Medium Earth Orbit Satellites Research Articles

Modeling of Solar Radiation Pressure for BDS-3 MEO Satellites with Inter-Satellite Link Measurements

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.

Effect of WHU/GFZ/CODE satellite attitude quaternion products on the GNSS kinematic PPP during the eclipse season

To ensure high-precision Global Navigation Satellite System (GNSS) applications, many analysis centers (ACs) have begun to provide satellite attitude products, which affect the modeling of phase variations and phase wind-up. Despite several studies having demonstrated the importance of providing attitude products, particularly eclipsing products, the performance of satellite attitude models for different ACs has not been further investigated. This study compared the satellite attitude models provided by Wuhan university (WHU), German Research Centre of Geosciences (GFZ), and Center for Orbit Determination in Europe (CODE), and investigated the impact of satellite attitude products on high-rate GNSS data processing (i.e., 1HZ). The satellite attitudes of most satellite blocks were consistent well with each other, except for the BDS-2 inclined geostationary orbit (IGSO), BDS-3 medium earth orbit (MEO), GPS IIIA, and GLONASS-M satellites. The differences in the yaw angle between the different ACs ranged as 10–180°. Compared to the good consistency of the wum and com products, gbm exhibited significant differences from the former for most constellations. Following the application of the satellite attitude products, the average 3D RMS value of the single-kinematic PPP was improved by 11% and 10% for the 30-s and 1-s sampling rate observations, respectively. Thus, these eclipsing satellites with inaccurate attitude models can be deleted while integrating more satellites into the GNSS data processing.

Calibration Method for Relativistic Navigation System Using Parallel Q-Learning Extended Kalman Filter.

For the relativistic navigation system where the position and velocity of the spacecraft are determined through the observation of the relativistic perturbations including stellar aberration and starlight gravitational deflection, a novel parallel Q-learning extended Kalman filter (PQEKF) is presented to implement the measurement bias calibration. The relativistic perturbations are extracted from the inter-star angle measurement achieved with a group of high-accuracy star sensors on the spacecraft. Inter-star angle measurement bias caused by the misalignment of the star sensors is one of the main error sources in the relativistic navigation system. In order to suppress the unfavorable effect of measurement bias on navigation performance, the PQEKF is developed to estimate the position and velocity, together with the calibration parameters, where the Q-learning approach is adopted to fine tune the process noise covariance matrix of the filter automatically. The high performance of the presented method is illustrated via numerical simulations in the scenario of medium Earth orbit (MEO) satellite navigation. The simulation results show that, for the considered MEO satellite and the presented PQEKF algorithm, in the case that the inter-star angle measurement accuracy is about 1 mas, after calibration, the positioning accuracy of the relativistic navigation system is less than 300 m.

Extension of the BDS IGSO and MEO satellite antenna patterns with FengYun-3C and LuTan-1 onboard data

The International Global Navigation Satellite System (GNSS) Service (IGS) has recommended calibrating the extended satellite antenna Phase Center Variation (PCV) model for all navigation satellites to support low-Earth-Orbit (LEO) satellite applications. Owing to the absence of ground-calibrated PCVs for the BeiDou Navigation Satellite System (BDS), tracking data from global ground stations were used for in-orbit estimations. However, limited by the observed maximum nadir angle, PCVs based on ground data cannot cover the entire range of nadir angles observed using by LEO satellites. In this study, the FengYun-3C and LuTan-1 missions were used to extend the PCVs of the BDS Inclined GeoSynchronous orbit (IGSO) and medium-Earth-orbit (MEO) satellites. The PCVs corresponding to the ionosphere-free linear combinations of B1I/B2I, B1I/B3I, and B1C/B2a were calibrated in-orbit by extending the maximum nadir angle from 9° to 10° for the IGSO and from 13° to 15° for the MEO. There was good consistency among the estimated PCVs of satellites of the same type. In addition, these estimated PCVs were close to the corresponding satellite block-specific values estimated based on ground tracking data. The impact of the extended PCVs of the BDS satellite antenna was investigated by comparing them with the unextended PCVs model in the receiver antenna PCVs pattern estimation and precise orbit determination of the FengYun-3C and LuTan-1 satellites. The results showed that the extended BDS satellite PCVs effectively reduced the unmodeled error of the unextended BDS satellite PCVs in the low-elevation region of the LEO receiver antenna PCV patterns. In addition, compared with the introduction of phase center offset alone, the introduction of ground-based PCVs can improve the overlapping orbit differences (OODs) of LEO satellites, and the extended BDS satellite PCVs can further improve the OODs. Taking B1C/B2a as an example, the improvement ratio of OODs in the 3D direction of Lutan-1A increased from 5.2 % to 8.0 %, and that of Lutan-1B can rise from 1.7 % to 4.2 %.

SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits

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.

Impacts of inter-satellite links on the ECOM model performance for BDS-3 MEO satellites

Inter-satellite link (ISL) plays an essential role in current and future Global Navigation Satellite System (GNSS). In this study, we investigate the impact of ISL observations on precise orbit determination for BeiDou-3 Navigation Satellite System (BDS-3) Medium Earth Orbit (MEO) satellites based on different Extended CODE Orbit Models (ECOM). Thanks to the better observation geometry of the Ka-band ISL data compared to the L-band data for BDS-3 MEO satellites, the ISL solution substantially reduces Orbit Boundary Discontinuity (OBD) errors, except for C30, which suffers from unstable Ka-band hardware delay. From the external quality analysis, ISL significantly enhances the reliability of the orbit of MEO satellites manufactured by the China Academy of Space Technology (CAST). The standard deviation (STD) of the satellite laser ranging (SLR) residuals is approximately 2.5 cm, and the root mean square (RMS) is reduced by 10–23% compared to L-band solutions. Besides, the Sun-elongation angle dependent systematic error in SLR residuals nearly vanishes based on the reduced 5-parameter ECOM (ECOM1) or extended 7-parameter ECOM (ECOM2) with ISL data. This is because the ISL reduces the correlation between state parameters and solar radiation pressure (SRP) parameters as well as those among SRP parameters, leading to a more accurate estimation of both orbit and SRP perturbations, particularly those along B direction. This confirms that the deficiency of the SRP models for BDS-3 CAST satellites can be compensated by using better observation geometry from ISL data. On the other hand, for the satellite manufactured by Shanghai Engineering Center for Microsatellites (SECM), the ISL allows for a more accurate estimation of the Bc1 parameter in the ECOM1 model. This only reduces linear systematic error, possibly because the impact generated by the satellite bus cannot be entirely absorbed by the B-direction parameters.

A Study on Anti-Jamming Algorithms in Low-Earth-Orbit Satellite Signal-of-Opportunity Positioning Systems for Unmanned Aerial Vehicles

Low-Earth-Orbit (LEO) satellite Signal-of-Opportunity (SOP) positioning technology has gradually matured to meet the accuracy requirements for unmanned aerial vehicle (UAV) positioning in daily scenarios. Advancements in miniaturization technology for positioning terminals have also made this technology’s application to UAV positioning crucial for UAV development. However, in the increasingly complex electromagnetic environment, there remains a significant risk of degradation in positioning performance for UAVs in LEO satellite SOP positioning due to unintentional or malicious jamming. Furthermore, there is a lack of in-depth research from scholars both domestically and internationally on the anti-jamming capabilities of LEO satellite SOP positioning technology. Due to significant differences in the downlink signal characteristics between LEO satellites and Global Navigation Satellite System (GNSS) signals based on Medium Earth Orbit (MEO) or Geostationary Earth Orbit (GEO) satellites, the anti-jamming research results of traditional satellite navigation systems cannot be directly applied. This study addresses the narrow bandwidth and high signal-to-noise ratio (SNR) characteristics of signals from LEO satellite constellations. We propose a Consecutive Iteration based on Signal Cancellation (SCCI) algorithm, which significantly reduces errors during the model fitting process. Additionally, an adaptive variable convergence factor was designed to simultaneously balance convergence speed and steady-state error during the iteration process. Compared to traditional algorithms, simulation and experimental results demonstrated that the proposed algorithm enhances the effectiveness of jamming threshold settings under narrow bandwidth and high-power conditions. In the context of LEO satellite jamming scenarios, it improves the frequency-domain anti-jamming performance significantly and holds high application value for drone positioning.

Earth Rotation Parameters Derived from BDS-3 New Signals B1C/B2a Dual-Frequency Combination Observations

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.

