Precise Orbit Research Articles

Analysis of BDS inter-satellite link ranging performance

The Ka-band inter-satellite link (ISL) is a key technology of BeiDou Global Navigation Satellite System (BDS-3) that can improve the system performance. Based on 30 days of ISL observations, we analyze the BDS-3 ISL ranging performance and the related influencing factors, such as satellite manufacturer, satellite orbit type and link type. The fitting residuals of the ISL geometry-free observations are used to characterize the measurement noise, and the post-fit ISL residuals from precise orbit determination (POD) and precise clock estimation (PCE) are used to further validate the ranging performance. The fitting residuals follow a normal distribution, and the average root mean square (RMS) value for all 421 links is approximately 2.5 cm. The satellite manufacturers, China Academy of Space Technology (CAST) and Shanghai Engineering Center for Microsatellites (SECM), have an obvious impact on the ISL measurement noise. The RMS of the ISL fitting residuals for the links established by the two CAST satellites is only 1.45 cm, while it can reach 3.34 cm for the links established by the two SECM satellites. This correlation between ISL ranging performance and the satellite manufacturer is also found in the POD and PCE post-fit ISL residuals. The RMS of PCE residuals is about 3.1 cm, while the POD residuals are larger with the RMS of 5.5 cm due to the effect of orbital errors, especially for the Inclined Geosynchronous Orbit (IGSO) and Geostationary Orbit (GEO) satellites. Overall, the ranging accuracy of the BDS-3 ISL is better than 5 cm according to the above analyses. Furthermore, the BDS-3 satellite orbit and clock results are evaluated by internal consistency check and external comparison to analyze the application of ISL observations.

Satellite laser ranging to Galileo satellites: symmetry conditions and improved normal point formation strategies

High-precision satellite laser ranging measurements to Galileo retroreflector panels are analyzed to determine the angle of incidence of the laser beam based on specific orientations of the panel with respect to the observing station. During the measurements, the panel aligns with respect to the observing station in such a way that multiple retroreflectors appear at the same range, forming regions of increased data density—separated by a few millimeters. First, measurements to a spare IOV-type retroreflector mounted on an astronomical mount at a remote location 32 km away from the Graz laser ranging station are performed. In addition, more than 100 symmetry passes to Galileo satellites in orbit have been measured. Two novel techniques are described to form laser ranging normal points with improved precision compared to traditional methods. An individual normal point can be formed for each set of retroreflectors at a constant range. The central normal point was shown to be up to 4 mm more accurate when compared with a precise orbit solution. Similar offsets are determined by applying a pattern correlation technique comparing simulated with measured data, and the first method is verified. Irregular reflection patterns of Galileo FOC panels indicate accumulated far-field diffraction patterns resulting from non-uniform retroreflector distributions.

An effective automatic processing engine for improving the multi-GNSS constellation precise orbit prediction

Orbit prediction (OP) recently tends to be a very crucial step for supporting real-time GNSS orbit services due to the dynamic stability of navigation satellite orbits. The OP performance depends on the length of the predicted orbits and the accuracy of precise orbit determination (POD) as basis. Considering this, a new automatic processing engine is established for improving the multiple global navigation satellite systems (multi-GNSS) constellation OP performance. From the architecture-oriented high-performance parallel processing perspective, the multi-node and multi-core computer sources are fully exploited to implement the hourly update of the current multi-GNSS POD. For MEO-type satellites (e.g., Galileo satellites), the accuracy of predicted orbits is improved from 3.8 cm, 6.5 cm, and 12.3 cm to 3.5 cm, 4.3 cm, and 6.3 cm, in the radial, cross, and along directions, respectively, compared to the three-hour POD update. Despite the shortened OP length, the OP performance of regional navigation satellite system (RNSS) satellites is still limited due to their regional observability. The BDS-IGSO and QZSS-IGSO satellitesexhibit radial directional orbital errors of up to 36.9 cm and 28.9 cm, respectively. Therefore, an orbit fitting (OF) processing method with orbit reconstruction is implemented into the processing engine. By utilizing this method, the radial orbital errors for BDS-IGSO and QZSS-IGSO satellites can be reduced to 7.0 cm and 10.4 cm, respectively. The mean real-time positioning errors are thus reduced from 28.3 to 18.4 cm and from 24.4 to 18.2 cm in the horizontal and vertical components, respectively.

