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The Copernicus Precise Orbit Determination (CPOD) Service is in charge of computing the precise orbits and auxiliary data files of the Copernicus Sentinel-1, −2, −3 and −6 missions, using the GPS&Galileo observations obtained on-board. The orbit products and auxiliary data files are provided to the corresponding Payload Data Ground Segments (PDGS) and Payload Data Acquisition and Processing (PDAP) components and to external users through the Copernicus Data Space Ecosystem (CDSE). The CPOD Service is supported by the CPOD Quality Working Group (QWG), a group of leading experts on GNSS (Global Navigation Satellite System) and POD, which provides independent orbit solutions and techniques to support the quality control (QC) and the validation of the operational products. The CPOD Service was initially developed in 2013, starting its operational phase in April 2014 after the successful launch of Sentinel-1A. The CPOD Service has accumulated almost 10 years of experience, including its initial development, operations, and periodic evolutions, to the point that currently it is a well-recognized POD Service. This paper shows in detail the architecture of the CPOD Service, its performance and its evolution over the years, and its future outlook. [ABSTRACT FROM AUTHOR]

Broadcast ephemeris plays an important role in positioning, navigation, and timing (PNT) services. With the rise of new constellations of Galileo and BDS3, satellite services are moving towards multi-GNSS fusion. Therefore, systematic evaluation of the multi-GNSS broadcast ephemeris and determination of the impact of ranging errors of different constellations in the multi-GNSS standard single point positioning (SPP) are necessary. In the contribution, the 120-day broadcast ephemeris from 1 January 2022 to 30 April 2022 and precise ephemeris provided by three analysis centers (German Research Center for Geosciences (GFZ), European Centre for Orbital Determination (CODE), and Wuhan University (WHU)) are used to analyze the orbits, clock offsets, and signal-in-space ranging error (SISRE) for GPS, GLONASS, Galileo, BDS2, BDS3, and QZSS (G, R, E, C2, C3, and J). The ephemeris analysis shows that the assessments using the precise ephemeris from the three analysis centers are consistent. The average daily SISREs for different constellations evaluated by GFZ products are 0.16 ± 0.07 m (E), 0.38 ± 0.19 m (J), 0.46 ± 0.19 m (C3), 0.50 ± 0.17 m (G), 1.30 ± 0.27 m (C2), and 2.40 ± 0.73 m (R), respectively. In addition, we propose a weight determination method using joint weighting of SISREs and satellite elevation angle (Ele + SIS) based on the analysis. One consecutive week of observations tracked by 23 permanent reference stations is selected, and a comparison experiment is conducted using the classical elevation angle weighting scheme (Ele) and the Ele + SIS scheme in dynamic SPP to verify the feasibility. Compared to the classic Ele scheme, the positioning accuracy of GREC2C3J combined SPP using the Ele + SIS scheme is improved by 34.2 % in the 3D direction, and the 95th percentile of the positioning errors is reduced by 31.5 %. The same dynamic SPP test using data after one year of modeling the Ele + SIS weighting scheme shows that the enhancement of the positioning accuracy of the Ele + SIS scheme decreases by only 3.7 %, which demonstrates that the Ele + SIS scheme can be used in real-time application. [ABSTRACT FROM AUTHOR]

The Event Horizon Telescope (EHT) is a ground-based array of Very Long Baseline Interferometry (VLBI) telescopes designed to image the event horizon of black holes. To overcome its limitations, this study explores a mission concept involving a two-satellite constellation of VLBI telescopes deployed in Medium Earth Orbit (MEO). Achieving high-resolution black hole images requires precise baseline determination at the millimetre level. To address this challenge, each satellite in the constellation is equipped with two Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) to enhance orbit determination. The results highlight the importance of integer ambiguity resolution and reveal that the ISL primarily improves baseline estimation along the link direction, with minimal impact along the black hole direction. Large intersatellite distances lead to sub-optimal relative orbit accuracy, challenging the attainment of the 3.5 mm relative position accuracy goal along the black hole direction. [ABSTRACT FROM AUTHOR]

The rapidly growing number of objects encircling our planet is an increasing concern. Collisions between these objects have already occurred and pose a potential threat in the future, resulting in the creation of countless debris fragments. In particular, the Low Earth Orbit (LEO) region is densely populated and highly contested. This underscores the critical importance of space surveillance in this area. Moreover, the utilization of Medium Earth Orbit (MEO) and Geosynchronous Earth Orbit (GEO) is also on the rise. To ensure the safety and functionality of operational satellites, it is paramount to accurately determine and continuously monitor the orbits of space objects, mitigating the risk of collisions. Precise and timely predictions of future trajectories are essential for this purpose. In response to these challenges, this survey paper provides a comprehensive review of various methods proposed in the literature for Orbit Determination (OD). It also identifies research gaps and suggests potential directions for future studies, emphasizing the pressing need for adequate Space Situational Awareness (SSA). [Display omitted] • Admissible Region is a robust, reliable cornerstone method for orbit determination. • Machine learning transforms orbit determination, boosting accuracy and efficiency. • Explainable AI is crucial for transparency and trust in orbit determination. • The recent focus on cislunar regime demands novel orbit determination methods. • Undervalued, space-based orbit determination is crucial for accurate cislunar missions. [ABSTRACT FROM AUTHOR]

In the framework of Space Traffic Management (STM) the growing number of space debris and the consequent increased risk of collisions have become a topic of great interest. Moreover, the difficulty of detecting and characterizing a Resident Space Object (RSO) in terms of orbital parameters makes this research field very challenging. In most cases the available observations have a very short duration and an accurate estimation of the orbit is very difficult. This paper introduces the Initial Orbit Determination via Artificial intelligence (IODA) algorithm, a reliable and accurate orbit estimator combining metaheuristic and artificial intelligence frameworks to perform precise orbit determination from Very Short Arcs (VSAs). Starting from an initial orbit estimate derived through an Artificial Bee Colony (ABC) algorithm, a Physics Informed Extreme Learning Machine is employed to increase the accuracy of the predicted orbit. Results on simulated data have shown the robustness of the algorithm to random parameters initialization and a percentage of success of 89% of retrieving the reference orbit with an error under 1 km and 0.01 km/s on the initial target's state. • Description of an AI-based orbit determination tool from very short arcs. • Combination of meta-heuristic and machine learning techniques for accurate orbit estimation. • Tests on simulated data for robustness against random parameters initialization. • Montecarlo simulation on simulated data for robustness against random mission scenarios. [ABSTRACT FROM AUTHOR]

With the rapid construction of the low-earth-orbit (LEO) constellation, LEO Enhanced Global Navigation Satellite System (LeGNSS) has become a hotspot in the research of GNSS applications and services, especially for fast convergence of precise point positioning (PPP). In this study, we analyze the impact of LEO satellites on the spatial geometry based on simulated LEO and real GNSS data, and evaluate the LeGNSS PPP performance with ionosphere-free (IF), undifferenced and uncombined (UDUC), and ionosphere-weighted (IW) models. Eight Multi-GNSS Experiment (MGEX) stations are selected for static and kinematic experiments. Results show that Position Dilution of Precision (PDOP) values of LeGNSS are about 0.5–1.2, which are improved by 38 % and 22 % compared with GPS-only and combined GPS, Galileo, and BDS (G\E\C) solutions. With LEO satellites, the positioning accuracy in east (E), north (N), and up (U) directions are improved by about 50 %, 30 %, and 50 % for the static mode, and about 35 %, 30 %, and 67 % for the kinematic mode. Moreover, the positioning accuracies of the IF, UDUC, and IW models are comparable. For convergence time, the static and kinematic results with LEO satellites are about 1.1 and 1.3 min, respectively, while those without LEO satellites are longer than 10.0 min. In addition, the model with inter-system bias (ISB) constraints can reduce the convergence time by within 1.0 min. [ABSTRACT FROM AUTHOR]

