerably smaller than that of GLONASS (2.33 m). The BDS-3 IGSO satellites had a SISRE of 0.90 m, which was greater than those of GPS and Galileo but comparable to that of QZSS IGSO (0.92 m). The average SISRE of BDS-3 GEO satellites was 1.15 m, which was greater than those of GPS and Galileo and slightly greater than that of QZSS0.95 m GEO satellites, but smaller than that of GLONASS.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Studies and Analysis of Combining BDS-3/GNSS Ultra-Rapid Orbit Products from Different IGS Analysis Centers

The third generation of China’s BeiDou Navigation Satellite System (BDS-3) began to provide global service at the end of 2018, and the completion of BDS was announced in July 2020, which includes GEO (Geostationary Earth Orbit), IGSO (Inclined Geosynchronous orbit), and MEO (Medium Earth Orbit) satellites. The resulting BDS orbits vary due to the inconsistent alignment strategies used by different analysis centers. Therefore, it is necessary to study the method of determining the BDS-3 orbit products combined from different analysis centers. In this research, the accuracy of the combined orbits for BDS-3 and other GNSS systems is evaluated and analyzed. To verify the reliability of the orbit combination method proposed in this paper, the GPS orbit is first selected for verification. Compared to the analysis centers, the mean Signal in Space User Ranging Error (SISURE) for GPS combined orbits is significantly reduced, and the mean SISURE of combined orbits for Block IIF, Block IIR, and Block III is 4.15 mm, 5.43 mm, and 5.63 mm, respectively. This demonstrates the effectiveness of the orbit combination method in this research. Besides, the accuracy of the combined orbits is improved by the ERP correction, and the mean RMS of the without Earth rotation Parameters (ERP) correction orbits and with ERP correction orbits is 4.78 mm and 4.53 mm, respectively. This demonstrates that orbit consistency corrections should be considered when performing orbit combinations. Compared to the GFZ orbits, the accuracy of the combined orbits has improved for GPS, GLONASS, GALILEO, and BDS is 8.2%, 9.9%, 9.9%, and 5.5%, respectively. It shows that the orbit combination method improves the orbital accuracy compared to the individual analysis center orbits. The mean RMS of the combined orbits for GPS, GLONASS, GALILEO, BDS MEO, and BDS IGSO is 1.7 cm, 2.61 cm, 2.52 cm, 2.59 cm, and 4.90 cm, respectively. The results demonstrate that the accuracy of the combined orbit for the BDS-3 MEO satellite is already similar to other systems; an orbit combination also available for the BDS-3 satellite.

Analysis of Precise Orbit Determination of BDS-3 MEO and IGSO Satellites Based on Several Dual-Frequency Measurement Combinations

The Chinese BeiDou-3 navigation satellite system (BDS-3) is capable of transmitting both old B1I, B3I signals and new B1C, B2a, B2b signals. Current BDS-3 precise orbits are generally calculated using a B1I/B3I combination considering overlap with the BeiDou-2 navigation satellite system (BDS-2). In this contribution, the observation quality of BDS-3 medium earth orbit (MEO) satellites and inclined geosynchronous orbit (IGSO) satellites are analyzed based on three aspects, i.e., carrier to noise ratio (C/N0), pseudo-range noise and pseudo-range multipath (MP). The C/N0 of the MEO satellite is 2~3 dB higher than that of the IGSO satellite at the same elevation angle. Meanwhile, the order of the Root Mean Square (RMS) values of both pseudo-range noise and MP is B1I < B1C < B3I < B2a ≈ B2b. Three kinds of combinations, i.e., B1CB2a, B1CB2b and B1IB3I, are selected for the BDS-3 precise orbit determination (POD) experiment. Orbits are assessed by the orbit-only signal-in-space range error (SISRE) computed between pairs of the three kinds of combinations in this contribution, CODE and GFZ final orbits. Orbit-only SISRE assessment shows that B1CB2a/CODE, B1CB2b/CODE, B1CB2a/GFZ and B1CB2b/GFZ are at the same level with CODE/GFZ, and the orbit-only SISRE is at the level of 5 cm for MEOs and 9 cm for IGSOs, respectively. Meanwhile, B1IB3I/CODE and B1IB3I/GFZ are about 1–2 cm worse. Inter-solution comparison between B1CB2a, B1CB2b and B1IB3I also indicate that B1CB2a and B1CB2b have good consistency, while B1IB3I shows poor performance. Satellite laser ranging (SLR) residuals indicate that the mean RMS is 3–4 cm for the four BDS-3 MEOs for CODE final orbit, GFZ final orbit, B1CB2a and B1CB2b combinations, while the mean RMS value for B1IB3I combination is a few millimeters worse, at approximately 4–5 cm.

