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The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations. [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]

In this paper, the inter-satellite link (ISL) aided X-ray pulsar-based navigation (XPNAV) system is studied to improve the survivability of space-borne gravitational wave detector. An unscented transform (UT) based distributed Kalman estimator is proposed for state estimation within less computational and communication costs. Three different navigation scenarios are designed based on a typical large-scale distributed heliocentric orbital space-borne gravitational wave detector, Laser Interferometer Space Antenna (LISA). Simulation results show that the positioning root-mean-square error (RMSE) reduces ̃28% after introducing the ISL to XPNAV. Moreover, the proposed distributed Kalman estimator and the classical Kalman estimator shows similar performance in XPNAV/ISL integrated navigation system with the positioning RMSE of ̃528 m and ̃520 m, respectively. Compared with the classical method, both analytical and simulating analyses demonstrate that the proposed algorithm efficiently reduces the computational costs to 1 / N 2 for a team with N agents and avoids additional communication needs simultaneously. The efficient distributed Kalman estimator-based XPNAV/ISL integrated navigation provides a high-performance autonomous navigation solution for interplanetary spacecraft formation flying missions. • Pulsar and inter-satellite link are used to aid space-borne gravitational wave detector. • We Introduce distributed estimator into autonomous navigation for formation flying. • Distributed estimator reduce computational costs within seldom loss of accuracy. [ABSTRACT FROM AUTHOR]

Mission planning for deep space detectors is a pivotal step in the successful execution of detection missions. Traditional planning approaches, which typically compartmentalize mission planning and data transmission scheduling, exhibit limitations in adapting to uncertainties and are often inadequate in responding to unforeseen opportunity targets. This paper introduces a mission planning method for deep space detectors designed to address these challenges. Firstly, a Markov Decision Process (MDP) model is formulated, integrating mission planning and data transmission scheduling, with a consideration for planning balance between detection missions and opportunity targets. Subsequently, a Planning Balance with Proximal Policy Optimization (PB-PPO) algorithm is proposed. The proposed algorithm, based in the Proximal Policy Optimization (PPO) algorithm, integrates an orthogonal initialization algorithm to afford improved control over parameter updates. Furthermore, a dynamic learning rate strategy is implemented to accelerate convergence speed. Experimental results show that, the PB-PPO achieves rewards that are 4.42%, 6.78%, 18.32%, and 26.81% higher than those obtained by compared algorithms. Additionally, the PB-PPO demonstrates the capability to address the planning balance between detection missions and opportunity targets, ensuring stable reward growth even when planning a significant number of opportunity targets. In summary, the PB-PPO integrates of MDP, deep reinforcement learning, and innovative strategies to make it a robust solution for detector mission planning in the complex and dynamic environment of deep space. • An MDP model is formulated to integrate mission planning and data transmission scheduling. • A deep reinforcement learning algorithm is introduced for the mission planning of deep space detectors. • The proposed approach effectively addresses the planning balance between detection missions and opportunity targets. [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]

Purpose: The purpose of this paper is to focus on the performance of three typical nonlinear least-squares estimation algorithms in atmospheric density model calibration. Design/methodology/approach: The error of Jacchia-Roberts atmospheric density model is expressed as an objective function about temperature parameters. The estimation of parameter corrections is a typical nonlinear least-squares problem. Three algorithms for nonlinear least-squares problems, Gauss–Newton (G-N), damped Gauss–Newton (damped G-N) and Levenberg–Marquardt (L-M) algorithms, are adopted to estimate temperature parameter corrections of Jacchia-Roberts for model calibration. Findings: The results show that G-N algorithm is not convergent at some sampling points. The main reason is the nonlinear relationship between Jacchia-Roberts and its temperature parameters. Damped G-N and L-M algorithms are both convergent at all sampling points. G-N, damped G-N and L-M algorithms reduce the root mean square error of Jacchia-Roberts from 20.4% to 9.3%, 9.4% and 9.4%, respectively. The average iterations of G-N, damped G-N and L-M algorithms are 3.0, 2.8 and 2.9, respectively. Practical implications: This study is expected to provide a guidance for the selection of nonlinear least-squares estimation methods in atmospheric density model calibration. Originality/value: The study analyses the performance of three typical nonlinear least-squares estimation methods in the calibration of atmospheric density model. The non-convergent phenomenon of G-N algorithm is discovered and explained. Damped G-N and L-M algorithms are more suitable for the nonlinear least-squares problems in model calibration than G-N algorithm and the first two algorithms have slightly fewer iterations. [ABSTRACT FROM AUTHOR]