The flex power technology in satellite navigation systems enhances anti-jamming capabilities but can impact the quality of GPS observations and the accuracy of low Earth orbit determination, such as GRACE Follow-On (GRACE-FO) mission. This study investigates the influence of GPS flex power on Hatch-Melbourne-Wübbena (HMW) linear combinations and GRACE-FO kinematic orbits from January 1 to September 30, 2020. Epoch-differenced K-Band Ranging (KBR) data is introduced in orbit determination during the flex power period to improve both absolute and inter-satellite relative accuracy. The analysis indicates that the influence of early flex power (before February 13, 2020) on HMW combinations and orbits is minimal, whereas the effect of later flex power (after February 14, 2020) is significant: (1) HMW combinations exhibit notable systematic discontinuities even with elevation angles greater than 50 degrees, causing the fixing rate of wide-lane ambiguities to drop from 96 % to 80 %. (2) Kinematic absolute orbits show significant deteriorations of approximately 9 mm and 4 mm in the three-dimensional direction for float and integer ambiguity resolution (FAR and IAR), while relative accuracy of FAR and IAR orbits decreases by 50 % and 46 %, respectively. However, using epoch-differenced KBR (DKBR) data, the accuracy of absolute orbits could be increased by up to 15 % and the accuracy of relative orbits could be improved by at least 69 %, which showcases a positive effect. Thus, this can be considered as an alternative method to improve the accuracy of GRACE-FO orbit during the flex power period. [ABSTRACT FROM AUTHOR]

The growth of both operational satellites and orbital debris is creating the requirement for more robust Space Surveillance and Tracking (SST)-related applications. These systems necessarily must leverage ground-based sensors (optical and radar) to realise higher performance solutions. In this context, the European Union Space Surveillance and Tracking (EUSST) consortium groups European national agencies and institutions, and is in charge of carrying out the following services: conjunction analysis, fragmentation analysis and re-entry prediction, and the Italian Air Force is in charge of the latter two. In this framework, the Italian SST Operational Centre (ISOC) has recently upgraded its system to the ISOC Suite, an integrated platform providing multiple functions and services in the SST domain. This paper presents the orbit determination functions provided by the novel ISOC Suite. First, a statistical index is computed to assess the measurements correlation to a catalogued object. If it is successful, the object predicted orbit is refined through measurements according either to batch or sequential filters; otherwise these are used to refine a first estimate of the target orbital state computed according to dedicated methodologies. After the presentation of the prototypal software architecture, the ISOC Suite performance are assessed and discussed both in terms of synthetic and real data. [ABSTRACT FROM AUTHOR]

• The software supports space geodetic data processing, precise positioning and orbit determination, and multi-source fusion navigation. • The core computational engines are written using C++ language and apply efficiency optimization algorithms such as parallel computing, with modular structure, cross-platform capabilities and efficient performance. • The software provides both client and server functions for high-precision navigation services, and centimeter-level multi-source fusion navigation can be achieved in urban scenarios though the integrated system of PPP-RTK/MEMS/VIS/LiDAR. The software platform named GNSS + REsearch, Application and Teaching (GREAT) has been designed and developed by Wuhan University for satellite geodesy and multi-source fusion navigation. GREAT is a comprehensive software platform based on C++ language, with modular structure, cross-platform capabilities and efficient performance. The software mainly focuses on space geodetic data processing, precise positioning and orbit determination, and multi-source fusion navigation. With the integration of multiple space geodetic techniques at observation level, GREAT can achieve the determination of global geodetic parameters. Meanwhile, GREAT can also achieve real-time precise orbit and clock determination by processing GNSS data from globally distributed stations, and the accuracies are about 3–6 cm for orbit and 0.1–0.4 ns for clock. Based on high-precision orbit and clock products, centimeter-level onboard positioning accuracies can be achieved with PPP-RTK in open-sky scenarios. Furthermore, centimeter-level multi-source fusion navigation can be achieved in urban scenarios though the integrated system of PPP-RTK/MEMS/VIS/LiDAR. Additionally, efficiency optimization algorithms such as parallel computing are applied to enable the software to handle the data-intensive and calculation-intensive situations. [ABSTRACT FROM AUTHOR]

High-precision Global Navigation Satellite System (GNSS) orbit and clock products are crucial for precise applications. An evenly distributed global network enables continuous tracking for GNSS satellites, while a regional network may result in tracking gaps in the areas where monitoring stations are not deployed. This also means that the orbit determination accuracy based on a regional network is not comparable to that with a global network. Integrating the measurements from regional ground stations and Low Earth Orbit (LEO) satellites onboard receivers is a potential approach for generating GNSS orbit and clock products with centimeter-level accuracy, which is particularly important for BDS and the local commercial providers relying on a regional network. In the integrated Precise Orbit Determination (POD), LEO satellites are used to compensate for the drawback of regional ground stations in the precise orbit and clock determination of GNSS satellites. To validate the role of LEO satellites in the orbit determination with a regional network, 6 International GNSS Service stations around China and 13 LEO satellites from January 20 to 26, 2019, including GRACE-C/D, SWARM-A/B/C, Jason-3, Sentinel-3A/B, and SAT-A/B/C/D/E are selected in this study to perform the integrated POD. The orbit and clock accuracies of GPS and LEO satellites are evaluated by comparison with precise products. The average Root Mean Square (RMS)of GPS orbit errors in the radial (R), along-track (T) and cross-track (N) directions are 2.27 cm, 3.45 cm, and 3.08 cm, respectively, and the clock accuracy is better than 0.15 ns based on a comparison with the final products provided by Center for Orbit Determination in Europe (CODE). The LEO orbit accuracy is better than 2 cm in the R direction, and the position errors are mostly within 4 cm. The results indicate that the integrated POD can generate high-precision orbit and clock products for GPS and LEO satellites based on regional network stations. Finally, the integrated POD products are assessed for Precise Point Positioning (PPP). Simulated kinematic PPP has a comparable performance in terms of the convergence time and positioning accuracy. With more LEO satellites available, the orbit and clock determination accuracy and PPP positioning accuracy can be improved. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector P 1 and a very short arc (VSA) of optical observations A 2 . Using the conservation laws of the two-body dynamics, we write the problem as a system of 8 polynomial equations in 6 unknowns. We prove that this system is generically consistent, namely, for a generic choice of the data P 1 , A 2 , it always admits solutions in the complex field, even when P 1 , A 2 do not correspond to the same celestial body. The consistency of the system is shown by deriving a univariate polynomial v of degree 8 in the unknown topocentric distance at the mean epoch of the observations of the VSA. Through Gröbner bases theory, we also show that the degree of v is minimum among the degrees of all the univariate polynomials solving this problem. Even though we can find solutions to our problem for a generic choice of P 1 , A 2 , most of these solutions are meaningless. In fact, acceptable solutions must be real and have to fulfill other constraints, including compatibility with Keplerian dynamics. We also propose a way to select or discard solutions taking into account the uncertainty in the data, if present. The proposed orbit determination method is relevant for different purposes, e.g., the computation of a preliminary orbit of an Earth satellite with radar and optical observations, the detection of maneuvres of an Earth satellite, and the recovery of asteroids which are lost due to a planetary close encounter. We conclude by showing some numerical tests in the case of asteroids undergoing a close encounter with the Earth. [ABSTRACT FROM AUTHOR]

In the geocenter motion determination using the Global Navigation Satellite Systems (GNSS), satellite clock offsets are usually estimated as white noise process. The correlation between geocenter coordinates (GCC) and the epoch-wise satellite clocks brings inferior GCC estimates, especially for the Z component. In this contribution, satellite clock offsets are described by the polynomial model, and the deviation of the model from the truth is estimated as a random parameter whose process noise is described by the variogram. Based on 3.7 years of BDS, Galileo and GPS observations from 98 global stations, we investigate the impact of the atomic clock model on GCC estimates. After employing the proposed model, the formal errors of GCC-Z component are reduced by 23–46%, 15–31% and 3–9% for BDS, Galileo and GPS, respectively. When the 7-parameter extended empirical CODE orbit model with the a priori box-wing model (BE7) is used, the atomic clock model reduces the correlation of the B1C parameter and GCC-Z component by 0.28, 0.23 and 0.07 for BDS, Galileo and GPS, respectively. Besides, a mitigation of about 60% is obtained at the 3rd and 5th BDS draconitic harmonics and a mitigation of 55% at the 3rd Galileo draconitic harmonic for the GCC-Z component. The proposed model also contributes to reduce the annual amplitudes of single BDS, Galileo and GPS solutions, improving the agreement with the Satellite Laser Ranging solutions. As an additional verification, the resulting satellite orbits are also improved by satellite clock modeling. When the BE7 model is applied, the day boundary discontinuities of daily orbits are reduced by 3.4–3.6%, and the RMS of orbit differences relative to the ESA precise orbits is reduced by 8.2–8.5% for BDS and Galileo. [ABSTRACT FROM AUTHOR]

