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Keywords = satellite orbit determination

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28 pages, 2841 KiB  
Article
A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators
by Dongdong Wang, Wenhe Liao, Bin Liu and Qianghua Yu
Sensors 2025, 25(15), 4733; https://doi.org/10.3390/s25154733 - 31 Jul 2025
Viewed by 205
Abstract
High-precision time–frequency systems are essential for low Earth orbit (LEO) navigation satellites to achieve real-time (RT) centimeter-level positioning services. However, subject to stringent size, power, and cost constraints, LEO satellites are typically equipped with oven-controlled crystal oscillators (OCXOs) as the system clock. The [...] Read more.
High-precision time–frequency systems are essential for low Earth orbit (LEO) navigation satellites to achieve real-time (RT) centimeter-level positioning services. However, subject to stringent size, power, and cost constraints, LEO satellites are typically equipped with oven-controlled crystal oscillators (OCXOs) as the system clock. The inherent long-term stability of OCXOs leads to rapid clock error accumulation, severely degrading positioning accuracy. To simultaneously balance multi-dimensional requirements such as clock bias accuracy, and frequency stability and phase continuity, this study proposes a linear quadratic Gaussian (LQG) frequency precision steering method that integrates a four-dimensional constraint integrated (FDCI) model and hierarchical weight optimization. An improved system error model is refined to quantify the covariance components (Σ11, Σ22) of the LQG closed-loop control system. Then, based on the FDCI model that explicitly incorporates quantization noise, frequency adjustment, frequency stability, and clock bias variance, a priority-driven collaborative optimization mechanism systematically determines the weight matrices, ensuring a robust tradeoff among multiple performance criteria. Experiments on OCXO payload products, with micro-step actuation, demonstrate that the proposed method reduces the clock error RMS to 0.14 ns and achieves multi-timescale stability enhancement. The short-to-long-term frequency stability reaches 9.38 × 10−13 at 100 s, and long-term frequency stability is 4.22 × 10−14 at 10,000 s, representing three orders of magnitude enhancement over a free-running OCXO. Compared to conventional PID control (clock bias RMS 0.38 ns) and pure Kalman filtering (stability 6.1 × 10−13 at 10,000 s), the proposed method reduces clock bias by 37% and improves stability by 93%. The impact of quantization noise on short-term stability (1–40 s) is contained within 13%. The principal novelty arises from the systematic integration of theoretical constraints and performance optimization within a unified framework. This approach comprehensively enhances the time–frequency performance of OCXOs, providing a low-cost, high-precision timing–frequency reference solution for LEO satellites. Full article
(This article belongs to the Section Remote Sensors)
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22 pages, 3073 KiB  
Article
Research on Sliding-Window Batch Processing Orbit Determination Algorithm for Satellite-to-Satellite Tracking
by Yingjie Xu, Xuan Feng, Shuanglin Li, Jinghui Pu, Shixu Chen and Wenbin Wang
Aerospace 2025, 12(8), 662; https://doi.org/10.3390/aerospace12080662 - 25 Jul 2025
Viewed by 209
Abstract
In response to the increasing demand for high-precision navigation of satellites operating in the cislunar space, this study introduces an onboard orbit determination algorithm considering both convergence and computational efficiency, referred to as the Sliding-Window Batch Processing (SWBP) algorithm. This algorithm combines the [...] Read more.
