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• Inter-satellite links (ISL) establishment within libration point constellation for orbit determination (OD). • Analyzed the factors that affect the accuracy of establishing ISLs for OD within the constellation. • Research on the impact of ISLs building interval on OD performance. • Discusses the OD accuracy after establishing ISLs between the libration point constellation and BDS. 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. [ABSTRACT FROM AUTHOR]

The ultra-sensitive accelerometer onboard low Earth orbit (LEO) satellite can measure the non-gravitational accelerations acting on the satellite in an adequate range and frequency bandwidth with high precision. By replacing the non-gravitational force models, accelerometer measurements are introduced in GNSS-based precise orbit and baseline determination (POD and PBD) to improve the quality of the derived orbit and baseline solutions. A modified accelerometer measurement processing strategy is employed, and 1 month of flight data collected by the GRACE and GRACE-FO missions are processed. For single-satellite POD, the obtained orbit solutions are evaluated through comparisons to the Jet Propulsion Laboratory reduced-dynamic orbits, independent satellite laser ranging (SLR) and K-Band ranging (KBR) measurements. Orbit comparison and SLR validation results show comparable accuracy of the orbit solutions derived with non-gravitational force models and accelerometer measurements. However, the KBR validation reports that the relative position precision is considerably improved by 22 and 27% for GRACE and GRACE-FO, respectively. For dual-satellite PBD, the obtained baseline solutions are also evaluated by the KBR measurements. The validation results reveal that the baselines are improved significantly with the high-precision accelerometer measurements. The KBR residuals are reduced from 0.59 to 0.43 mm for GRACE, and from 0.62 to 0.48 mm for GRACE-FO, with the precision being notably improved by 27 and 23%, respectively. Furthermore, in addition to the analysis in the time domain, we find that the performances of the accelerometer measurements are more remarkable in the frequency domain for both POD and PBD, where more than 67% of the KBR residuals are reduced within the frequency interval of 1.5 to 5 cycles per revolution. These results, therefore, demonstrate the great potential of high-precision accelerometer measurements in dynamic POD and PBD, which can offer more precise relative orbits for formation-flying LEO satellites, particularly in the frequency domain. [ABSTRACT FROM AUTHOR]

Satellite laser ranging (SLR) is the space geodetic technique with the highest degree of range, measuring precision and distances right down to the millimeter level. Thanks to the improvement of SLR station layouts and the advance of SLR technology, in recent years, more research has been conducted to determine Global Navigation Satellite System (GNSS) satellite orbits using SLR data. The primary goal of this contribution is to investigate the accuracy of BeiDou Navigation-3 (BDS-3) Satellite precise orbit determination (POD) using solely SLR data, as well as explore the impact of various factors on that accuracy. Firstly, we used actual SLR data to make the POD for BDS-3 satellites, and the POD accuracy was positively connected with the orbital arc lengths. The 9-day median root mean square (RMS) in radial (R), along-track (T), and cross-track (N) directions were estimated at 4.7–8.2, 22.1–35.2, and 27.4–43.8 cm, respectively, for comparison with WUM precise orbits. Then, we explored the impact of SLR observations and stations on POD accuracy. For 9-day orbital arc lengths, five station or 20 observation arcs may offer an orbit with a 1 m precision. Six to eight stations or 30–35 observation arcs allow an improved orbit accuracy up to approximately 0.5 m. Furthermore, we examined how measurement errors and orbit modeling errors affect the SLR-only POD accuracy using simulated SLR data. For orbital arc lengths of 9 days, each cm of random error leads to a 9.3–11.0 cm decrease in orbit accuracy. The accuracy of an orbit is reduced by 10.1–15.0 cm for every 1 cm of systematic error. Moreover, for solar radiation pressure (SRP) errors, the effect of POD accuracy is 20.5–45.1 cm, respectively. [ABSTRACT FROM AUTHOR]