• Orbit maneuver-free approach to the angle-only relative orbit determination for is proposed. • The angles-only orbital observability problem is solved by introducing radial basis function neural network to capture the nonlinearity of the perturbed dynamics. • The RBFNN frame including training data acquisition, data pre-processing, and the network design for angles-only orbit determination problem is developed. • The validity of the proposed algorithm is evaluated by numerical simulations. • The anti-noise, generalization performance, and the sensitivity of the solution are checked. Angles-only orbit determination during space situational awareness missions for non-cooperative targets such as space debris is subject to the well-known observability problem, that is, the orbital state is weakly observable or even unobservable because of missing range measurements. The key point to solve this problem is how to quickly capture the nonlinearity of orbit dynamics if only one space-based passive sensor is available to observe the target and translational maneuvers are not executed. To solve the short-arc angles-only problem, this study develops a simple and fast orbit determination method by exploiting the advantages of radial basis function neural network (RBFNN). Emphasis was placed on the design of the RBFNN, which was trained to construct a mapping network model from line-of-sight (LOS) measurements to the relative orbit. First, the perturbed relative orbit dynamics considering the Earth's non-spherical J2 term and air drag was established with the LOS measurement model. Second, a RBFNN-based angles-only orbit determination frame was developed, in which the generator of the training dataset, data preprocessing algorithm, and RBF network structure were designed. Finally, the proposed method was verified and tested using a set of numerical simulations of low-Earth orbit cases. The anti-noise and generalization performance of the designed network and the sensitivity of the solution accuracy to the measurement frequency and span were presented and discussed. Additionally, the advantages of the RBFNN-based method were confirmed by comparison with the results obtained using the BPNN (Back Propagation Neural Network)-based method. The simulation results show that the average orbit prediction error for LEO scenarios is approximately 0.08% using the index of initial relative distance, where only three sets of LOS angles are measured within a span of 24 s. [ABSTRACT FROM AUTHOR]

Satellite laser ranging (SLR) is the only stand-alone and external tool for verifying the accuracy of microwave-based GNSS orbits. On February 2, 2023, the International Laser Ranging Service initiated the SLR global tracking campaign for the complete BeiDou-3 medium Earth orbit (MEO) constellation. This initiative provides an opportunity to unveil the potential issue for BeiDou-3 MEO orbit modeling. An examination of the SLR validation results of precise BeiDou-3 MEO orbits across different IGS/Multi-GNSS Experiment (MGEX) analysis centres (ACs) reveals that the SLR residual standard deviation for BeiDou-3 SECM-B MEOs C225 and C226 orbits reaches 18 cm. This figure is approximately four to nine times those for other BeiDou-3 MEOs. This contradicts the fact that the orbit quality of C225 and C226 is comparable to other satellites. By analyzing the correlation between SLR residuals and de-trend clock residuals, detector-specific bias performance, and the distribution characteristics of SLR residuals relative to satellite azimuth and nadir angles, we diagnose that abnormal SLR validation results for C225 and C226 originate from a large deviation in the official horizontal offsets for the laser retroreflector arrays (LRAs) in the satellite reference frame. LRA horizontal offsets for C225 and C226 are estimated based on SLR residuals. With our adjusted LRA offset estimates, the SLR residual metrics for C225 and C226 orbits (across various IGS/MGEX ACs) are comparable to the results obtained for other BeiDou-3 MEOs. Additionally, our adjustments enable the identification of their orbit modeling errors across different IGS/MGEX ACs according to the pattern of SLR residual variation. From the study, spacecraft manufacturers should be encouraged to conduct a comprehensive review of ground calibrations for BeiDou LRA offsets. This is crucial for optimizing BeiDou orbit model and enhancing its applications in high-precision geosciences. [ABSTRACT FROM AUTHOR]

Global ionosphere maps (GIM), a grid model generated based on observations from global GNSS stations, is often used for ionospheric delay correction and total electron content (TEC) analysis, and is an important data for ionospheric modeling and code bias estimation, as well as related applications. Understanding the spatial variation characteristics of the grid TEC in GIM data can help the better use of GIM data. In this paper, the GIM data of CODE (Center for Orbit Determination in Europe) analysis center for a total of 15 years from 2008 to 2022 are used to analyze the variation of TEC of adjacent grid points and the difference of TEC of four grid points in each grid. The results show that the mean values of the grid TEC variations range from about 0.26–1.86 TECu in the longitude direction and 0.36–2.76 TECu in the latitude direction, and most of the differences in the TECs of neighboring grid points are within ± 2 TECu. In the low solar activity years, the STD of the TEC of the four grid points in most of the grids in the GIM data is less than 1.2 TECu, indicating that the TEC values of the four grid points in most of the grids in their GIMs are relatively close to each other and the differences are small, whereas the differences are larger in the high solar activity years. In other words, the TEC values of the areas covered by the GIM grids in the low solar activity years are close. The results of the study can provide some references and lessons for the interpolation and application of the TEC of the GIM grid, and the TEC modeling of the single-station area. [ABSTRACT FROM AUTHOR]

In order to avoid harmful interference in the radio-frequency spectrum, geosynchronous (GEO) satellite operators coordinate their plans with one another by publicly describing their preferred orbital positions and frequency bands in an assignment process managed by the International Telecommunication Union (ITU), a specialized agency of the United Nations. But once assignments are determined, how well do satellite operators comply with them? This work describes a method for assessing GEO satellite operators' compliance with the physical component of the ITU's satellite network assignments in the geostationary belt using publicly available data. The positions of real, cataloged GEO satellites, measured in longitudinal degrees, are compared with data describing ITU satellite networks published by the Union's Space Services Department to determine whether satellites are operating near an active network assigned to one of their corresponding ITU administrations. Compliance for three satellites that perform relatively frequent longitudinal-shift maneuvers in GEO — Telesat's Nimiq 2 , Russia's Luch (Olymp) , and China's SJ-17 — is assessed over a multi-year study period and discussed. This work illustrates how historical compliance assessment can contribute to the identification and characterization of anomalous satellite behaviors, such as re-positioning the same satellite repeatedly to bring many ITU satellite networks into use, performing non-cooperative close approaches with nearby neighbors, and rendezvous operations, in the Nimiq , Luch , and SJ-17 examples, respectively. • Geosynchronous orbit is the only orbital regime with an existing slotting scheme. • Keeping to assigned orbital positions and frequencies prevents harmful interference. • Once assignments are determined, satellite operators do not always comply with them. • Publicly available data can be used to assess compliance with orbital assignments. • Patterns of violation to guidelines in GEO should inform new rules in LEO. [ABSTRACT FROM AUTHOR]

This paper investigates the practicality of an autonomous and resilient positional navigation using corner cube reflectors on the lunar surface. The proposed approach stands as an efficient navigation solution when the current system, e.g. GPS, is unavailable due to being attacked, jammed or spoofed by a third party. The paper provides a complete setup of the mathematical models using a nonlinear least squares algorithm and covariance analysis. A study is done that determines how the blockage of the Earth affects the proposed solution’s ability to perform positional navigation. Numerical simulations are presented to show the accuracy, performance and practicality of the proposed solution. The results of the proposed solution are compared with the results of an Earth-based ground station system that uses radio frequency to track the given satellite. The results show that the lunar reflector-based system generates more accurate results than the Earth-based ground station system. [ABSTRACT FROM AUTHOR]

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]

• 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]