Impacts of satellite clock errors on GPS/BDS/Galileo real-time PPP time transfer

By utilizing the real-time precise orbit and clock products provided by International GNSS Service (IGS), it is feasible to calculate real-time PPP (RTPPP) time and frequency transfer. The quality of these real-time precise products has a significant effect on the performance of clock comparisons and time transfer. This paper focuses on real-time clock comparisons with IGS real-time multi-GNSS precise products, which tries to explore the potential of GNSS RTPPP time transfer in time and frequency community. By using real-time precise satellite orbit and clock products from two IGS analysis centers, i.e. CNES and WHU, the clock comparisons and time transfer performance of four time links are comprehensively investigated. It is shown that the statistical uncertainty of real-time clock comparison based on multi-GNSS is within 0.15 ns, and GPS RTPPP provides time transfer results with better performance than BDS-3 and Galileo. In addition, the deviations occur in remote time links results of BDS-3 and Galileo-only between using CNES and WHU, the maximum difference can reach up to 1.10 ns. It is shown that real-time BDS-3 and Galileo satellite products of CNES and WHU are inconsistent, and will affect the time transfer performance. The paper also investigates the receiver clock offset solutions determined by using different available satellites. The results show that there are significant satellite-related biases between different satellites, especially for BDS-3 and Galileo. Thus, the reference time scales determined by using different satellites are inconsistent, and further, the time transfer for long baseline time links will be affected as there are few common view satellites for remote stations.

Improving Thermospheric Density Predictions in Low‐Earth Orbit With Machine Learning

AbstractThermospheric density is one of the main sources of uncertainty in the estimation of satellites' position and velocity in low‐Earth orbit. This has negative consequences in several space domains, including space traffic management, collision avoidance, re‐entry predictions, orbital lifetime analysis, and space object cataloging. In this paper, we investigate the prediction accuracy of empirical density models (e.g., NRLMSISE‐00 and JB‐08) against black‐box machine learning (ML) models trained on precise orbit determination‐derived thermospheric density data (from CHAMP, GOCE, GRACE, SWARM‐A/B satellites). We show that by using the same inputs, the ML models we designed are capable of consistently improving the predictions with respect to state‐of‐the‐art empirical models by reducing the mean absolute percentage error (MAPE) in the thermospheric density estimation from the range of 40%–60% to approximately 20%. As a result of this work, we introduce Karman: an open‐source Python software package developed during this study. Karman provides functionalities to ingest and preprocess thermospheric density, solar irradiance, and geomagnetic input data for ML readiness. Additionally, it facilitates developing and training ML models on the aforementioned data and benchmarking their performance at different altitudes, geographic locations, times, and solar activity conditions. Through this contribution, we offer the scientific community a comprehensive tool for comparing and enhancing thermospheric density models using ML techniques.

Assessing Thermospheric Neutral Density Models Using GEODYN's Precision Orbit Determination

AbstractThis study focuses on utilizing the increasing availability of satellite trajectory data from global navigation satellite system‐enabled low‐Earth orbiting satellites and their precision orbit determination (POD) solutions to expand and refine thermospheric model validation capabilities. The research introduces an updated interface for the GEODYN‐II POD software, leveraging high‐precision space geodetic POD to investigate satellite drag and assess density models. This work presents a case study to examine five models (NRLMSIS2.0, DTM2020, JB2008, TIEGCM, and CTIPe) using precise science orbit (PSO) solutions of the Ice, Cloud, and Land Elevation Satellite‐2 (ICESat‐2). The PSO is used as tracking measurements to construct orbit fits, enabling an evaluation according to each model's ability to redetermine the orbit. Relative in‐track deviations, quantified by in‐track residuals and root‐mean‐square errors (RMSe), are treated as proxies for model densities that differ from an unknown true density. The study investigates assumptions related to the treatment of the drag coefficient and leverages them to eliminate bias and effectively scale model density. Assessment results and interpretations are dictated by the timescale at which the scaling occurs. DTM2020 requires the least scaling (∼−7%) to achieve orbit fits closely matching the PSO within an in‐track RMSe of 7 m when scaled over 2 weeks and 2 m when scaled daily. The remaining models require substantial scaling of the mean density offset (∼30 − 75%) to construct orbit fits that meet the aforementioned RMSe criteria. All models exhibit slight over or under‐sensitivity to geomagnetic activity according to trends in their 24‐hr scaling factors.