In response to the increasing demand for high-precision navigation of satellites operating in the cislunar space, this study introduces an onboard orbit determination algorithm considering both convergence and computational efficiency, referred to as the Sliding-Window Batch Processing (SWBP) algorithm. This algorithm combines the strengths of data batch processing and the sequential processing algorithm, utilizing measurement data from multiple historical and current epochs to update the orbit state of the current epoch. This algorithm facilitates rapid convergence in orbit determination, even in instances where the initial orbit error is large. The SWBP algorithm has been used to evaluate the navigation performance in the Distant Retrograde Orbit (DRO) and the Earth–Moon transfer orbit. The scenario involves a low-Earth-orbit (LEO) satellite establishing satellite-to-satellite tracking (SST) links with both a DRO satellite and an Earth–Moon transfer satellite. The LEO satellite can determine its orbit accurately by receiving GNSS signals. The experiments show that the DRO satellite achieves an orbit determination accuracy of 100 m within 100 h under an initial position error of 500 km, and the transfer orbit satellite reaches an orbit determination accuracy of 600 m within 3.5 h under an initial position error of 100 km. When the Earth–Moon transfer satellite exhibits a large initial orbital error (on the order of hundreds of kilometers) or the LEO satellite’s positional accuracy is degraded, the SWBP algorithm demonstrates superior convergence speed and precision in orbit determination compared to the Extended Kalman Filter (EKF). This confirms the proposed algorithm’s capability to handle complex orbital determination scenarios effectively. Full article
(This article belongs to the Section Astronautics & Space Science)
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22 pages, 3128 KiB  
Article
Initial Values Determination of Thrust Parameters for Continuously Low-Thrust Maneuvering Spacecraft
by Wen Guo, Xuefeng Tao, Min Hu and Wen Xue
Appl. Sci. 2025, 15(14), 8064; https://doi.org/10.3390/app15148064 - 20 Jul 2025
Viewed by 259
Abstract
Continuous low thrust is widely used in orbit transfer maneuvers. If the unknown maneuvers are not correctly compensated, the orbiting accuracy will be seriously affected. We propose a rapid method for pre-identifying thrust acceleration based on single-arc orbit determination in order to determine [...] Read more.
Continuous low thrust is widely used in orbit transfer maneuvers. If the unknown maneuvers are not correctly compensated, the orbiting accuracy will be seriously affected. We propose a rapid method for pre-identifying thrust acceleration based on single-arc orbit determination in order to determine the orbit of non-cooperative continuous low-thrust maneuvering spacecraft. The single-arc orbit determination results of two ground-based radar observations with a certain time interval are used to inversely determine the direction and magnitude of acceleration of the spacecraft under continuous thrust based on their relationship with satellite orbit parameters. The solution error is relatively small when using this method, even over a short period of time when data are sparse. The results can then be applied to the orbital adjustment of a satellite. The results show that when the satellite climbs with maximum tangential acceleration, the interval between the two radar observations is greater than 7 h, and the proposed method can rapidly pre-identify tangential thrust acceleration with a solution error of less than 5%. When the satellite adjusts the orbital plane with the maximum normal acceleration, the average relative measurement error of the normal acceleration is about 20% when the time interval between two observations is 24 h. The longer the observation interval and the greater the thrust acceleration, the smaller the relative error. The calculation results can be used as the initial value for precision orbit determination of continuous low-thrust maneuvering spacecraft. Full article
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23 pages, 3056 KiB  
Article
Methodology for Evaluating Collision Avoidance Maneuvers Using Aerodynamic Control
by Desiree González Rodríguez, Pedro Orgeira-Crespo, Jose M. Nuñez-Ortuño and Fernando Aguado-Agelet
Remote Sens. 2025, 17(14), 2437; https://doi.org/10.3390/rs17142437 - 14 Jul 2025
Viewed by 202
Abstract
The increasing congestion of low Earth orbit (LEO) has raised the need for efficient collision avoidance strategies, especially for CubeSats without propulsion systems. This study proposes a methodology for evaluating passive collision avoidance maneuvers using aerodynamic control via a satellite’s Attitude Determination and [...] Read more.
The increasing congestion of low Earth orbit (LEO) has raised the need for efficient collision avoidance strategies, especially for CubeSats without propulsion systems. This study proposes a methodology for evaluating passive collision avoidance maneuvers using aerodynamic control via a satellite’s Attitude Determination and Control System (ADCS). By adjusting orientation, the satellite modifies its exposed surface area, altering atmospheric drag and lift forces to shift its orbit. This new approach integrates atmospheric modeling (NRLMSISE-00), aerodynamic coefficient estimation using the ADBSat panel method, and orbital simulations in Systems Tool Kit (STK). The LUME-1 CubeSat mission is used as a reference case, with simulations at three altitudes (500, 460, and 420 km). Results show that attitude-induced drag modulation can generate significant orbital displacements—measured by Horizontal and Vertical Distance Differences (HDD and VDD)—sufficient to reduce collision risk. Compared to constant-drag models, the panel method offers more accurate, orientation-dependent predictions. While lift forces are minor, their inclusion enhances modeling fidelity. This methodology supports the development of low-resource, autonomous collision avoidance systems for future CubeSat missions, particularly in remote sensing applications where orbital precision is essential. Full article
(This article belongs to the Special Issue Advances in CubeSat Missions and Applications in Remote Sensing)
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22 pages, 23032 KiB  
Article
Statistical Approach to Research on the Relationship Between Kp/Dst Geomagnetic Indices and Total GPS Position Error
by Mario Bakota, Igor Jelaska, Serdjo Kos and David Brčić
Remote Sens. 2025, 17(14), 2374; https://doi.org/10.3390/rs17142374 - 10 Jul 2025
Viewed by 332
Abstract
This study examines the impact of geomagnetic disturbances quantified by the Kp and Dst indices on the accuracy of single-frequency GPS positioning across mid-latitudes and the equatorial zone, with a focus on temporal and spatial positioning errors variability. GNSS data from a globally [...] Read more.