Precise Point Positioning (PPP) augmentation corrections can enhance the accuracy of Global Navigation Satellite System (GNSS) positioning. Three prominent PPP augmentation services: the third generation of BeiDou Navigation Satellite System (BDS-3) PPP-B2b, Europe's Galileo High Accuracy Service (HAS) and Quasi-Zenith Satellite System (QZSS) Centimeter Level Augmentation Service (CLAS), are evaluated and compared, contributing to the optimal utilization of these services. Based on a 25-day dataset in March 2023, all the three services have made significant improvements in GPS orbit accuracy compared to the broadcast ephemeris. Galileo HAS achieved the highest three-dimension (3D) orbit accuracy for both GPS and Galileo (10.5 and 10.4 cm), followed by CLAS (48.1 and 16.3 cm) and PPP-B2b (GPS: 73.0 cm, BDS-3: 44.6 cm). This distinct performance of PPP-B2b orbits is found for the first time to be related to the large constellation rotation errors, which accounts for roughly half of the orbit errors of along and cross components. Regarding clock errors, PPP-B2b and HAS enhanced GPS clock accuracy to 0.20 ns (70 %) and 0.17 ns (74 %), respectively, over the broadcast clock (0.66 ns), while CLAS shows a much smaller improvement. Moderate correlations of 0.3–0.8 between orbit and clock errors are observed for the three augmentation corrections. For signal in space ranging error (SISRE), HAS (GPS:5.5 cm, Galileo:4.9 cm) outperforms PPP-B2b (GPS:14.3 cm, BDS-3:8.9 cm) and CLAS (GPS:23.6 cm, Galileo:13.7 cm). The 2-hourly kinematic positioning results with an accuracy of better than 20 cm (95th percentile) for the horizontal and vertical component, could be achieved for both PPP-B2b and HAS within 20 min within their service area. It is not recommended rely solely on the orbit/clock/code bias of CLAS for precise positioning, as the positioning accuracy is influenced by the SISRE. PPP-RTK of CLAS achieves horizontal 10 cm (95th percentile) and rapid convergence of mostly less than a minute by incorporating phase bias and atmospheric corrections. [ABSTRACT FROM AUTHOR]

Precise Orbit Determination (POD) of Satellite Laser Ranging (SLR)-tracked satellites is stepping towards millimeter-level precision, which requires further refinement of satellite perturbation models and consideration of more detailed perturbation force models that were not previously taken into accounted. Atmospheric drag is one of the main perturbative forces acting on a Low Earth Orbit (LEO) satellite, however, the atmospheric wind speed associated with atmospheric drag has not been considered in International Laser Ranging Service (ILRS) regular data processing. Therefore, in order to analyze the magnitude of atmospheric wind speed influence on POD of SLR satellites, this paper applies HWM14 (Horizontal Wind Model 14) atmospheric wind speed model to perform POD of LARES, Ajisai, Starlette, Stella, Larets satellites and analyses the results. The results show that after applying HWM14 atmospheric wind speed model, the SLR observation residual WRMS (Weighted Root Mean Square) value for LARES, Starlette, Stella, Larets satellites reach 1.04 cm, 2.13 cm, 1.73 cm, 3.36 cm, respectively, which are reduced by 0.10 cm, 0.30 cm, 0.00 cm, 0.05 cm, respectively. However, for Ajisai, one has an almost the same orbit residual WRMS value of 2.88 cm. The 3D (three-dimensional) orbit overlapping arcs error for LARES is 17.53 cm, which is reduced by 1.75 cm; for Starlette it is 19.12 cm, which is reduced by 0.96 cm; for Stella there is almost same orbit overlapping arcs error of 34.9 cm. The accuracy of orbit forecast for 1 day and 3 days for LARES reaches 147.57 cm and 163.96 cm, respectively, which is improved by 0.04 cm and 20.73 cm in the T (Tangential) direction, respectively. The accuracy of orbit forecast for 1 day and 3 days for Stella reaches 191.77 cm and 308.52 cm, respectively, which is improved by 1.95 cm and 6.74 cm in the T direction, respectively. The accuracy of orbit forecast for 1 day and 3 days for Larets reaches 6.18 m and 145.26 m, respectively, which is improved by 7.81 m and 473.61 m in the T direction, respectively. Above results display that considering HWM14 atmospheric wind speed model has a certain improvement for POD of LARES, Starlette, Stella and Larets. Therefore, the influence of atmospheric wind speed should be considered in the SLR POD and regular data processing. [ABSTRACT FROM AUTHOR]

User differential range error (UDRE) is used to bound satellite clock and orbit errors in satellite-based augmentation system (SBAS). The code carrier incoherence (CCI) originated from satellite payload faults may degrade generated satellite corrections and corresponding UDRE/DFRE bounding. To ease the burden on UDRE caused by the CCI induced ranging error, a code carrier coherence (CCC) monitor is implemented. With SBAS evolving towards L1-L5 dual-frequency multi-constellation direction, ionosphere-free smoothing is preferred for both ground and airborne data processing, saving the great effort of bounding the ionosphere correction. Due to the more pronounced CCI fault in the L5 signal compared to the L1 signal, its impact on user positioning is magnified. It has been analyzed that the presence of satellite clock failure CCI fault does not undermine the accuracy of the generated satellite corrections. However, to enhance the system availability, the satellite clock failure should be considered and a dual-frequency CCC monitor is required to monitor the measurements from both frequencies, while excluding the effects of ionosphere delay. One solution is to add another L1-like monitor for monitoring the additional L5 signal. Since only ionosphere-free errors need to be bounded in the dual-frequency system, an ionosphere-free monitor is another choice. Furthermore, a chi-squared monitor is proposed combining of three ionosphere-free statistics to monitor both frequencies simultaneously. These options are compared on the protected fault space and the performance on the probability of missed detection. It is concluded that the chi-squared monitor is an optimal choice, which protects user against an arbitrary CCI fault space excluding the ones with the form of ionosphere anomalies, and at the same time, achieves lower probability of missed detection than other monitors with the same fault magnitude. [ABSTRACT FROM AUTHOR]

This tutorial covers the use of absolute astrometry, in particular from the combination of the Hipparcos and Gaia missions, to identify faint companions to nearby stars and to measure the masses and orbits of those companions. Absolute astrometry has been used with increasing success to discover new planets and brown dwarfs and to measure masses and orbits for systems with periods as long as centuries. This tutorial summarizes the nature of the underlying astrometric data, the approach typically used to fit orbits, and the assumptions about that data implicit throughout the process. It attempts to provide intuition for the sensitivity of astrometry as a function of stellar and companion properties and how the available constraints depend on the character and quantity of data available. This tutorial is written for someone with some background in astronomy but with no more than a minimal acquaintance with astrometry or orbit fitting. [ABSTRACT FROM AUTHOR]

The Haiyang-2D (HY2D) satellite is the fourth ocean dynamics environment monitoring satellite launched by China. The satellite operates on a re-entry frozen orbit, which necessitates orbital maneuvers to maintain its designated path once the satellite's sub-satellite point deviates beyond a certain threshold. However, the execution of orbit maneuvers presents a significant challenge to the field of Precise Orbit Determination (POD). The thesis selects the on-board GPS data of HY2D satellite in December 2023 and five maneuvering days of that year. Employing a multifaceted approach that includes the assessment of observational data quality, orbit overlap, external orbit validation, and SLR (Satellite Laser Ranging) verification, the research delves into precise orbit determination during both maneuver and non-maneuver periods. The results indicate that: (1) The average number of satellites tracked by the receiver is 6.4; (2) During the non-maneuver periods, the average RMS (Root Mean Square) value of the radial difference in the 6-h overlapping arc segment is 0.66 cm, and the three-dimensional position difference is about 1.16 cm; (3) When compared with the precision science orbits (PSO) provided by CNES (Centre National d'Études Spatiales), the average values of the RMS values of the differences in the radial (R), transverse (T), and normal (N) directions during the non-maneuver and maneuver periods are respectively 1.32 cm, 2.31 cm, 1.92 cm and 3.04 cm, 8.78 cm, 2.72 cm. (4) The SLR verification of the orbit revealed a residual RMS of 2.24 cm. This suggests that by incorporating the modeling of maneuver forces during the maneuver periods, the impact of orbital maneuvers on orbit determination can be mitigated. [ABSTRACT FROM AUTHOR]