• 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]

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]

• We introduce a graph theory model and utilize dispatchable STN to address the mission planning problem for deep space detectors. • The proposed algorithm efficiently decreases the network scale and streamline the computational workload. • Our proposed algorithm effectively tackles the challenge of dynamic mission scheduling to effectively handle emergencies. Deep space exploration activities can effectively promote the development and application of space technology, which holds significant scientific and strategic value. The multi-mission and long-period detector is executed in deep space, and numerous temporal constraints are generated by mission planning. Moreover, scheduled missions may face external uncertainties, hindering their smooth execution. Therefore, temporal constraint processing strategies that possess dynamic adjustment capabilities play a crucial role in ensuring the successful execution of deep space detectors. Existing methods primarily concentrate on investigating fixed mission series, with limited efficiency in planning. Specifically, these methods do not rigorously enforce temporal constraints and lack the capability to handle the disruptions caused by emergencies, which hinder the smooth execution of planned missions. In this paper, we propose a dynamic temporal constraints algorithm, aiming to efficiently plan missions subject to temporal constraints and let it possess a certain degree of dynamic adjust capability. The simulation results demonstrate the effective simplification of redundant temporal constraints in mission networks by the proposed algorithm. In comparison to the classical algorithm, the computation time exhibits a clear advantage. Furthermore, the proposed algorithm possesses the capability to perform local, small-scale dynamic adjustments in response to emergencies that may disrupt the normal execution of missions. Consequently, this research establishes a robust basis for addressing temporal constraints in deep space detectors. [ABSTRACT FROM AUTHOR]

An experimental satellite mission termed atmospheric density detection and precise orbit determination (APOD) was developed by China and launched on 20 September 2015. The micro-electro-mechanical system (MEMS) GPS receiver provides the basis for precise orbit determination (POD) within the range of a few decimetres. The in-flight performance of the MEMS GPS receiver was assessed. The average number of tracked GPS satellites is 10.7. However, only 5.1 GPS satellites are available for dual-frequency navigation because of the loss of many L2 observations at low elevations. The variations in the multipath error for C1 and P2 were estimated, and the maximum multipath error could reach up to 0.8 m. The average code noises are 0.28 m (C1) and 0.69 m (P2). Using the MEMS GPS receiver, the orbit of the APOD nanosatellite (APOD-A) was precisely determined. Two types of orbit solutions are proposed: a dual-frequency solution and a single-frequency solution. The antenna phase center variations (PCVs) and code residual variations (CRVs) were estimated, and the maximum value of the PCVs is 4.0 cm. After correcting the antenna PCVs and CRVs, the final orbit precision for the dual-frequency and single-frequency solutions were 7.71 cm and 12.91 cm, respectively, validated using the satellite laser ranging (SLR) data, which were significantly improved by 3.35 cm and 25.25 cm. The average RMS of the 6-h overlap differences in the dual-frequency solution between two consecutive days in three dimensions (3D) is 4.59 cm. The MEMS GPS receiver is the Chinese indigenous onboard receiver, which was successfully used in the POD of a nanosatellite. This study has important reference value for improving the MEMS GPS receiver and its application in other low Earth orbit (LEO) nanosatellites. [ABSTRACT FROM AUTHOR]