Satellite laser ranging to BeiDou-3 satellites: initial performance and contribution to orbit model improvement

In January 2023, the International Laser Ranging Service (ILRS) approved the tracking of 20 additional BeiDou-3 Medium Earth Orbit (BDS-3 MEO) satellites, integrating them into the ILRS tracking network. Before that, only 4 BDS-3 MEO satellites had been tracked. BDS satellites employ highly advanced GNSS components and technological solutions; however, microwave-based orbits still contain systematic errors. Satellite Laser Ranging (SLR) tracking is thus crucial for better identification and understanding of orbit modeling issues. Orbit improvements are necessary to consider BDS in future realizations of terrestrial reference frames, supporting the determination of global geodetic parameters and utilizing them for the co-location of GNSS and SLR in space. In this study, we summarize the first 6 months of SLR tracking 24 BDS-3 MEO satellites. The study indicates that the ILRS network effectively executed the request to track the entire BDS-3 MEO constellation. The number of observations is approximately 1300 and 450 for high- and low-priority BDS-3 satellites, respectively, over the 6 months. More than half of the SLR observations to BDS-3 MEO satellites were provided by 5 out of the 24 laser stations, which actively measured GNSS targets. For 14 out of 24 BDS-3 MEO satellites, the standard deviation of SLR residuals is at the level of 19–20 mm, which is comparable with the quality of the state-of-the-art Galileo orbit solutions. However, the SLR validation of the individual satellites revealed that the BDS-3 MEO constellation consists of more ambiguous groups of satellites than originally reported in the official metadata files distributed by the BDS operators. For 8 BDS-3 satellites, the quality of the orbits is noticeably inferior with a standard deviation of SLR residuals above 100 mm. Therefore, improving orbit modeling for BDS-3 MEO satellites remains an urgent challenge for the GNSS community.

Orbit determination of Earth-Moon libration point navigation constellation based on Inter-satellite links

Earth-Moon libration point navigation constellation has a merit of fully covering the cislunar space and providing navigation services with merely a small number of satellites. Furthermore, this type of constellation itself can achieve orbit determination by using only its Inter-satellite links (ISL) owing to the well-known gravitational asymmetry near the libration points. This paper adopts a representative four-satellite navigation constellation including three satellites located near the libration point L3, L4, L5, and an extra one in Distant Retrograde Orbit (DRO), and studies the orbit determination accuracy of the constellation under two conditions: establishing ISLs within itself (called Solely libration point satellites) and establishing additional ISLs with BeiDou Navigation Satellite System (BDS) (called Libration + BeiDou satellites). The simulation results indicate that, for the Solely libration point satellites scenario with the 1 m range error and solar radiation pressure (SRP) error with the level of 10% deviation between ball model and macro model, the final orbit accuracies for L3, L4, L5, and DRO satellites can respectively achieve 11.3 m, 12.7 m, 12.6 m, and 7.3 m. Reducing the link interval can significantly shorten the arc length to achieve final accuracy, whileas it has less impact on the final orbital accuracy. When the link interval is set as 240, 60, 10, and 2 min, the arc lengths at the final accuracy of better than 15 m are about 35, 29, 23, and 20 days, respectively. To balance the communication burden and the orbit determination arc length, the recommended ISL building interval is 10 min. Errors coming from range measurement model and dynamic model, in addition, are key factors in orbit determination, which can result in meters to tens of meters of orbital accuracy. For the Libration + BeiDou satellites scenario, the augmented ISLs to BDS can substantially improve constellation orbital accuracy and shorten the orbit determination arc length. When the DRO satellite attached to the Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites of BDS respectively, the improved accuracy are 37.1%, 61.2%, and 42.2%, while the shortened arc length are 20.1%, 28.3%, and 28.1%, respectively. The research findings presented in this paper can serve as a reference for the construction and assessment of navigation constellations in the Earth-Moon system.

Gravity field recovery of inter-satellite links between Beidou navigation satellite system (BDS) and LEO based on geodesy and time reference in space (GETRIS)

The goal of this contribution is to construct the inter-satellite links (ISLs) between Global Navigation Satellite System (GNSS) and Low Earth Orbit (LEO) satellite to recover the Earth’s gravity field based on the concept of Geodesy and Time Reference in Space (GETRIS). Taking the constellation of the Beidou Navigation Satellite System (BDS) as an example, several types of high-low satellite-to-satellite tracking (H-L SST) modes combining BDS and GETRIS are used to research the tracking mode of high orbit satellites and the distribution of LEO satellite constellations to explore the optimal mode for gravity field recovery. The effects of multiple H-L SST modes on the accuracy of gravity field recovery are studied. In addition, the contribution of each error source is also analyzed. Finally, this study varies LEO satellite constellations to show reduced errors in the temporal gravity field solutions for the improved ISLs. The results showed that the Inclined GeoSynchronous Orbit (IGSO) satellite greatly improved the Geosynchronous orbit (GEO) satellite tracking LEO satellite mode in the high latitude regions. Compared with the Medium Earth Orbit (MEO) satellite tracking LEO satellite, the error of gravity field recovered by combining with GEO, IGSO and MEO can be reduced by 16 %. The largest error is the non-tidal signal, followed by the ocean tidal model difference, and the smallest is the instrument error. For a single LEO satellite, the combination model is more sensitive to the satellite orbital altitude, the cumulative error was decreased from 5.08 mm (550 km) to 0.33 mm (250 km). For LEO constellations, adding inclined orbit satellites can improve the accuracy of the solution to some extent. But the optimal solution can be obtained by the constellation composed of polar orbit satellites with different Right Ascension of Ascending Node (RAAN), the cumulative errors are 0.27 mm (two satellites), 0.19 mm (three satellites), and 0.19 mm (four satellites).