The increasing proliferation of space debris, intermittent space incidents, and the rapid emergence of massive LEO satellite constellations pose significant threats to satellites in orbit. Ground-based optical observations play a crucial role in space surveillance and space situational awareness (SSA). The Zhulong telescopic observation network stands as a pivotal resource in the realm of space object tracking and prediction. This publicly available network plays a critical role in furnishing essential data for accurately delineating and forecasting the orbit of space objects in Earth orbit. Comprising a sophisticated array of hardware components including precise telescopes, optical sensors, and image sensors, the Zhulong network synergistically collaborates to achieve unparalleled levels of precision in tracking and observing space objects. Central to the network's efficacy is its ability to extract positional information, referred to as angular data, from consecutive images. These angular data serve as the cornerstone for precise orbit determination and prediction. In this study, the CPF (Consolidated Prediction Format) orbit serves as the reference standard against which the accuracy of the angular data is evaluated. The findings reveal that the angular data error of the Zhulong network remains consistently below 3 arcseconds, attesting to its remarkable precision. Moreover, through the accumulation of angular data over time, coupled with the utilization of numerical integration and least squares methods, the Zhulong network facilitates highly accurate orbit determination and prediction for space objects. These methodologies leverage the wealth of data collected by the network to extrapolate trajectories with unprecedented accuracy, offering invaluable insights into the behavior and movement of celestial bodies. The results presented herein underscore the immense potential of electric optic telescopes in the realm of space surveillance. By harnessing the capabilities of the Zhulong network, researchers and astronomers can gain deeper insights into the dynamics of space objects, thereby advancing our understanding of the cosmos. Ultimately, the Zhulong telescopic observation network emerges as a pioneering tool in the quest to unravel the mysteries of the universe. [ABSTRACT FROM AUTHOR]

The On-orbit geometric calibration of geostationary cameras is literally considered a primary prerequisite for the quantitative applications involving accurate geometric positioning, tracking and identification of space-aeronautics moving targets. Affected by the solar illumination angles and the orbital heat flux of the satellite, the thermal environment around the camera turns out to be of difference in different imaging time and areas, which will cause uncertain spatial thermal deformation among the installation structures, and then change the camera's geometric positioning model and the final positioning accuracy inevitably. In terms of the problems mentioned above, a novel installation angles estimation method based on Time-Series Prediction Method is proposed to correct the positioning error caused by the spatial thermal deformation of the geostationary satellites. The installation angles estimation algorithm based on Time-Series Prediction Method model is described elaborately. This proposed method overcomes the dependence of conventional methods on the quantity and quality of GCPs, and is able to estimate the angle biases of the installation structure of the camera. Experimental results show that 92.5% and 97.63% of the positioning errors in the testing dataset corrected by the proposed method can be within 2 pixels and 3 pixels, respectively, which is better than that of ± 18 pixels before correction. Generally, this method could be a supplementary to the conventional methods to correct the positioning error caused by spatial thermal deformation of geostationary payloads. [ABSTRACT FROM AUTHOR]

The study introduces the concept of regional GPS orbit determination, whereby GPS satellite positions are determined using GPS measurements from locally or regional distributed stations. The importance and characteristics of regional GPS orbit are briefly discussed. The technique used to determine the regional GPS satellite position is coined Inverse Single Point Positioning (ISPP). Code-based pseudorange is used and improved using residual correction model. Two designs of station distribution are selected in this study, which only cover stations in Malaysia and stations situated 8000 km from a reference point in Malaysia. The root-mean-squared-error (RMSE) of ISPP when compared against final ephemeris were 660.65 m and 27.61 m, while the 3D RMSE of positioning were 1.612 m and 1.324 m for the first and second designs, respectively, lower than the accuracy of broadcast ephemeris. Three parameters are identified as factors affecting accuracy of ISPP, namely geometry of station distribution, nature of measurement used, and technique of orbit determination. Further research will be required to fully realize a functional regional GPS orbit. [ABSTRACT FROM AUTHOR]

The orbit solution of near-Earth asteroids heavily relies on ground-based optical observations. The orbit uncertainty is limited by the insufficient observation quantity and quality. The Chinese Tianwen-2 mission targets a near-Earth asteroid (469219) Kamo'oalewa and a main-belt comet, 311P/PANSTARRS. To accurately determine the orbit of Kamo'oalewa, more optical observations are needed. Autonomous observation experiments focusing on Kamo'oalewa were carried out using the 2.16-m telescope at the Xinglong Observatory of the National Astronomical Observatory of China. We found that this telescope could observe near-Earth asteroids as faint as a magnitude of 22.8. Based on the stacking method and trailed star extraction algorithm, 14 optical observations were obtained from 2022 to 2024. The orbit for Kamo'oalewa was determined by combining our observations with historical observations between 2004 and 2024. The inclusion of our observations results in improved orbital uncertainties of Kamo'oalewa by 18.67, 7.93, and 11.12 km (1σ) in the X, Y , and Z directions, respectively. Furthermore, by combining all existing and simulated observations, the uncertainty of the orbital determination of Kamo'oalewa was analysed. When using an additional 180 group observations from 3 Chinese observatories over 2 yr, the orbital uncertainties of Kamo'oalewa in the 3 directions could be reduced to 30 km (1σ). [ABSTRACT FROM AUTHOR]

In this paper, we propose a gate recurrent unit (GRU) method to forecast ionospheric the total electron content (TEC) at different latitudes and longitudes. This method aims to address the issues of low accuracy in traditional neural networks and the challenges faced in training long-term time series. We construct a GRU model using TEC data from the European Orbit Determination Center (CODE) for the years 2016 to 2018, geomagnetic indices, and solar activity indices (16 points along the latitude and longitude lines of 120°E and 30°N). Comparative experiments are carried out with the international reference ionosphere (IRI) model and the long short-term memory (LSTM) model. The results show that the GRU model outperforms other models in terms of accuracy. On geomagnetic quiet days, the 5-day predicted average residual can reach 0.51 TECU, while on storm days it can reach 0.72 TECU. The root mean square error (RMSE) for these days is 0.64 TECU and 1.01 TECU, respectively. The correlation coefficients are 0.98 and 0.93, respectively. The RMSE of the GRU model ranges from 0.60 TECU to 2.62 TECU for both geomagnetic quiet days and storm days. In terms of TEC forecast accuracy in 2018, the RMSE of the GRU model is 1.6 TECU, which is smaller than that of the IRI model and LSTM model. These results demonstrate that the GRU model performs better than the IRI model and LSTM model. [ABSTRACT FROM AUTHOR]

Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with only thirty thousand larger than ten cm being tracked. To avert a chain reaction of collisions, known as Kessler Syndrome, it is essential to accurately track and predict debris and satellites' orbits. Current approximate physics-based methods have errors in the order of kilometers for seven-day predictions, which is insufficient when considering space debris, typically with less than one meter. This failure is usually due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, and unknown characteristics such as the mass or geometry of the space object. Operators can enhance Orbit Prediction accuracy by deriving unmeasured objects' characteristics and improving non-conservative forces' effects by leveraging data-driven techniques, such as Machine Learning. In this survey, we provide an overview of the work in applying Machine Learning for Orbit Determination, Orbit Prediction, and atmospheric density modeling. [Display omitted] • Survey the introduction of new statistical techniques for Orbital Estimation. • Overview of deep learning techniques to improve empirical atmospheric density models. • Systematically study trends in Orbital Estimation using ML-based enhancements. • Define potential applications of Machine Learning approaches to Orbit Determination. [ABSTRACT FROM AUTHOR]