Precise Orbit Determination of the MESSENGER Spacecraft

The NASA MESSENGER mission explored Mercury for more than four years to investigate the properties of the planet. To safely operate in the harsh conditions around Mercury, the spacecraft was in a highly eccentric orbit with a low periapsis altitude. The radiation environment had a strong impact on the spacecraft orbit evolution because of the proximity of Mercury to the Sun. A detailed modeling of the nonconservative forces is then a key factor to enhance the precise orbit determination of the spacecraft. We present here refined models of the nonconservative forces, including thermal reradiation effects, that enabled significant improvements in the trajectory reconstruction. A crossover analysis based on the Mercury Laser Altimeter (MLA) data was carried out to cross-check the accuracy of the orbit determination results. The trajectories retrieved by using the refined spacecraft dynamical model provide reduced height misfit at crossover points, indicating a high-quality reconstruction. Our new solutions of the spacecraft orbits are then archived to be used as auxiliary information for the data analysis of other MESSENGER instruments.

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.

Multi-GNSS Precise Point Positioning enhanced by the real navigation signals from CENTISPACETM LEO mission

The Low Earth Orbit (LEO) satellites can significantly reduce the convergence time of Precise Point Positioning (PPP), as the rapid motion of LEO satellites leads to the fast changes of the observation geometry. This helps to accelerate the separation of ambiguity as well as receiver’s positions. In this study, the real dual-frequency navigation signals of the CENTISPACETM ESAT1 satellite are used to enhance the Multi-GNSS Precise Point Positioning (PPP). The onboard GPS, Galileo and BDS-3 observations are used to derive the precise orbits of ESAT1, while the clock is determined based on the data from a ground network established by Wuhan University. With them, the impact of the ESAT1 on float PPP with single, dual, and three constellations (GPS-only, Galileo-only, BDS-3 only, GPS/Galileo, GPS/BDS-3, Galileo/BDS-3, and GPS/Galileo/BDS-3) is analyzed in terms of convergence time and positioning accuracy. The analysis reveals that the average convergence time in the east direction is reduced by 7.9, 2.4, 12.0, 2.0, 3.4, 2.6 and 1.3 min respectively. Additionally, the 3D accuracy improves around 3.2, 4.1, 5.8, 1.1, 0.3, 1.5 and 0.6 cm respectively. Furthermore, the contribution of ESAT1 observations for Mult-GNSS PPP with Ambiguity Resolution (PPP-AR) is also investigated. The average Time to First Fix (TTFF) of each solution can be reduced about 8.1, 5.2, 4.9, 1.3, 0.9, 1.1 and 0.4 min, respectively. Overall, the PPP and PPP-AR are benefited with LEO signals, in particularly for the single-system solutions, and the results demonstrate the promising contribution of LEO on high-accuracy positioning.

Validation of long arc orbit determination method based on orbital residuals analysis and determination of coordinates of Chinese SLR stations using the LAGEOS satellites

Satellite Laser Ranging (SLR) technology is one of the main technologies in the field of space geodesy, it has played an extremely important role in laser ranging data application and research. As a commonly used geodynamic satellites, the main contribution of LAGEOS and LAGEOS-2 is the solution of orbit determination and station coordinates. At present, there are 8 analysis centers of the International Laser Ranging Service (ILRS) to release the precise orbit products for the two LAGEOS satellites. However, there is currently no relevant research on the analysis of the consistency of these orbits. So, the authors would evaluate the accuracies of them, and the results show that the orbital accuracies of the two LAGEOS satellites are 3 ∼ 5 cm. SLR is regarded as one of the important input data of the International Terrestrial Reference Frame (ITRF), the analysis center of ILRS provides weekly solutions of station coordinates for ITRF. But, due to the limitation of SLR observation conditions, for example most observations of Chinese SLR stations can be made at night, and laser ranging test cannot be conducted in rainy days, the orbit solution of the seven-day arc may have the problem of less data. Therefore, this paper proposed a method for computing the station coordinates based on long arc orbit determination, and we developed the LAODGEO software (Long Arc Orbit Determination Software for Geodynamic Satellite), which is used to solve the orbits of two LAGEOS satellites and station coordinates of five SLR stations in China. The results show that the obtained orbital precision is basically superior to 3.70 cm, and the 3DRMS values between station coordinates solved by us and the coordinates published by SLRF2014 are mostly smaller than 0.013 m, which is consistent with research results domestic and overseas.