This study examines the impact of geomagnetic disturbances quantified by the Kp and Dst indices on the accuracy of single-frequency GPS positioning across mid-latitudes and the equatorial zone, with a focus on temporal and spatial positioning errors variability. GNSS data from a globally distributed network of 14 IGS stations were analyzed for September 2017, featuring significant geomagnetic activity. The selection of stations encompassed equatorial and mid-latitude regions (approximately ±45°), strategically aligned with the distribution of the Dst index during geomagnetic storms. Satellite navigation data were processed using RTKLIB software in standalone mode with standardized atmospheric and orbital corrections. The GPS was chosen over GLONASS following preliminary testing, which revealed a higher sensitivity of GPS positional accuracy to variations in geomagnetic indices such as Kp and Dst, despite generally lower total error magnitudes. The ECEF coordinate system calculates the total GPS error as the vector sum of deviations in the X, Y, and Z axes. Statistical evaluation was performed using One-Way Repeated Measures ANOVA to determine whether positional error variances across geomagnetic activity phases were significant. The results of the variance analysis confirm that the variation in the total GPS positioning error is non-random and can be attributed to the influence of geomagnetic storms. However, regression analysis reveals that the impact of geomagnetic storms (quantified by Kp and Dst) displays spatiotemporal variability, with no consistent correlation to GPS positioning error dynamics. The findings, as well as the developed methodology, have qualitative implications for GNSS-dependent operations in sensitive sectors such as navigation, timing services, and geospatial monitoring. Full article
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19 pages, 3553 KiB  
Article
Research on the Autonomous Orbit Determination of Beidou-3 Assisted by Satellite Laser Ranging Technology
by Wei Xiao, Zhengcheng Wu, Zongnan Li, Lei Fan, Shiwei Guo and Yilun Chen
Remote Sens. 2025, 17(14), 2342; https://doi.org/10.3390/rs17142342 - 8 Jul 2025
Viewed by 340
Abstract
The Beidou Global System (BDS-3) innovatively achieves autonomous navigation using inter-satellite links (ISL) across the entire constellation, but it still faces challenges such as the limitations of the prior constraint orbital accuracy and the overall constellation rotation. The gradual availability of satellite laser [...] Read more.