The Tsinghua scientific satellite is a Chinese spherical micro satellite for Earth gravity and atmospheric scientific measurements. The accurate orbits of this satellite are the prerequisites to satisfy the mission objectives. A commercial off-the-shelf dual-frequency GNSS receiver is equipped on the satellite for precise orbit determination (POD). The in-flight performances of the receiver are assessed. Regular long-duration gaps up to 50 min are observed in GNSS data, and the typical data availability is about 60–70% each day. The RMS of code noises is 0.24 m and 0.30 m for C1 and P2 codes, respectively. The RMS of fitting residuals of the carrier phase geometry-free L1–L2 combination is 2.4 mm. The GNSS receiver antenna center offsets (ACOs) and antenna center variations (ACVs) maps are estimated using in-flight data for both dual-frequency and single-frequency POD. Significant improvements in POD performances are obtained when the measurement models are updated by using the ACO and ACV maps' corrections. With the updated measurement model, the RMS of the orbit overlap differences is 1.23 cm in three dimensions for dual-frequency POD, which is reduced by 27%. Meanwhile, two different empirical acceleration types are employed and compared for dual-frequency POD, and the results show that consistency on the 5 cm level is demonstrated for orbit solutions obtained with the updated measurement model. After correcting the ACO and ACV maps, the precision of single-frequency orbit solutions is better than 10 cm, which is improved by 32%. The results indicate that the antenna center modeling can significantly improve the consistency of Tsinghua scientific satellite precise orbits, which will be conducive to the realization of the mission objectives. [ABSTRACT FROM AUTHOR]

Single-frequency (SF) precise orbit determination (POD) using space-borne Global Positioning System (GPS) measurements is a prerequisite for the success of many low-cost small/micro low Earth orbit (LEO) satellite missions. The first-order ionospheric effects are usually eliminated by group and phase ionospheric correction (GRAPHIC) combinations. GPS receiver antenna GRAPHIC residual variations (GRVs) are important systematic error sources in SF orbit determination. Azimuth and elevation dependent GRVs are estimated and obtained based on the GRAPHIC combination residuals in an in-flight calibration. One month of data from GRACE-A, GRACE-B, CHAMP and HY-2A satellites is used to assess the potential of receiver antenna GRVs in SF orbit determination. It is the first time to study the impact of receiver antenna GRVs on SF orbit determination for different LEO satellites, which exhibit different altitudes and data qualities. The impact of receiver antenna GRVs on SF orbit determination is significant. The use of in-flight determined receiver antenna GRVs leads to a better consistency between SF and dual-frequency POD solutions. The improvements are more obvious for GRACE-A and CHAMP satellites, whose receiver antenna GRV patterns demonstrate clear characteristics of systematic deviations. After correcting the receiver antenna GRVs, the root-mean-square of satellite laser ranging validation residuals are 3.11 cm, 2.31 cm, 2.86 cm and 5.29 cm for GRACE-A, GRACE-B, CHAMP and HY-2A satellites, respectively, which are reduced by 11.1%, 4.6%, 14.6% and 4.7%, respectively. At last, a set of a priori GDV corrections of GPS transmitter antennas are used in SF orbit determination and its effects on receiver antenna GRVs estimation and SF orbit determination are analyzed. Applying these corrections can slightly improve the SF orbit quality of GRACE-A satellite. [ABSTRACT FROM AUTHOR]