Precise relative position determination is a prerequisite for radar interferometry by formation flying satellites. It has been shown that this can be achieved by high-quality, dual-frequency GPS receivers that provide precise carrier-phase observations. The precise baseline determination between satellites flying in formation can significantly improve the accuracy of interferometric products, and has become a research interest. The key technologies of baseline determination using spaceborne dual-frequency GPS for gravity recovery and climate experiment (GRACE) formation are presented, including zero-difference (ZD) reduced dynamic orbit determination, double-difference (DD) reduced dynamic relative orbit determination, integer ambiguity resolution and relative receiver antenna phase center variation (PCV) estimation. We propose an independent baseline determination method based on a new strategy of integer ambiguity resolution and correction of relative receiver antenna PCVs, and implement the method in the NUDTTK software package. The algorithms have been tested using flight data over a period of 120 days from GRACE. With the original strategy of integer ambiguity resolution based on Melbourne-Wübbena (M-W) combinations, the average success rate is 85.6%, and the baseline precision is 1.13 mm. With the new strategy of integer ambiguity resolution based on a priori relative orbit, the average success rate and baseline precision are improved by 5.8% and 0.11 mm respectively. A relative ionosphere-free phase pattern estimation result is given in this study, and with correction of relative receiver antenna PCVs, the baseline precision is further significantly improved by 0.34 mm. For ZD reduced dynamic orbit determination, the orbit precision for each GRACE satellite A or B in three dimensions (3D) is about 2.5 cm compared to Jet Propulsion Laboratory (JPL) post science orbits. For DD reduced dynamic relative orbit determination, the final baseline precision for two GRACE satellites formation is 0.68 mm validated by K-Band Ranging (KBR) observations, and average ambiguity success rate of about 91.4% could be achieved. [ABSTRACT FROM AUTHOR]

Two classic empirical solar radiation pressure (SRP) models, the Extended Center for Orbit Determination in Europe (CODE) Orbit Model ECOM 5 and ECOM 9 have been widely used for Global Positioning System (GPS) Medium Earth Orbit (MEO) satellites precise orbit determination (POD). However, these two models are not suitable for BeiDou Geostationary Earth Orbit (GEO) satellites due to their special attitude control mode. With the experimental design method this paper proposes a new empirical SRP model for BeiDou GEO satellites, which is featured by three constant terms in DYX directions, two sine terms in DX directions and one cosine term in the Y direction. It is the first time to reveal that the periodic terms in the D direction are more important than those in YX directions for BeiDou GEO satellites. Compared with ECOM 5 and ECOM 9, the BeiDou GEO satellite orbits are significantly stabilized with the new SRP force model. The average orbit overlapping root mean square (RMS) achieved by the proposed model is 7.5 cm in the radial component, which is evidently improved over those of 37.4 and 13.2 cm for ECOM 5 and ECOM 9, respectively. In addition, the correlation coefficients between GEO orbit overlaps precision and the elevation angle of the Sun have been decreased to −0.12, 0.21, and −0.03 in radial, along-track and cross-track components by using the proposed model, while they are −0.94, −0.79 and −0.29 for ECOM 5 and −0.70, 0.21 and 0.10 for ECOM 9. Moreover, the standard deviation (STD) of Satellite Laser Ranging (SLR) data residuals for the GEO satellite C01 is reduced by 37.4% and 16.1% compared with those of ECOM 5 and ECOM 9 SRP models. [ABSTRACT FROM AUTHOR]

A method of estimating the relative clocks between two spaceborne global positioning system (GPS) receivers based on the single-difference (SD) observations is investigated in this paper. Especially, the advantages of introducing a double-difference (DD) solution constraint, including the orbits and ambiguities, are discussed with the simulated data and the real data of Gravity Recovery And Climate Experiment (GRACE) satellites. The theoretical accuracy analysis shows that the accuracy of the relative clocks is improved and the edge effects are eliminated with a DD solution constraint. The simulations indicate a potential accuracy improvement of at least 30% of the relative clocks with the constraint. Furthermore, one month׳s real data is processed and the overlapping data arcs are used to validate the accuracy of the relative clock solutions. The average overlapping root mean square (RMS) of the relative clock solutions is approximate 99 ps and 31 ps without and with the DD solution constraint, respectively. Moreover, the jumps of the day boundaries are weakened evidently by adding the DD solution constraint. This paper demonstrates that the accuracy and stability of the estimated relative clocks between two low earth orbit (LEO) satellites from SD observations are improved obviously with the DD solution constraint. [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 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 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]

TianQin is a geocentric space-based gravitational-wave observatory mission consisting of three drag-free controlled satellites in an equilateral triangle with an orbital radius of 1 0 5 km. The constellation faces the white-dwarf binary RX J0806.3 + 1527 located slightly below the ecliptic plane, and is subject to gravitational perturbations that can distort the formation. In this study, we present combined methods to optimize the TianQin orbits so that a set of 5-year stability requirements can be met. Moreover, we discuss slow long-term drift of the detector pointing due to orbital precession, and put forward stable orbits with six other pointings along the lunar orbital plane. Some implications of the findings are pointed out. [ABSTRACT FROM AUTHOR]