The Beidou Global System (BDS-3) innovatively achieves autonomous navigation using inter-satellite links (ISL) across the entire constellation, but it still faces challenges such as the limitations of the prior constraint orbital accuracy and the overall constellation rotation. The gradual availability of satellite laser ranging (SLR) data, with advantages of high precision and no ambiguous parameters, can provide new ideas for solving the current problem. This work firstly deduces the mathematical model for orbit determination by combining inter-satellite links and the introduced satellite laser ranging observations, then designs orbit determination experiments with different prior orbit constraints and different observation data, and finally evaluates the impacts of the prior orbits and the introduction of SLR observations from two dimensions: orbit accuracy and constellation rotation. The experimental results using one month of measured data show the following: (1) There is good consistency among different days, and the accuracy of the prior orbits affects the performance of the orbit determination and the consistency. Compared with broadcast ephemerides, using precise ephemerides as prior constraints significantly improves the consistency, and the orbit accuracy can be increased by about 75%. (2) The type of observation data affects the performance of the orbit determination. Introducing SLR observations can improve the orbit accuracy by approximately 13% to 26%. (3) Regardless of whether broadcast ephemerides or precise ephemerides are used as prior constraints, the constellation translation and rotation still exist after introducing SLR observations. Among the translation parameters, TX is the largest, followed by TY, and TZ is the smallest; all three rotation parameters (RX, RY, and RZ) show relatively large values, which may be related to the limited number of available satellite laser ranging stations during this period. (4) After considering the constellation translation and rotation, the orbit accuracy under different prior constraints remains at the same level. The statistical root mean square error (RMSE) indicates that the orbit accuracy of inclined geosynchronous orbit (IGSO) satellites in three directions is better than 20 cm, while the accuracy of medium earth orbit (MEO) satellites in along-track, cross-track, and radial directions is better than 10 cm, 8 cm, and 5 cm, respectively. Full article
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26 pages, 4569 KiB  
Article
Orbit Determination for Continuously Maneuvering Starlink Satellites Based on an Unscented Batch Filtering Method
by Anqi Lang and Yu Jiang
Sensors 2025, 25(13), 4079; https://doi.org/10.3390/s25134079 - 30 Jun 2025
Viewed by 436
Abstract
Orbit determination for non-cooperative low Earth orbit (LEO) objects undergoing continuous low-thrust maneuvers remains a significant challenge, particularly for large satellite constellations like Starlink. This paper presents a method that integrates the unscented transformation into a batch filtering framework with an optimized rho-minimum [...] Read more.
Orbit determination for non-cooperative low Earth orbit (LEO) objects undergoing continuous low-thrust maneuvers remains a significant challenge, particularly for large satellite constellations like Starlink. This paper presents a method that integrates the unscented transformation into a batch filtering framework with an optimized rho-minimum sigma points sampling strategy. The proposed approach uses a reduced dynamics model that considers Earth’s non-spherical gravity and models the combined effects of low-thrust and atmospheric drag as an equivalent along-track acceleration. Numerical simulations under different measurement noise levels, initial state uncertainties, and across multiple satellites confirm the method’s reliable convergence and favorable accuracy, even in the absence of prior knowledge of the along-track acceleration. The method consistently converges within 10 iterations and achieves 24 h position predictions with root mean square errors of less than 3 km under realistic noise conditions. Additional validation using a higher-fidelity model that explicitly accounts for atmospheric drag demonstrates improved accuracy and robustness. The proposed method can provide accurate orbit knowledge for space situational awareness associated with continuously maneuvering Starlink satellites. Full article
(This article belongs to the Section Remote Sensors)
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28 pages, 7488 KiB  
Article
Modeling and Analysis of Staged Constellation Deployment from a Single-Unit System
by Daniel Cumbo and Marc Anthony Azzopardi
Aerospace 2025, 12(7), 586; https://doi.org/10.3390/aerospace12070586 - 29 Jun 2025
Viewed by 239
Abstract
A novel satellite architecture and deployment method is proposed to reduce the logistical cost and complexity of launching and dispersing satellite constellations. The architecture consists of a primary satellite that separates into multiple smaller units, which are subsequently dispersed using differential drag. An [...] Read more.
A novel satellite architecture and deployment method is proposed to reduce the logistical cost and complexity of launching and dispersing satellite constellations. The architecture consists of a primary satellite that separates into multiple smaller units, which are subsequently dispersed using differential drag. An algorithm is developed to determine the required disengagement velocities and optimal timing for separation maneuvers. Two case studies with orbital simulations demonstrate the feasibility of this approach for constellation deployment and phasing. The results indicate that while mission-specific factors influence deployment dynamics, informed selection of the disengagement velocities is crucial for minimizing phase times and mitigating potential delays. The findings confirm the feasibility of the proposed architecture and dispersal method, offering a cost-effective alternative to traditional deployment strategies for future satellite constellations. Full article
(This article belongs to the Section Astronautics & Space Science)
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18 pages, 1319 KiB  
Article
Autonomous Orbit Determination of LLO Satellite Using DRO–LLO Links and Lunar Laser Ranging
by Shixu Chen, Shuanglin Li, Jinghui Pu, Yingjie Xu and Wenbin Wang
Aerospace 2025, 12(7), 576; https://doi.org/10.3390/aerospace12070576 - 25 Jun 2025
Viewed by 395
Abstract
A stable and high-precision autonomous orbit determination scheme for a Low Lunar Orbit (LLO) spacecraft is proposed, leveraging satellite-to-satellite tracking (SST) measurement data and lunar laser ranging data. One satellite orbits around the LLO, while the other satellite orbits around the Distant Retrograde [...] Read more.