Classic initial orbit determination (IOD) methods are mainly based on the hypothesis of unperturbed Keplerian motion and are inapplicable for Libration point orbits (LPOs). To this end, this paper proposes a neural network–assisted method for accurate and efficient IOD of LPOs. The proposed method consists of a long short-term memory (LSTM) neural network–based initial guess generator (IGG) combined with a second-order optimal corrector. First, the LSTM neural network is developed to compensate for the residuals between the two-body IOD solution and the true solution to generate a more accurate initial guess. Two sample forms, one in the rotating frame and the other in the inertial frame, are investigated and compared to select the better form to train the LSTM neural network. Then, a second-order optimal corrector is proposed based on the second-order state transition tensor and a two-step procedure, which takes the initial guess from the LSTM neural network and iteratively obtains a more accurate IOD solution. Finally, the proposed method is applied to solve the IOD problem in two Earth–Moon LPO scenarios: a 4:1 synodic resonant Near-rectilinear Halo orbit (NRHO) and a transfer trajectory from a lunar orbit to the 4:1 NRHO. Numerical simulations show that the estimated errors are reduced by 99% using the proposed LSTM-based IGG. Moreover, for a comparable level of accuracy, the second-order optimal corrector converges one time faster than the first-order corrector. [ABSTRACT FROM AUTHOR]

Space cameras play a pivotal role in various fields, such as astronomical exploration. When operating in orbit, these cameras encounter the relative motion between the target and the camera during the exposure, resulting in image motion, which affects the imaging quality. Therefore, it is necessary to compensate for this image motion. This paper investigates the in-orbit image motion compensation (IMC) method for space cameras with a long integration time based on a two-axis pointing platform. Firstly, the mechanical design of the camera is introduced. Secondly, the in-orbit IMC model for the camera is analyzed, and the angular motion needed for compensating for the image motion by the two-axis pointing platform are derived. Factors influencing the compensation accuracy are also analyzed. The effectiveness of the IMC model is verified through simulations. Finally, the in-orbit experimental results indicate that the energy concentration of the target star images obtained exceeded 70%, demonstrating excellent performance in space cameras and effectively enhancing imaging quality using IMC technology. [ABSTRACT FROM AUTHOR]

To improve the quality of a medical image, it is essential to employ equipment that is equipped with a higher-intensity magnetic field. This poses unique challenges for healthcare providers, particularly those who have limited resources and an urgent need for efficiency. Interpolation is the most efficient technique for transforming low-resolution photos into high-resolution images through a straightforward calculation. The interpolation technique yields images with reduced clarity, especially along seamless boundaries, leading to the omission of crucial details. This study suggests employing the residual variational autoencoder model for the purpose of reconstructing highresolution images. The model comprises three components: an encoder, a decoder, and a latent space. According to the test findings, the suggested model performs better than state-of-the-art techniques already in use, including interpolation, multi-level densely connected super-resolution networks, and variational autoencoders. The evaluation of Structural Similarity and Peak signal-to-noise ratio metrics reveals a significant improvement, with an approximate 5-10% rise in Structural Similarity and a 10-15% increase in Peak signal-to-noise ratio compared to the state-of-the-art. [ABSTRACT FROM AUTHOR]

Summary: Modern satellite communication systems are designed to serve dispersed users with changing operational requirements. Allocating resources to meet these requirements becomes highly complex when the size, location, and allocated frequency of satellite beams are flexible. We developed solution techniques that generate feasible beam patterns and frequency allocations to maximize the total demand met across all users. In our approach, an integer program selects an optimal set of beams from a heuristically generated pool of feasible candidate beams. The challenge is in how to efficiently build a pool of good quality candidate beams from exponentially many possible solutions. An innovative column generation‐style heuristic to generate mathematically justifiable beams is presented to address this challenge. We also derived two other heuristic candidate beam generation algorithms to compare and contrast performance and robustness characteristics of different algorithmic choices. We tested the performance of our three new approaches on 12 operational instances that vary in user distribution, user numbers, and demand distribution. While the methods performed differently under varying operational scenarios, the column generation‐based methods provided the best trade‐off between computation time and solution quality in most cases. We further tested our two best performing algorithms for scalability. Our column generation‐based methods were able to provide good quality solutions with up to 400 beams and 5,000 users. Our work provides valuable insights for real‐life implementation: an end‐user of our system can select the solution approach based on their business need, computational (time) budget, and the desired solution quality. [ABSTRACT FROM AUTHOR]

Spacecraft positioning plays a crucial role in scientific space mission design, as well as in the further scheduling of scientific observations for such a mission. We examine the application of global navigation satellite systems (GNSS) to solve the orbit determination problem in a pure space very long baseline interferometer (VLBI) project. A network of GPS, GLONASS, Galileo and BeiDou navigation satellites may be a more efficient solution to determining the position and velocity of space radio telescopes and space interferometer baselines. For such a project, it is necessary to take into account the special conditions of GNSS observations, as well as the high accuracy of determining not only position but also velocity. In this paper, we estimate visibility of navigation satellite systems for Low and Medium orbits of a pure space-VLBI system and simulate GNSS code and phase measurements. Orbit determination was performed on smoothed code measurements. Phase measurements simulated with a step of 1 s and combined in Doppler measurements yield average position and velocity errors of 1.01 m and 8.8 mm/s in Medium Earth orbit. The results showed that GNSS observations are sufficient to solve the problems of orbit determination of a space-VLBI interferometer both in Low-Earth and Medium Earth orbits. • Simulated GNSS observations for medium and low Earth orbits using special noise model. • Calculated the visibility of navigation satellites for low and medium Earth orbits. • Obtained navigation solution for space radio interferometers in low and medium orbits. • GNSS observations provide sufficient accuracy of orbit determination. [ABSTRACT FROM AUTHOR]

Next to the legacy frequency division multiple access (FDMA) signals in the L1 and L2 band, modernized GLONASS satellites of the M+, K1, and K2 generation also transmit new code division multiple access (CDMA) signals on L3, and, in part, the L1 and L2 frequencies. Depending on the specific satellite platform, either a common antenna or two distinct antennas are used for the individual signals. As a novel feature, the new CDMA navigation messages provide information on the antenna phase center locations as well as the spacecraft orientation during rate-limited noon and midnight turns. We establish a comprehensive set of phase center positions for the individual GLONASS antennas from manufacturer data and information in the CDMA navigation messages, inferred from the comparison of FDMA and CDMA broadcast ephemerides, and obtained from antenna baseline estimates using a triple-frequency carrier phase combination. Based on these, reference values for the signal-specific PCOs of each block of modernized GLONASS spacecraft are derived that may be used to extend the current antenna model of the International GNSS Service (IGS) to all frequency bands. Complementary to the analysis of antenna phase center information, the new CDMA attitude model for GLONASS-K satellites is reviewed. Algorithms for computing relevant parameters of the rate-limited yaw slews including the ramp-up and -down phase based on the Sun/orbit geometry are derived that enable a concise attitude modeling in GLONASS orbit determination and precise point positioning. The model is validated through comparison with yaw angle estimates derived from triple-frequency observations showing consistency at the 1° level for the K2 satellite. On the other hand, unexpected accelerations during noon turns of GLONASS-M+ are identified, which may cause short-term yaw angle deviations of up to 20° relative to attitude models in common use within the IGS. [ABSTRACT FROM AUTHOR]

The Sentinel-6A mission extends the set of satellites dedicated to continuous ocean altimetry measurements, which started with TOPEX/Poseidon in 1992. To utilize these measurements, high-accuracy orbit solutions with radial position errors of less than 1.5cm (RMS) are required. For precise orbit determination (POD), a dedicated GPS/Galileo triple-frequency receiver (PODRIX) is available. Complementary to this, the TriG receiver provides GPS-only observations for POD and radio occultations. Previous research has shown that reduced-dynamic orbit solutions with PODRIX GPS/Galileo measurements meet the mission requirement for radial position accuracy of 1.5 cm (RMS). However, baseline estimation between the PODRIX and TriG antennas still reveals obvious inconsistencies in the along- and cross-track directions. In this study, we present a comprehensive reprocessing of orbit solutions using three years of Sentinel-6A flight data from both receivers covering January 2021 to December 2023. Cross-comparison between both receivers shows that inconsistencies can be removed by applying a yaw bias and a timing error correction. A comparative analysis of macro-models demonstrates strong correlation of cross-track empirical accelerations with the Sun elevation above the orbital plane when using nominal surface properties reported by the manufacturer. Adjusted macro-models improve performance at the expense of requiring increased surface areas or reflectivity coefficients. In addition to improved radiation pressure models, newly estimated antenna patterns and a time-varying gravity field were used in the analysis. The reprocessed data confirm good agreement of the results of both receivers except for a relative timing error of 1.3 μ s, and the yaw bias correction of −0.43° removes previously-observed systematic differences in the estimated empirical accelerations. Satellite laser ranging results based on SLRF2020 station coordinates demonstrate a 5—6 mm (1D RMS) accuracy of the GNSS-based POD solutions across the IGb14/IGS20 reference frame transition in November 2022. [ABSTRACT FROM AUTHOR]