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.

Satellite-Terrestrial Integrated 6G: An Ultra-Dense LEO Networking Management Architecture

With the rapid development of low earth orbit (LEO) satellites, the ultra-dense LEO satellite-terrestrial integrated networking has become a promising paradigm to provide wide coverage, high capacity and flexible services for the sixth generation (6G) mobile communication networks. However, the natural heterogeneity, high dynamics, and large scale of ultradense LEO satellite networks pose new challenges to network control and management. To this end, in this article, we propose a medium earth orbit (MEO), low earth orbit (LEO) and satellite Earth stations (SESs) integrated multi-layered management architecture for the ultra-dense LEO satellite network, where global controllers and local controllers are introduced to reduce the network management complexity. With the aid of this hybrid multi-layered management framework, we can efficiently implement the network status control, mobility management, resource management, and service management in the satelliteterrestrial integrated network. To obtain proper global and local controllers with high management efficiency in the hybrid multilayered network management architecture, we further propose a novel and efficient grouping and clustering method for the ultradense LEO satellite network, where each group manager MEO satellite and cluster head (CH) LEO satellites are respectively considered as the global and local controllers of each LEO satellite group. Numerical simulations are carried out to evaluate the superiority and effectiveness of the proposed hybrid multilayered ultra-dense LEO networking management architecture.

SISRE of BDS-3 MEO: Evolution as well as Comparison between D1 and B-CNAV (B-CNAV1, B-CNAV2) Navigation Messages

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%.

Contribution of BDS-3 observations to the precise orbit determination of LEO satellites: a case study of TJU-01

The precise orbit determination (POD) of scientific low Earth orbit (LEO) satellites is a prerequisite for the successful implementation of scientific missions. In recent years, global navigation satellite systems have become the main means of determining the orbits of LEO satellites. The global navigation satellite system receiver onboard the Tianjin University No. 1 (TJU-01) satellite receives both GPS and BDS-2/3 signals, with the addition of BDS-2/3 observations playing an important role in improving the POD of LEO satellites. This study comprehensively analyzes the spaceborne GPS/BDS data quality, including BDS-2/3 and GPS code multipath errors. Appreciable code multipath errors are found for the B1I signal of BDS-2 medium Earth orbit (MEO) satellites at elevations higher than 40°, whereas slight near-field relevant multipath errors of both frequencies are found for GPS and BDS-3 MEO satellites. The GPS and BDS-2/3 code multipath errors are estimated through elevation/azimuth-relevant piece-wise modeling and applied in the POD calculations. Several schemes, namely GPS-based, BDS-based, BDS-based without geo-synchronous (GEO) satellites, and GPS/BDS combined schemes, are designed to evaluate the POD performance. Fourteen days of data are calculated and the average three-dimensional (3D) orbital root mean square (RMS) of orbit overlapping differences obtained from GPS-based and BDS-based POD (without GEO satellites) solutions are 37.4 and 27.1 mm, respectively. The BDS-based solutions are obviously better than the GPS-based solutions, mainly owing to better data availability. The GPS/BDS combined solutions have the best accuracy, with a 3D RMS value of 20.6 mm. In addition, when BDS GEO satellites are included, the 3D RMS of the overlapping orbit differences reduces to 32.9 and 27.4 mm for BDS-based and GPS/BDS combined solutions, respectively. Double-difference (DD) and single-difference (SD) integer ambiguity resolution (IAR) are adopted to further improve the POD performance. The fixed orbit of the TJU-01 satellite is solved through DD IAR and SD IAR, and the contribution of the TJU-01 satellite to ambiguity fixing is analyzed. Relative to the float solution, the improvements made using the two ambiguity fixing approaches are equivalent, both being approximately 13%. The importance of this research is not only the precise determination of the orbit of TJU-01 for occultation service but also the demonstration of the contribution of BDS observations to the performance of the POD of LEO satellites.