A stable and high-precision autonomous orbit determination scheme for a Low Lunar Orbit (LLO) spacecraft is proposed, leveraging satellite-to-satellite tracking (SST) measurement data and lunar laser ranging data. One satellite orbits around the LLO, while the other satellite orbits around the Distant Retrograde Orbit (DRO). An inter-satellite ranging link is established between the two satellites, while the LLO satellite conducts laser ranging with a Corner Cube Reflector (CCR) on the lunar surface. Both inter-satellite ranging data and lunar laser ranging data are acquired through measurements. By integrating these data with orbital dynamics and employing the Extended Kalman Filter (EKF) method, the position and velocity states of the two formation satellites are estimated. This orbit determination scheme operates independently of ground measurement and control stations, achieving a high degree of autonomy. Simulation results demonstrate that the position accuracy of the LLO satellite can reach 0.1 m, and that of the DRO satellite can reach 10 m. Compared to the autonomous orbit determination scheme relying solely on SST measurement data, this proposed scheme exhibits several advantages, including shorter convergence time, higher convergence accuracy, and enhanced robustness of the navigation system against initial orbit errors and orbital dynamic model errors. It can provide a valuable engineering reference for the autonomous navigation of lunar-orbiting satellites. Full article
(This article belongs to the Special Issue Precise Orbit Determination of the Spacecraft)
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32 pages, 1934 KiB  
Review
A Library of 77 Multibody Solar and Extrasolar Subsystems—A Review of Their Dynamical Properties, Global Mean-Motion Resonances, and the Landau-Damped Mean Tidal Fields
by Dimitris M. Christodoulou, Silas G. T. Laycock and Demosthenes Kazanas
Astronomy 2025, 4(3), 11; https://doi.org/10.3390/astronomy4030011 - 23 Jun 2025
Viewed by 465
Abstract
We revisit 77 relaxed (extra)solar multibody (sub)systems containing 2–9 bodies orbiting about gravitationally dominant central bodies. The listings are complete down to (sub)systems with 5 orbiting bodies and additionally contain 33 smaller systems with 2–4 orbiting bodies. Most of the multiplanet systems (68) [...] Read more.
We revisit 77 relaxed (extra)solar multibody (sub)systems containing 2–9 bodies orbiting about gravitationally dominant central bodies. The listings are complete down to (sub)systems with 5 orbiting bodies and additionally contain 33 smaller systems with 2–4 orbiting bodies. Most of the multiplanet systems (68) have been observed outside of our solar system, and very few of them (5) exhibit classical Laplace resonances (LRs). The remaining 9 subsystems have been found in our solar system; they include 7 well-known satellite groups in addition to the four gaseous giant planets and the four terrestrial planets, and they exhibit only one classical Laplace resonant chain, the famous Galilean LR. The orbiting bodies (planets, dwarfs, or satellites) appear to be locked in/near global mean-motion resonances (MMRs), as these are determined in reference to the orbital period of the most massive (most inert) body in each (sub)system. We present a library of these 77 multibody subsystems for future use and reference. The library listings of dynamical properties also include regular spacings of the orbital semimajor axes. Regularities in the spatial configurations of the bodies were determined from patterns that had existed in the mean tidal field that drove multibody migrations toward MMRs, well before the tidal field was erased by the process of `gravitational Landau damping’ which concluded its work when all major bodies had finally settled in/near the global MMRs presently observed. Finally, detailed comparisons of results help us discern the longest commonly-occurring MMR chains, distinguish the most important groups of triple MMRs, and identify a new criterion for the absence of librations in triple MMRs. Full article
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25 pages, 4360 KiB  
Article
Positioning-Based Uplink Synchronization Method for NB-IoT in LEO Satellite Networks
by Qiang Qi, Tao Hong and Gengxin Zhang
Symmetry 2025, 17(7), 984; https://doi.org/10.3390/sym17070984 - 21 Jun 2025
Viewed by 624
Abstract
With the growth of Internet of Things (IoT) business demands, NB-IoT integrating low earth orbit (LEO) satellite communication systems is considered a crucial component for achieving global coverage of IoT networks in the future. However, the long propagation delay and significant Doppler frequency [...] Read more.