Abstract We study the dynamic orbit about Phobos of the Martian Moon eXploration (MMX) spacecraft and simulate gravity field estimation using Doppler, image landmarks, and LIght Detection And Ranging (LIDAR) data based on a mission plan of MMX and investigate whether the differences in the internal density structure of Phobos can be detected through this mission. Degree 2 Stokes coefficients of the Phobos gravity field, $${\overline{C} }_{20}$$ C ¯ 20 and $${\overline{C} }_{22}$$ C ¯ 22 , which are necessary to obtain the moment of inertia by combining with the libration amplitude, could be determined with an accuracy within the order of 0.1% using datasets from two-dimensional (2D) quasi-satellite orbits (QSOs). If observations from 3D-QSO could be realized at low altitude, coefficients up to degree and order 5 could be estimated, which could be used to detect regional density anomalies. Moreover, the observation data from the ascending trajectory after landing on the Phobos surface can be used to detect local density anomalies around the landing site, which could help interpret the origin of the samples and understand the internal structure of Phobos. Graphical Abstract

Abstract A Low Earth Orbit (LEO) constellation augmenting satellite navigation is important in the future development of Global Navigation Satellite System (GNSS). GNSS augmented by LEO constellations can improve not only the accuracy of Positioning, Navigation, and Timing (PNT), but also the consistency and reliability of secure PNT system. This paper mainly analyzes the diverse demands of different PNT users for LEO augmented GNSS, including the precision demand in real-time, the availability demand in special areas, the navigation signal enhancement demand in complex electromagnetic environments, and the integrity demand with high security. Correspondingly, the possible contributions of LEO constellations to PNT performance are analyzed from multiple aspects. A particular attention is paid to the special PNT user requirements that cannot be fulfilled with existing GNSS, such as the PNT service demand in the polar regions and the onboard GNSS orbit determination demand of some LEO satellites. The key technologies to be considered in the constellation design, function realization, and payload development of the LEO-augmented navigation system are summarized.

To meet various requirements of the future deep space missions of China, State Key Laboratory of Astronautic Dynamics constructs a new orbit determinatin software with parallel observations process. By using 32 threads, the computational efficiency per iteration (including spacecraft’s integration) could be promoted to 10 times as that of single-threaded orbit determination. Suppose the number of observations is pp, the number of estimated parameters (including spacecraft’s state) is qq, the amount of computation of one observation is xx, the amount of computation of one Givens transformation is yy and the best number of threads is proved to be [p⋅(x+y)/(q⋅y)]1/2{\left[p\cdot \left(x+y)\text{/}\left(q\cdot y)]}^{1\text{/}2} for one-step threads combination. The root mean square of the postfit residuals of China’s deep space monitoring network (CDSMN) and China’s Very Long Baseline Interferometry (VLBI) network (CVN) observations in the Earth-Mars transfer phase and the Mars-orbiting phase are almost the same: about 0.3 m for Ranging, about 0.3 mm/s for Doppler, about 3 cm for VLBI delay and about 0.5 mm/s for VLBI delay rate. It is also found that all the four types of observations of CDSMN and CVN are needed in orbit determination for deep space maneuver and braking at periareion calculation. In the Mars-orbiting phase, the position accuracy after orbit determination under CDSMN-only tracking mode can reach about 1 km.

We assess the orbit accuracy and time synchronization error using the L1 and C1 observables during the different solar activities. In general, GPS single-frequency (SF) observable can be used for commercial applications in satellite industry. The accuracy of satellite orbit determination using the SF observations is dominated by solar activities. The solar activities are indexed by the F10.7 value. The different solar activities lead to the ionosphere perturbation, triggering off the occurrence probability of ionospheric irregularities. The ionospheric irregularity affects the amplitude and phase of GPS signal. The affected amplitude and phase are indexed by the S4 value. We determine the GRACE satellite orbit using the SF GPS observations and compare the resulting orbit to that derived by dual-frequency observations for the effectiveness. The SF phase data are very sensitive to the variation in electron density and indirectly affects both the orbit accuracy and the time synchronization error. This is most likely caused by the phase ambiguity disturbed by the ionosphere. However, the C1 is relatively free from such a disturbance due to the strong signal-to-noise ratio (SNR) and the phase shift keying technique. The C1 performs the consistent solution over the low and high solar activities. However, this is not the case for the L1. The L1-derived orbit solution during the high solar activities is worse than that during the low solar activities. On the other hand, the time synchronization errors derived by the L1 and C1 are also different. The L1-derived time synchronization error has a relatively large perturbation as compared to the C1-derived one, which shows a consistent solution for a long-term period. This work suggests that the C1 observable is able to produce a consistent the orbit solution and time synchronization for the commercial applications of the satellite industry. [ABSTRACT FROM AUTHOR]

With the rapid development of technologies such as autonomous driving and robotic navigation, the demand for accurate and reliable positioning results with BDS has increased. The current status and future development of BDS high precision services are reviewed. The operational PPP-B2b of BDS-3 achieves positioning accuracy at decimeter-level within 14 min and has the drawbacks in regional coverage and long convergence time compared with the international counterparts, such as CLAS of QZSS and HAS of Galileo. A development frame for multi-layer BDS high-precision services is proposed by considering its construction cost, compatibility of user terminal, operating maintenance burden, and service level. The global high-precision service with the improved orbit and clock accuracy enhanced with the inter-satellite link is taken as the most fundamental layer. By incorporating inter-satellite link observations, the orbit errors URE and clock errors are significantly reduced to approximately 0.05 m and 0.16 ns, respectively, which will expand PPP service to global. Based on this, the regional PPP-AR and PPP-RTK services with improved convergence performance are taken as the second layer. With PPP-AR, the convergence time drops to 10 min. With PPP-RTK, the convergence time would be further shortened to less than 3 min. The LEO enhanced PPP service is taken as the third layer which overcomes both drawbacks of the long convergence time of the inter-satellite link enhanced service (the first layer) and the regional coverage of the PPP-AR/PPP-RTK services (the second layer). The simulation results show that by introducing a LEO constellation of 288 satellites, the LEO enhanced PPP can achieve positioning accuracy better than 5 cm within approximately 1 min. In addition, the integration of LEO constellation and PPP-RTK is further proposed to enable instantaneous convergence. The implementation challenges are also presented. [ABSTRACT FROM AUTHOR]

The Cassini spacecraft performed several flybys of Saturn's largest moon, Titan, collecting valuable data. During several passes, altimetric data were acquired. Here, we focus on altimetric measurements collected by Cassini's radar when flying over the same region at different epochs in order to correlate such measurements (crossovers) and investigate differences in altimetry. In our study, we assess altimetric errors associated with three distinct methods for extracting topography from Cassini's radar data: the maximum likelihood estimator (MLE), the threshold method, and the first moment technique. Focusing on crossover events, during which Cassini revisited specific areas of Titan's surface, we conduct a detailed examination of the consistency and accuracy of these three topography extraction methods. The proposed analysis involves closely examining altimetric data collected at different epochs over identical geographical regions, allowing us to investigate potential errors due to the variations in off-nadir angle, relative impact, uncertainties, and systematic errors inherent in the application of these methodologies. Our findings reveal that the correction applied for the off-nadir angle to the threshold and first moment methods significantly reduces the dispersion in the delta difference at the crossover, resulting in a dispersion of the order of 60 m, even lower than what is achieved with the MLE (~70 m). Additionally, an effort is made to assess the potential of Cassini for estimating the tidal signal on Titan. Considering the altimetric errors identified in our study and the relatively low number of crossovers performed by Cassini, our assessment indicates that it is not feasible to accurately measure the tidal signal on Titan using the currently available standard altimetry data from Cassini. Our assessment regarding the accuracy of the Cassini altimeter provides valuable insights for future planetary exploration endeavors. Our study advances the understanding of Titan's complex landscape and contributes to refining topographical models derived from Cassini's altimetry observations. These insights not only enhance our knowledge of Saturn's largest moon but also open prospects for Titan surface and interior exploration using radar systems. [ABSTRACT FROM AUTHOR]