The TH-2 satellite system, including the TH-2A and TH-2B, is the first distributed interferometric synthetic aperture radar (InSAR) satellite system in China. During the in-orbit operation, the TH-2A satellite should perform three maneuvers per day to keep the formation flying geometry. We estimate those maneuvers in the precise orbit determination (POD) by the GPS and BDS2 measurements on board, respectively. The residuals of the POD show that the effects caused by orbital maneuvers can be well eliminated for both the GPS and BDS2 data. The precision of the BDS2-based POD is better than 8.0 cm in the three-dimensional direction (3D) compared with the orbit derived from the GPS observations. Such a precision level of the satellite orbit satisfies the InSAR mission requirement of the TH-2. In addition, the relative error of velocity changes is employed to evaluate the maneuver estimations by the POD using the regional navigation system of BDS2. The results show that the relative error of velocity changes between the GPS- and BDS2-based POD is less than 7.0%, which indicates that the maneuver performance extracted from the regional BDS2 data is as good as that extracted from the global GPS data. In the GNSS fused processing, we found that the independent receiver clock offsets should be taken into account, since the time tag corrections for the GPS and BDS2 observations collected on the TH-2 spaceborne receivers were different. The precision of the GPS and BDS2 (GC) combined single point positioning (SPP) can be improved by 12–14% compared with the GPS-only solution when the position dilution of precision (PDOP) of GPS exceeds three. The overlap comparisons of the GC combined orbits show that the internal orbit precision of the TH-2 satellites is better than 0.7 cm. However, the improvement of the GC combined POD result is only 3–4% with respect to the GPS-only solution, which is limited to the precision of the precise orbit and clock products of BDS2 at the present stage. [ABSTRACT FROM AUTHOR]

TH-2 is China's first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi'an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD. [ABSTRACT FROM AUTHOR]

The satellite attitude error is transmitted to the gravity field through KBR antenna phase center correction and non-conservative force conversion, which affects the accuracy of gravity field inversion. Therefore, obtaining high-precision satellite attitude is one of the important research contents of gravity field inversion. Each satellite of GRACE-FO is equipped with three SCs and an IMU for satellite attitude measurement, and fusion of these two types of data can obtain high-precision satellite attitude. In this paper, we use kalman filter to fuse the original GRACE-FO 1A observation data, and take into account the calibration of the installation matrix of the SCs during the fusion process. Meanwhile, a quaternion integrator that takes angle increments as inputs is derived from the equivalent rotation vector differential equation to address the computational inefficiency of first-order quaternion integrator, the accuracy and computational efficiency are verified using measured data. The experimental results show that after the calibration of the installation matrix of the SCs, the system bias of 2 0 ′ ′ caused by switching from three SCs observations to two SCs observations can be eliminated. The standard deviation of the attitude difference between the obtained attitude in this paper and the attitude calculated by JPL is at most 6 ′ ′ and the proposed incremental quaternion integrator has the same accuracy as the first-order quaternion integrator but with computational efficiency improved by at least 35%. • Attitude determination is critical for gravity field inversion and Orbit determination. • The installation matrix calibration method is simple and effective. • The incremental quaternion integrator is high-precision and computationally efficient. [ABSTRACT FROM AUTHOR]

The TianQin-1 satellite, which was launched on 20 December 2019 into a Sun-synchronous orbit with an altitude of 628 km, is the first technology demonstration satellite for the TianQin project. A micro-electro-mechanical system (MEMS) global positioning system (GPS) receiver is installed on the satellite for precise orbit determination (POD). In addition to the conventional nadir-pointing mode, a specific Sun-pointing mode was used by the satellite owing to the limitation of system resources. The in-flight performance of the MEMS GPS receiver was assessed. The average numbers of available satellites for dual-frequency navigation in the nadir-pointing and Sun-pointing modes are 7 and 5, respectively. The qualities of the P2 code and carrier phase observations are basically equal for both modes. The average root mean square of the multipath errors for C1 observations in the Sun-pointing mode is 0.29 m, slightly larger than that in the nadir-pointing mode. In the Sun-pointing mode, the body of the TianQin-1 satellite rotates around the Sun-pointing axis, which may provide favourable geometric conditions for the estimation of the antenna phase center offset (PCO) corrections in the X, Y, and Z directions. Its feasibility is demonstrated using the simulated data. The GPS measurements of TianQin-1 are then used to estimate the PCO corrections in all three directions while in the Sun-pointing mode and in the Z direction while in the nadir-pointing mode. Satellite laser ranging validation shows that the orbit accuracy of TianQin-1 is approximately 5.90 cm in the nadir-pointing mode. In the Sun-pointing mode, the three-dimensional position difference of 5-h overlap decreased from 8.87 cm to 8.73 cm when the antenna PCO corrections were used in the POD. [ABSTRACT FROM AUTHOR]