Configuration Design Method of Mega Constellation for Low Earth Orbit Observation

The configuration optimization design of Low Earth Orbit observation mega constellation in complex space environment is a nonlinear problem that is difficult to solve analytically. In this paper, a constellation design method is proposed, considering satellite imaging width, formation flying of subgroup satellites, and global uniform coverage by payloads. Firstly, a configuration of satellites with the same subsatellite trajectory is proposed, and its orbital analytical expression under J2 perturbation is provided. Then, the relative motion feature points are extracted near the orbit of each satellite, and a group of uniform natural accompanying satellites are set to corresponding points. Afterwards, the orbit parameters of satellite and its companions are set as initial values, and the precise orbits under the High Precision Orbit Propagator model are solved in the neighborhood by using the Nondominated Sort Particle Swarm Optimization algorithm. Finally, the correctness of the configuration design method is verified by numerical simulation.

Orbit stabilization for the new insertion devices in SSRF

During the Shanghai Synchrotron Radiation Facility (SSRF) beamline project, fourteen new insertion devices (IDs) have been successfully installed and transitioned to operation. However, these new IDs led to considerable closed orbit distortions in the SSRF storage ring. In the canted beamlines, the theoretical current values of dipoles required for the closed dual-canted angle were established, however, errors in the actual machine make a significant effect on closed orbit. To address this, an adjustment configuration, based on the response matrix, was developed for the closed dual-canted angles. Additionally, an orbit feedforward compensation system equipped with corrector coils, was employed. As a result, the maximum horizontal and vertical orbit distortions induced by the IDs were successfully decreased to less than 5.0 μm and 3.5 μm, respectively. Furthermore, a specialized local fast feedback system was designed to maintain the precise orbit and angle stability for the Hard X-ray Nanoprobe beamline.

A Novel Method for Improving LEO Kinematic Real-Time Precise Orbit Determination With Neural Networks

A Novel Method for Improving LEO Kinematic Real-Time Precise Orbit Determination With Neural Networks

Method and Application of High-Precision Open-Loop Velocity Measurement of Tianwen-1 Probe

In view of the requirements of Tianwen-1 missions on precision orbit determination and scientific application, this paper proposes a high-precision open-loop velocity measurement method based on ground-based radio. At first, relying on space–ground TT&C resources of the Tianwen-1 probe, the paper designs an open-loop velocity measurement strategy based on China’s deep-space network. Then, it proposes a core algorithm of open-loop velocity measurement based on local cross-correlation reconstruction to obtain instantaneous Doppler frequency observables. This algorithm is characterized by a high ability to avoid phase lock loss, convenient and efficient implementation, and flexible parameter configuration and is suitable for high-precision velocity measurement in the case of high dynamics and low signal-to-noise ratios. On this basis, the similarity and difference of velocity observables between open-loop and baseband velocity measurements are analyzed comparatively. Finally, on the basis of the open-loop velocity measurement method, the paper carries out tests on high precision orbit determination with independent support of velocity measurement, as well as on Mars radio occultation. According to the research results, the accuracy of open-loop velocity measurement can reach 0.05 mm/s (in 1-s integration time), which is 2 to 3 times better than that of baseband velocity measurement. Open-loop velocity measurement can independently support orbit determination accuracy of 50 m of the Tianwen-1 probe and effectively support autonomous retrieval of Martian ionospheric electron density profiles. Thus, this method can be effectively applied to future missions of deep-space exploration and research of planetary radio science.

Array-Aided Precise Orbit and Attitude Determination of CubeSats using GNSS

Array-Aided Precise Orbit and Attitude Determination of CubeSats using GNSS

Physics-informed neural network reconciles Australian displacements and tectonic stresses

Stress orientation information is invaluable to evaluate active tectonic forces within the Earth’s crust. The global dataset provided by the World Stress Map offers a rich resource of stress indicators, facilitating the calibration of mechanical models to extract complete stress and displacement fields. However, traditional inversion processes are hampered by the manual tuning of geomechanical properties and boundary conditions to reconcile simulations with observations. In this study, we introduce ML-SEISMIC (machine learning for stress estimation integrating satellite image and computational modelling), a physics-informed deep neural network approach to autonomously align stress orientation data with an elastic model. It nearly completely bypasses the need for explicit boundary condition inputs and yields comprehensive distributions of material properties, displacements, and stress tensors. Application of this methodology to Australia, coupled with precise global navigation satellite systems observations, unveils a robust and scale-independent interpolation framework. Additionally, it pinpoints regions where stress orientation reinterpretation is warranted. Our results present a streamlined yet powerful process, offering a substantial leap forward in geodynamic investigations. This approach promises to unify velocity and stress orientation observations with physical models, ushering in a new era of insights into Earth’s dynamic processes.