BDS and Galileo: Global Ionosphere Modeling and the Comparison to GPS and GLONASS

The ionospheric delay is one of the important error sources in the Global Navigation Satellite System (GNSS) data processing. With the rapid construction and development of GNSS, the abundant satellite resources have brought new opportunities for ionospheric monitoring. To further investigate the performances and abilities of Galileo and BDS in ionosphere modeling, we study the ionosphere modeling based on the 15th order spherical harmonic function, and 364 stations around the world are selected for global ionospheric modeling of GPS, GLONASS, Galileo and BDS systems under ionospheric quiet and active conditions, respectively. The results show that the average biases of the ionospheric models built by GPS, GLONASS and Galileo are relatively small, which are within 2 Total Electron Content Unit (TECU) as compared to the Center for Orbit Determination in Europe (CODE) global ionospheric map (GIM), while the average biases of the models built by BDS are between 6 and 8 TECU during the ionospheric quiet and active days, respectively. In addition, in order to analyze the modeling performances before and after using BDS geostationary earth orbit (GEO) satellites, BDS is divided into two groups, in which one group contains medium earth orbit (MEO), inclined geosynchronous orbit (IGSO) and GEO satellites; and the other group contains only MEO and IGSO satellites. The results show that the influence of GEO satellites on ionospheric modeling is less than 1 TECU. Due to the distribution of the stations, the 0-value region in the ionospheric model is mainly distributed in the mid and high-latitude regions of the southern hemisphere. Since the ionospheric parameters are lumped with the Differential Code Bias (DCB), we also estimate the DCB parameters and analyze their performances. The DCB estimated in ionosphere modeling shows strong stability, with the average biases of GPS, GLONASS, Galileo and BDS under 0.25 ns, 0.25 ns, 0.2 ns and 0.42 ns, respectively. We also estimate other DCB types of the four GNSS systems. The results show that the DCB is stable and shows consistency with Chinese Academy of Sciences (CAS) DCB products.

TID evaluation based on variabilities of space radiation and device failure dose in typical navigation satellite orbits

Navigation satellites mainly operate in Medium Earth Orbit (MEO), Geostationary Earth Orbit (GEO), and Inclined Geosynchronous Satellite Orbit (IGSO). These orbits lie in or repeatedly cross the outer Van Allen belt of Earth. With large uncertainty, the radiation in these orbits mainly comes from electrons trapped in the outer radiation belt and solar energetic protons. The accurate design of the radiation shielding structure plays an important role in improving the efficiency of satellites. We introduce a method that incorporates the radiation variability in space and failure dose uncertainty of devices to evaluate the survival probability of devices caused by the Total Ionizing Dose (TID) effect. After fitting the failure dose data of operational amplifier TL084 by the Weibull distribution, we calculate the Confidence Levels (CLs) of all possible parameters of the distribution. Based on these parameters and the cumulative probability distribution of TID from space, we evaluate the effects of shielding thickness and mission duration on TL084's failure possibility at different CLs in MEO/GEO/IGSO. Furthermore, the required shielding thickness and the expected survival duration to ensure that TL084 could operate safely at specific CL are also investigated. By using this method, we could approach a balance among the device's ability, the shielding thickness, the expected duration of safe operation, and the confidence level of the design.

Improving BDS broadcast ephemeris accuracy using ground-satellite-link observations

The BeiDou Navigation Satellite System (BDS) employs a hybrid constellation including GEO (Geosynchronous Earth Orbit), IGSO (Inclined Geosynchronous Orbit), and MEO (Medium Earth Orbit) satellites, where the GEO and IGSO satellites are critical to providing continuous and reliable Positioning, Navigation, and Timing (PNT) services in the Asia–Pacific region. To handle the inconsistency between the satellite orbits and clocks in the broadcast ephemeris, which are determined by the Orbit Determination and Time Synchronization (ODTS) and the Two-way Satellite Time Frequency Transfer (TWSTFT) technique, respectively, we present the strategies using ground-satellite-link observations to improve the accuracy of broadcast ephemeris. The clock differences between the ODTS and TWSTFT techniques are used for correcting the radial orbit component to derive the refined orbits, which are used to generate the refined broadcast ephemeris. The test results show the precision of the refined orbits is improved by 50–60% in the 3-h to 12-h predicted arcs for the GEO satellites, and by 40–50% for the IGSO satellites. Moreover, the validation using satellite laser ranging observations shows the mean precision of the refined broadcast ephemeris is improved by 27% compared to the original one. Applying the proposed strategies in the BDS Operational Control Segment (OCS), the time evolution of BDS Single Point Positioning (SPP) in the period from Jan. 2016 to April 2021 is evaluated. The SPP accuracy is improved from 1.94, 2.06 and 3.29 m to 1.39, 1.85, and 2.39 m in the north, east, and up components, respectively. Further update with the inclusion of BDS-3 satellites improve the corresponding SPP precision to 0.68, 0.70 and 1.91 m.

Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between −2×10−18 and 2×10−18 s/s2. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4.0 × 10−14 s/s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites.