With the growth of Internet of Things (IoT) business demands, NB-IoT integrating low earth orbit (LEO) satellite communication systems is considered a crucial component for achieving global coverage of IoT networks in the future. However, the long propagation delay and significant Doppler frequency shift of the satellite-to-ground link pose substantial challenges to the uplink and downlink synchronization in LEO satellite-based NB-IoT networks. To address this challenge, we first propose a Multiple Segment Auto-correlation (MSA) algorithm to detect the downlink Narrow-band Primary Synchronization Signal (NPSS), specifically tailored for the large Doppler frequency shift of LEO satellites. After detection, downlink synchronization can be realized by determining the arrival time and frequency of the NPSS. Then, to complete the uplink synchronization, we propose a position-based scheme to obtain the Timing Advance (TA) values and pre-compensated Doppler shift value. In this scheme, we formulate a time difference of arrival (TDOA) equation using the arrival times of NPSSs from different satellites or at different times as observations. After solving the TDOA equation using the Chan method, the uplink synchronization is completed by obtaining the TA values and pre-compensated Doppler shift value from the terminal position combined with satellite ephemeris. Finally, the feasibility of the proposed scheme is verified in an Iridium satellite constellation. Compared to conventional GNSS-assisted methods, the approach proposed in this paper reduces terminal power consumption by 15–40%. Moreover, it achieves an uplink synchronization success rate of over 98% under negative SNR conditions. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Future Wireless Networks)
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18 pages, 1397 KiB  
Article
GPS and Galileo Precise Point Positioning Performance with Tropospheric Estimation Using Different Products: BRDM, RTS, HAS, and MGEX
by Damian Kiliszek
Remote Sens. 2025, 17(12), 2080; https://doi.org/10.3390/rs17122080 - 17 Jun 2025
Viewed by 514
Abstract
The performance of Precise Point Positioning (PPP) using different Global Navigation Satellite System (GNSS) product sets, including broadcast ephemerides, International GNSS Service Real-Time Service (IGS-RTS) corrections, Galileo High Accuracy Service (HAS) corrections, and precise products from the Center for Orbit Determination in Europe [...] Read more.
The performance of Precise Point Positioning (PPP) using different Global Navigation Satellite System (GNSS) product sets, including broadcast ephemerides, International GNSS Service Real-Time Service (IGS-RTS) corrections, Galileo High Accuracy Service (HAS) corrections, and precise products from the Center for Orbit Determination in Europe (CODE) Multi-GNSS Experiment (MGEX), has been evaluated. The availability of solutions, convergence time, position accuracy and Zenith Tropospheric Delay (ZTD) estimation across these products were analyzed using simulated real-time and postprocessing static modes, using data from globally distributed stations with a 1 s observation interval. The results indicate that precise products from the MGEX provide the highest accuracy, achieving centimeter-level precision in post-processed mode. Real-time simulated solutions, such as HAS and IGS-RTS, deliver promising results, with Galileo HAS meeting its target accuracy of 20 cm horizontally and 40 cm vertically and a convergence time under 5 min. However, Global Positioning System (GPS) performance within HAS is limited by a significantly lower correction availability—around 67% on average compared to over 95% for Galileo—which negatively impacts PPP performance. ZTD estimation results show that real-time services (HAS, IGS-RTS) achieved errors within 1–3 cm, sufficient for meteorological applications. This study highlights the growing importance of HAS in real-time positioning applications and suggests further improvements in GPS for enhanced performance. Full article
(This article belongs to the Special Issue Advances in Multi-GNSS Technology and Applications)
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11 pages, 2051 KiB  
Review
Review of the Problem of the Earth Shape
by Petr Vaníček, Pavel Novák and Marcelo Santos
Geomatics 2025, 5(2), 24; https://doi.org/10.3390/geomatics5020024 - 13 Jun 2025
Viewed by 482
Abstract
The determination of the shape of the Earth has been one of the fundamental problems geodesy was supposed to solve; it has been and possibly still is the main geodetic problem. It is thus appropriate for geodesists to look at this problem [...] Read more.