Theory of Functional Connections and Nelder–Mead optimization methods applied in satellite characterization

The growing population of man-made objects with the build up of mega-constellations and the multiplication of space debris not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but also poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, the applications of two optimization procedures are proposed and analyzed to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder–Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. We propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second proposed procedure takes advantage of the Nelder–Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.

Joint determination of Venus gravity and atmospheric density through EnVision radio science investigation

The ESA mission EnVision will address its main scientific questions through a detailed mapping of the surface and interior properties of Venus. A precise reconstruction of the spacecraft trajectory is a key requirement for the EnVision scientific investigations, including radio science. To precisely constrain the orbit evolution, refined models of the dynamical forces are included in the Precise Orbit Determination (POD) process. We developed a methodology based on a batch-sequential filter that enables a joint estimation of Venus gravity and atmospheric density. Our approach yields an accurate compensation of atmospheric mismodeling, simulated through semi-empirical predictions of the atmospheric density provided by general circulation models (GCM), e.g., Venus Climate Database (VCD). Numerical simulations of the EnVision radio science investigation were carried out by using a perturbative analysis of the dynamical forces, which accounts for atmospheric density errors ≥ 200%. By adjusting a set of atmospheric scale factors, our proposed strategy enables an estimation of the atmospheric density at the spacecraft altitudes with an accuracy of 25%. The improved dynamical model yields accuracies in the orbit reconstruction of 1–2 m, 30–40 m and 20–30 m in the radial, transverse and normal directions.

USER IMPLEMENTATION AND ASSESSMENT OF BDS-3 PRECISE POINT POSITIONING AUGMENTATION SERVICE WITH NO ECONOMIC COST

Abstract. The satellite-based precise point positioning (PPP) service enables users with high accuracy positions without Internet connections. Currently, two types of satellite-based PPP services are available. One type is commercial service, such as Trimble CenterPoint RTX service. The second type is non-commercial and cost-free service, including the BDS-3 satellite-based PPP service based on PPP-B2b signals. This service is currently open access to all receiver manufacturers. This contribution firstly presents a detailed instruction on how to apply PPP-B2b signals into positioning. Afterwards, the performance of BDS-3 PPP service is validated with both static and kinematic experiments carried out in Wuhan, China, during day of year 168 and 172, 2022. Results indicate that PPP-B2b signals mainly improve BDS-3 clock precision and GPS orbit accuracy. With BDS-3 PPP-B2b augmentation messages, the static satellite-based PPP shows 3.9/6.9/10.3 mm daily solution repeatability in E/N/U directions, respectively. An average of 13.9 min convergence time and 3.42/2.16/6.65 cm E/N/U positioning accuracy are achieved in the simulated kinematic mode. During a 28-min stepper motor driven movement test, 3.48/14.88 cm 2D/3D kinematic positioning accuracy is obtained using the BDS-3 PPP service.

TEST OPTICAL OBSERVATIONS OF THE COSMOS 1408 FRAGMENTS

The non-functioning spacecraft COSMOS 1408 (NSSDCA/COSPAR ID: 1982-092A) was destroyed as a result of tests involving Russian anti-satellite weapons on 15 November 2021. This led to the creation of a significant debris cloud that poses a threat to other objects in low Earth orbit (LEO), particularly those in close orbits. More than 1500 of these fragments reached trackable sizes. Such events require rapid and immediate monitoring through all available ground tracking means, including radar and optical observation. The following study presents the results of optical observations of the selected fragments of COSMOS 1408 in Ukraine. These observations were carried out by the telescope OES30 from the National Space Facilities Control and Test Center of the State Space Agency of Ukraine and the Fast Robotic Telescope (FRT) of the Research Institute "Mykolaiv Astronomical Observatory" in February 2022. The observations demonstrated that Ukrainian optical sensors are capable of tracking LEO space debris objects with radar cross-sections (RCS) less than 0.1 square meters when relatively accurate ephemeris data is available. The astrometric reduction has been performed for the acquired frames with fragments of the satellite, which revealed that orbital parameters of a significant part of the targeting objects were close to the orbital parameters of the original satellite before the event. Furthermore, the results of processing the available observations indicated that the range of apogee heights significantly exceeds the range of perigee heights. These findings align with conclusions drawn by previous researchers. In the future, it will be essential to assess the capabilities of sensors for observing the aftermath of object destruction in LEO, especially during the initial hours and days following such events when precise debris orbit data may be lacking.