BDS near real-time maneuver detection based on triple-differenced phase observations

The BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites need frequent orbital maneuvers to keep them in position due to various perturbations. However, common users cannot obtain the exact maneuver times, which may yield a decline in the real-time service performance of the BDS. To solve this problem, we presented a near real-time maneuver detection method for BDS based on triple-differenced phase observations, which can automatically detect the exact start and end times of satellite orbital maneuvers. In this method, the carrier-phase triple-differences residuals are firstly computed using the precise station coordinates, broadcast ephemeris and dual-frequency observations of ground tracking stations. Afterward, the residuals are be modeled using linear regression to identify maneuver times. The observations from the BDS Experimental Tracking Stations (BETS) and the reference time announced by the Beijing Satellite Navigation Center (BSNC) from Day of year (DOY) 100 to DOY 300, 2017 are used to evaluate the performance of the proposed method. The detected maneuver periods are consistent with the announced ones, except the detected start times lag 42 min and end times advance 23 min on average. Then, the detected times are further validated by dynamic precise orbit determination (POD) after the maneuver. The phase residuals and 3D RMS of the orbit differences of maneuvered satellites proved that the accuracy of detected maneuver times is better than 5-minute. At last, the kinematic precise point positioning (PPP) validation is implemented to evaluate the effect of more accurate GEO and IGSO satellites to BDS positioning. Results show that both the convergence and accuracy of BDS PPP are improved by adding one satellite that has ended maneuvering.

Improving the Orbits of the BDS-2 IGSO and MEO Satellites with Compensating Thermal Radiation Pressure Parameters

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively.

Research on the Influence of the Residual Effects of TWSTFT on the Triangular Closure Difference

The triangular closure (TC) method of two-way satellite time and frequency transfer (TWSTFT) can be utilized to conveniently and quickly evaluate the time transfer performance between ground stations without additional equipment. To expand the application of the TC method and make it applicable to inclined geosynchronous orbit (IGSO) satellites, we analyze the influence of various residual effects of TWSTFT on the triangular closure difference (TCD). Relying on the two-way comparison network of the National Time Service Center of the Chinese Academy of Sciences, TC experiments were carried out using a geostationary orbit (GEO) satellite (CHINASAT-12) and an IGSO satellite (BDS I1-S). The results show that the Sagnac effect and ionospheric delay can be ignored without affecting the TCD, whereas the equipment delay and geometric path asymmetry effect cannot be ignored. Specifically, as a systematic error, the equipment delay has a great impact on the TCD and must be corrected. In contrast, the geometric path asymmetry effect caused by the relative motion of satellites and ground stations is small in magnitude for GEO satellites and can be ignored. However, for IGSO satellites, the geometric path asymmetry effect can reach the nanosecond level; thus, it also has a great impact on the TCD and cannot be ignored. Using the correction method proposed in this paper, subnanosecond time synchronization exactness can be achieved in TC experiments based on both types of satellites. Therefore, we have successfully expanded the application of the TC method to IGSO satellites. Theoretically, the TC method can also be applied to medium earth orbit and other satellites.

Using BDS MEO and IGSO Satellite SNR Observations to Measure Soil Moisture Fluctuations Based on the Satellite Repeat Period

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

The improvement of BDS Observation Geometry with LEO constellations in Orbit Determination

The ability of low earth orbit (LEO) satellites with space-borne global navigation satellite system (GNSS) to improve the accuracy of GNSS satellite orbit determinations has been demonstrated. In this paper, the ability of LEO satellites to improve the observation geometry in the process of the determination of BeiDou Navigation Satellite System (BDS) satellite orbits is the focus. First, the visible BDS satellite model with ground stations and LEO satellites is derived, and the definition of the position dilution of precision (PDOP) is proposed for assessing the observation geometries of BDS satellite orbit determination. Then, the observation geometry of BDS geosynchronous earth orbit (GEO), inclined geosynchronous satellite orbit (IGSO) and medium earth orbit (MEO) satellites are individually analysed by regional ground stations. By designing LEO satellites with different inclinations, altitudes and right ascensions of ascending nodes (RAANs), the PDOP improvements achieved through combinations with different orbital LEO satellites are calculated. Finally, the PDOP improvements caused by incorporating different numbers of LEO constellations are compared. The results show that LEO satellites can improve the observation geometries of BDS satellites, especially when the monitoring of observation configurations by only ground stations is very poor. The PDOP improvements of BDS GEO satellites caused by LEO satellites are more significant than those of IGSO or MEO satellites; i.e., the improvement percentage of C04 is better than 60%. Generally, LEO satellites with high altitudes are more suitable for PDOP improvements to BDS satellites than are LEO satellites with low altitudes; moreover, LEO satellites with high inclinations are more suitable for PDOP improvements to BDS GEO satellites than LEO satellites with low inclinations are. The influence of the RAAN on the PDOP improvements of IGSO and MEO satellites is relatively larger than its influence on the PDOP improvement of GEO satellites. The PDOP improvement percentage and stability of BDS satellites, especially GEO satellites, increase with the number of incorporated LEO satellites. When incorporating the LEO constellation 16/4/1:1000 km, 70°, the maximum improvements of the GEO and IGSO satellites are above 84% and 77%. The improvements of the GEO, IGSO and MEO satellites are above 81%, 42% and 58% respectively.