The determination of the shape of the Earth has been one of the fundamental problems geodesy was supposed to solve; it has been and possibly still is the main geodetic problem. It is thus appropriate for geodesists to look at this problem periodically, and this is what the authors of this paper aim to do. About 50 years ago, geodesists started using satellites as a new and very powerful tool. Many problems that were either impossible to solve or that presented almost unsurmountable hurdles to solutions have now been solved relatively simply, so much so that in the eyes of some people, satellites can solve all geodetic problems, and attempts are being made to show that this is indeed the case. We feel that the time has come to show that even satellites have their limitations, the main one being that for them to remain in their orbit, they must fly quite high, typically at several hundred kilometres. The gravitational field of the Earth (and that of any celestial body) smoother as one gets higher and higher. In other words, the gravitational field at the satellite orbit altitude loses detailed information that one can see at the surface of the Earth. In this contribution, we shall try to explain what satellites have contributed to the study of the shape of the Earth and what issues remain to be sorted out. Full article
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17 pages, 474 KiB  
Article
User Experience-Oriented Content Caching for Low Earth Orbit Satellite-Enabled Mobile Edge Computing Networks
by Jianhua He, Youhan Zhao, Yonghua Ma and Qiang Wang
Electronics 2025, 14(12), 2413; https://doi.org/10.3390/electronics14122413 - 13 Jun 2025
Viewed by 287
Abstract
In this paper, we investigate a low Earth orbit (LEO) satellite-enabled mobile edge computing (MEC) network, where multiple cache-enabled LEO satellites are deployed to address heterogeneous content requests from ground users. To evaluate the network’s capability in meeting user demands, we adopt the [...] Read more.
In this paper, we investigate a low Earth orbit (LEO) satellite-enabled mobile edge computing (MEC) network, where multiple cache-enabled LEO satellites are deployed to address heterogeneous content requests from ground users. To evaluate the network’s capability in meeting user demands, we adopt the average quality of experience (QoE) of the users as the performance metric, defined based on the effective transmission rate under communication interference. Our analysis reveals that the average QoE is determined by the content caching decisions at the satellites, thereby allowing us to formulate an average QoE maximization problem, subject to practical constraints on the satellite caching capacity. To tackle this NP-hard problem, we design a two-stage content caching algorithm that combines divide-and-conquer and greedy policies for efficient solution. The numerical results validate the effectiveness of the proposed approach. Compared with several benchmark schemes, our algorithm achieves notable improvements in terms of the average QoE while significantly reducing caching costs, particularly under resource-constrained satellite settings. Full article
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20 pages, 6028 KiB  
Article
Improving Orbit Prediction of the Two-Line Element with Orbit Determination Using a Hybrid Algorithm of the Simplex Method and Genetic Algorithm
by Jinghong Liu, Chenyun Wu, Wanting Long, Bo Yuan, Zhengyuan Zhang and Jizhang Sang
Aerospace 2025, 12(6), 527; https://doi.org/10.3390/aerospace12060527 - 11 Jun 2025
Viewed by 435
Abstract
With the rapidly increasing number of satellites and orbital debris, collision avoidance and reentry prediction are very important for space situational awareness. A precise orbital prediction through orbit determination is crucial to enhance the space safety. The two-line element (TLE) data sets are [...] Read more.
With the rapidly increasing number of satellites and orbital debris, collision avoidance and reentry prediction are very important for space situational awareness. A precise orbital prediction through orbit determination is crucial to enhance the space safety. The two-line element (TLE) data sets are publicly available to users worldwide. However, the data sets have uneven qualities and biases, resulting in exponential growth of orbital prediction errors in the along-track direction. A hybrid algorithm of the simplex method and genetic algorithm is proposed to improve orbit determination accuracy using TLEs. The parameters of the algorithm are tuned to achieve the best performance of orbital prediction. Six satellites with consolidated prediction format (CPF) ephemeris and four satellites with precise orbit ephemerides (PODs) are chosen to test the performance of the algorithm. Compared with the results of the least-squares method and simplex method based on Monte Carlo simulation, the new algorithm demonstrated its superiorities in orbital prediction. The algorithm exhibits an accuracy improvement as high as 40.25% for 10 days of orbital prediction compared to that using the single last two-line element. In addition, six satellites are used to evaluate the time efficiency, and the experiments prove that the hybrid algorithm is robust and has computational efficiency. Full article
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