ANALYSIS OF THE INFLUENCE OF THE OBJECT’S ELEVATION ON LASER MEASUREMENTS OBTAINED IN BOROWIEC IN 2016–2023

This paper presents an analysis of how an object’s position above the horizon affects laser measurements obtained in laser station in Borowiec. The objects used for this analysis were active satellites from LEO (Low Earth Orbit) and MEO (Medium Earth Orbit) regimes, as well as space debris from LEO regime. The data used for this analysis spanned from the second half of 2016 to the first half of 2023. The results of tests performed at the BORL station indicate that for LEO objects, it is least effective to make observations when the object is close to the zenith, i.e. 80–90 degrees above the horizon. The highest returns are obtained when the object is at an elevation of 20–39 degrees. These results apply to both active satellites and space debris objects from the LEO regime. In the case of MEO satellites the highest returns are received when the object is at an elevation of 50–79 degrees.

Spacecraft autonomous navigation using line-of-sight directions of non-cooperative targets by improved Q-learning based extended Kalman filter

Autonomous optical navigation is one of the most promising techniques to estimate the position and velocity of a spacecraft in Earth orbit without the supports of Earth-based tracking stations. To improve the navigation performance, this paper presents a novel autonomous optical navigation method, where a star camera on the spacecraft is utilized to measure the line-of-sight (LOS) directions of a number of non-cooperative space targets, whose position vectors are supposed to be not precisely known in advance, and an improved Q-learning based extended Kalman filter (IQEKF) is developed to obtain the accurate motion state estimate of both the spacecraft and the space targets based on the LOS direction measurements. The main advantage of the presented method is that the LOS directions of the space targets can be acquired with high-accuracy by using the state-of-the-art star camera, such that the superior navigation accuracy is achievable. In addition, the whole motion state of the spacecraft, such as position, velocity, and attitude, can be obtained with the star camera, in the case that the space targets and the stars are observed simultaneously. The high performance of the presented autonomous navigation method is illustrated through a representative simulation of a medium Earth orbit (MEO) satellite. Furthermore, the simulation results indicate that the IQEKF yields more accurate solutions than the traditional navigation filtering algorithms.

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).

Long‐Term In Situ Performance Comparison of Si and GaAs Solar Arrays in Medium Earth Orbit

The present work analyzes the long‐term in situ comparison of Si and GaAs solar array based on two BeiDou Navigation Satellite System satellites in medium Earth orbit (MEO). From the 6 year long‐term perspective, both Si and GaAs solar arrays exhibit significant yearly periodic variations in remote sensing current and temperature due to periodic variations in the Sun–satellite distance. The practical in situ photogenerated current degradation of Si and GaAs solar arrays in MEO orbits is analyzed by the light intensity and working temperature after calibrating. The annual degradation coefficients of Si and GaAs solar arrays are calculated to be 0.986 and 0.990, respectively, which means 13.2% and 9.6% current degradation for Si and GaAs solar arrays at the end of the 10 year life MEO satellite. Also, this article examines the temperature of the MEO orbit, with the working temperature ranging from −144.7 to 56.3 °C for Si solar array and −136.9 to 60.9 °C for GaAs solar array. The present work provides a critical accurate degradation parameter for the MEO satellite's precise design and the space application of the low‐cost silicon solar cell.

Detection and Analysis of Radiation Doses in Multiple Orbital Space during Solar Minimum

Based on orbit detection data acquired by a positive channel Metal Oxide Semiconductor (PMOS) dose detectors on FY4-A (GEO), BD3-M15 (MEO), and YH1-01A (LEO) between November 2018 and November 2022, investigations reveal variations in total dose and the mechanism of radiation dose increase within the geostationary earth orbit (GEO), medium earth orbit (MEO), and low earth orbit (LEO) during the transition from the 24th to the 25th solar cycles. It provides the radiation dose parameters for the study of the space environment from different altitude orbits, and also provides an important basis for studying the solar minimum activity and dose generation The data indicate directional disparities in radiation doses among the orbital regions, with the hierarchy being FY4-A > YH1-01A > BD3-M15. Furthermore, the results show that the total doses of FY4-A and BD3-M15 were higher than that of YH1-01A by two orders of magnitude, with BD3-M15 > FY4-A > YH1-01A. The monthly radiation dose rates of FY4-A in GEO and BD3-M15 in MEO exhibited positive correlation with their corresponding APs during the solar minimum. Notably, for FY4-A, the monthly radiation dose rate during geomagnetic disturbed periods exceeded that of the dose rate during geomagnetic quiet periods by one order of magnitude. This analysis revealed the substantial impact of geomagnetic storms and space environment disturbances on radiation doses detected by MEO and GEO orbital satellites. These perturbations, attributable to medium- and small-scale high-energy electron storms induced by reproducible coronal holes, emerged as key driving factors of the increase in radiation doses in MEO and GEO environments.