We study the dynamic orbit about Phobos of the Martian Moon eXploration (MMX) spacecraft and simulate gravity field estimation using Doppler, image landmarks, and LIght Detection And Ranging (LIDAR) data based on a mission plan of MMX and investigate whether the differences in the internal density structure of Phobos can be detected through this mission. Degree 2 Stokes coefficients of the Phobos gravity field, C ¯ 20 and C ¯ 22 , which are necessary to obtain the moment of inertia by combining with the libration amplitude, could be determined with an accuracy within the order of 0.1% using datasets from two-dimensional (2D) quasi-satellite orbits (QSOs). If observations from 3D-QSO could be realized at low altitude, coefficients up to degree and order 5 could be estimated, which could be used to detect regional density anomalies. Moreover, the observation data from the ascending trajectory after landing on the Phobos surface can be used to detect local density anomalies around the landing site, which could help interpret the origin of the samples and understand the internal structure of Phobos. [ABSTRACT FROM AUTHOR]

Commonly, Global Positioning System (GPS)-based precise orbit determination (POD) of a low Earth orbiting (LEO) satellite is conducted by introducing fixed GPS orbits and clock corrections that were derived in a previous independent network solution using ground-based GPS receivers only. There have been a number of studies showing that the integration of LEO GPS observations can be advantageous in global network solutions, particularly when it comes to estimating geodetic parameters, such as the Earth's center-of-mass. There has been an increase in GPS data available from LEO CubeSats over the past few years, such as from the Spire satellites, which are equipped with dual-frequency GPS receivers. The goal of the present study is to determine how GPS observations collected by specific Spire satellites affect global network solutions when combined with GPS observations from ground stations of the International GNSS Service. To obtain a combined GPS-LEO solution, GPS observations collected from receivers of selected Spire satellites and additional scientific LEOs are used to obtain combined GPS-LEO solutions by performing one joint least-squares adjustment process. Using this method, LEO satellite orbit parameters are determined along with GPS orbit parameters and geodetic parameters, namely GNSS station coordinates, Earth rotation parameters (ERPs), and the Earth's center-of-mass. The influence of the Spire LEOs is assessed by analyzing different solutions that use GPS observations from different Spire and LEO satellites. Besides comparing the different global network solutions with one another, a comparison to a solution using only terrestrial GPS data is performed as well. As part of the quality assessment of the GPS-LEO solution, quality characteristics are analyzed, which are the geodetic parameters, orbit overlaps at arc boundaries, and formal errors determined for the estimated parameters. The results show that the estimation of the Earth's center-of-mass coordinates benefits from including GPS-LEO observations. The solution is more improved by integrating GPS-LEO observations from scientific LEOs than from GPS-Spire-included solutions. The analysis reveals that GPS orbits are improved using the LEO-integrated approach, while orbit misclosures of LEO and Spire trajectories currently indicate a decrease in LEO orbit precision due to LEO orbit modeling deficiencies. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

• Comparison of the nominal and quaternion attitude realisation of TOPEX/Poseidon. • Angular differences in roll, pitch, yaw, and the solar array rotation angle. • Influence on the radial position of the altimeter antenna due to mismodelling. • Similar results with slight improvements for the quaternion attitude realisation. • Change in the radial position up to 2.5 cm in case of mismodelling in roll/pitch. The altimetry mission TOPEX/Poseidon was operational between 1992 and 2005 and provided innovative insight into global and regional sea level changes and their variability. The correct modelling of the spacecraft orbit in precise orbit determination requires detailed information on the attitude of the spacecraft body and the solar array. Since the availability of attitude observations in form of quaternion data for this mission is limited, the nominal orientation model has to be used mainly. In this study, we compare the nominal and quaternion-based approaches of the TOPEX/Poseidon attitude realisation and validate the nominal model w.r.t. the observed attitude. We found good agreement between both approaches in the spacecraft-related roll, pitch, yaw, and solar array angles with slight differences of up to 0.31 ° on average. The best accordance is obtained in the yaw angles. A general angular offset of 0.12 ° and - 0.19 ° on average is found in the pitch and solar array angle differences, respectively. Parameters estimated in the orbit computation process also reflect the good agreement between both orientation models with slightly better results when using the observed attitude. However, in some intervals, the nominal model lacks detailed information about the correct attitude. These can be adjusted using the information from the quaternion data. Such intervals indicate off-nominal spacecraft attitude events like drifts or offsets. Purely geometrically analysed, mispointing in the roll and pitch components of about 0.25 ° results in a change of the altimeter phase centre position in the radial direction of about 7 mm, which directly impacts the sea-level heights determined from altimetry measurements. [ABSTRACT FROM AUTHOR]

Based on the broadcast ephemeris of a global navigation satellite system (GNSS) uploaded from the ground, an orbital-based terrestrial reference frame (TRF) can be produced in consistence with the ground-based TRF. High-precision inter-satellite link (ISL) ranging technology makes satellite autonomous orbit determination (AOD) possible. Therefore, if the broadcast ephemeris cannot be uploaded, the GNSS satellites can independently maintain the accuracy of the orbital-based TRF. In this paper, orbital-based TRF realized by the autonomous orbit determination (AOD) based on BDS-3 ISL measurements is compared with the ITRF2014. The accuracy of the orbital-based TRF realized by the AOD is evaluated. The comparison between the AOD orbits and the post-processed precise orbits over 60 days via the 7 parameters Helmert transformation shows that the maximum differences of the three-axis translation between the orbital-based TRF and ITRF2014 are 1.25 m, 1.32 m and 0.47 m, and the maximum difference of the scale is 6.2 ppb. The differences of the three-axis rotation parameters between the orbital-based TRF and ITRF2014 are related to whether the orientation correction method is applied. Since the long-term orbit prediction (OP) generated by the orbit dynamics models can predict the right ascension of the ascending node (RAAN) and the inclination accurately in Geocentric Celestial Reference System (GCRS), in the orientation correction method, the long-term OP is used as the reference to constrain the rotation differences. If the orientation correction method is not applied, the maximum differences of the three-axis rotation parameters are 65.0 mas, 77.1 mas, 122.5 mas; however, if the orientation correction method is applied, the maximum differences of the three-axis rotation parameters are reduced to 32.5 mas, 46.9 mas and 67.1 mas. Part of the residual rotation differences are caused by the prediction errors of the rapid Earth rotation parameters (ERPs) from International Earth Rotation and Reference Systems Service (IERS) bulletin A. Over 60 days, the differences between the rapid ERPs from IERS bulletin A and the final estimated ERPs from IERS bulletin B are equal to 2.56 mas, 15.03 mas and 84.12 mas in X, Y, Z axis, respectively. The influence of the orbit prediction accuracy on the orbit-based TRF based on the AOD method is also analyzed. If precise satellite orbits with an accuracy of 0.10 m are applied as long-term orbit prediction, the accuracy of the orbital TRF is improved significantly. During 60 days, the maximum differences of the three-axis translation are reduced to 0.10 m, 0.10 m, and 0.12 m, the maximum differences of the three-axis rotation are reduced to 3.03 mas, 3.47 mas, and 4.94 mas, and the maximum difference of the scale is reduced to 1–2 ppb. [ABSTRACT FROM AUTHOR]