Search Results (288)

This paper proposes a convolutional Long Short-Term Memory (ConvLSTM) network integrated with multi-channel features dedicated to ionospheric total electron content (TEC) forecasting. To improve generalization, solar, and geomagnetic activity indices are added as auxiliary channel inputs. The model is built upon an Encoder–Decoder (ED) architecture enhanced with residual connections and convolutional channel projection, which collectively improve the synergy among its core components. Based on this framework, we developed ED-ConvLSTM-Res, a multi-channel feature-based global ionospheric TEC prediction model. Comprehensive accuracy evaluation and comparative tests were carried out using datasets from the solar minimum year of 2019 and the current solar maximum year of 2024. The results indicate that the proposed model consistently achieves strong predictive performance compared with other models, along with a significantly enhanced feature representation capability. Specifically, the Root Mean Square Errors (RMSE) of the ED-ConvLSTM-Res model’s predictions in 2019 and 2024 are 1.28 TECU and 5.28 TECU, respectively, while the corresponding Mean Absolute Errors (MAE) are 0.87 and 3.87, and the coefficients of determination (R²) are 0.95 and 0.94. In the current high solar activity year 2024, the proposed model achieves error reductions of 13.6% in MAE and 11.6% in RMSE compared with the Center for Orbit Determination in Europe (CODE)’s one-day-ahead forecast product, c1pg. These results confirm that the proposed model not only outperforms the ConvLSTM model without additional indices and c1pg but also exhibits strong generalization capability, maintaining stable performance with low errors under both high and low solar activity conditions. Full article

When a navigation constellation depends exclusively on inter-satellite links for autonomous orbit determination, the absence of inertial frame orientation measurements can result in the accumulation of rotational errors across the entire constellation. To address these challenges, this study introduces inter-satellite orientation information in the inertial frame to provide the BeiDou satellite constellation with a stable inertial orientation reference. The results demonstrate that (1) incorporating space-based orientation observations with satellite-to-ground data significantly enhances orbit determination accuracy, reducing the three-dimensional orbit error from 2.604 m to 0.611 m. (2) Introducing a single orientation data point per epoch improves orbit determination accuracy from 2.604 m to 0.982 m. Compared to the scanning mode, the staring mode achieves higher performance. (3) When the error of space-based orientation data remains below 10 mas, the resulting spatial reference frame accuracy is better than 50 cm for the satellites. This research provides technical support for the construction of next-generation BDS. Full article

This paper presents an angles-only navigation (AON) method utilizing optical observations of a single satellite with known ephemeris and prior altitude constraints given by an altimeter or known topography, which can enable near-ground platforms to achieve autonomous navigation in GNSS-denied environments. By leveraging a star tracker to measure the line-of-sight (LOS) direction of a satellite against a star background, the observer’s location is resolved via triangulation under geometric constraints. Theoretical error models are derived to analyze the influence of satellite position errors, LOS direction errors, and altitude uncertainties on geolocation accuracy. Numerical simulations validate the error propagation mechanisms, demonstrating that geolocation error is primarily determined by the perpendicular projection of orbital error relative to the LOS, increases linearly with LOS distance, and is sensitive to altitude errors at low elevation angles. Ground-based experiments conducted using Globalstar satellites achieve geolocation accuracy within 250 m (RMS), consistent with theoretical predictions. The proposed method offers a practical, low-cost solution for high-precision passive navigation in maritime and terrestrial applications. Full article

In LEO constellation–augmented navigation, the transmitting antenna phase center offset (PCO) and the equipment delay associated with the downlink signals of LEO satellites constitute major error sources that must be precisely characterized. Previous studies primarily focused on single or small-scale satellite scenarios, lacking comprehensive evaluations regarding the influence of constellation scale, orbital altitude, ground station configuration, and various error sources. To address this gap, we propose a joint estimation method utilizing observations from a limited number of regional ground stations in China that simultaneously track GNSS and LEO satellites. The method is specifically designed to accommodate practical constraints on ground station distribution within China. Initially, a batch least-squares estimation strategy is employed to simultaneously determine the ionosphere-free PCO and initial equipment delays for all LEO satellites in a constellation-wide solution. Subsequently, the estimated PCO parameters are fixed, and the equipment delays are further refined using a precise point positioning (PPP) approach. To systematically evaluate the method’s performance under realistic conditions, we analyze the impact of orbital altitude, constellation size, ground station number, data processing duration, and orbit/clock biases through comprehensive simulations. The results indicate: (1) the Z-direction component of the PCO (pointing toward the Earth’s center) and equipment delay is more sensitive to orbit and clock errors; (2) Increasing the number of LEO satellites generally improves the estimation accuracy of equipment delays, but the marginal gain diminishes as the constellation size expands; (3) sub-centimeter PCO accuracy and equipment delay accuracies better than 3 cm can still be achieved using only 3–4 regionally distributed ground stations over an observation period of 5–7 days. Full article

We present new spectroscopic orbits for the bright binaries Mizar B, 3 Pup, $\nu$ Gem, 2 Lac, and $\varphi$ Aql. Our analysis is based on medium-resolution ($R\approx$ 12,000) échelle spectra obtained with the 0.81-m telescope and fiber-fed eShel spectrograph of the Three College Observatory (Greensboro, NC, USA) between 2015 and 2024. Orbital elements were inferred with an affine-invariant Markov-chain Monte-Carlo sampler; convergence was verified through the integrated autocorrelation time and the Gelman–Rubin statistic. Errors quote the 16th–84th-percentile credible intervals. Compared with previously published orbital solutions for the studied stars, our method improves the root-mean-square residuals by 25–50% and bring the 1$\sigma$ uncertainties on the radial velocity (RV) semi-amplitudes down to 0.02–0.15 km $s^{-1}$. These gains translate into markedly tighter mass functions and systemic RVs, providing a robust dynamical baseline for future interferometric and photometric studies. A complete Python analysis pipeline is openly available in a GitHub repository, ensuring full reproducibility. The results demonstrate that a Bayesian RV analysis with well-motivated priors and rigorous convergence checks yields orbital parameters that are both more precise and more reproducible than previous determinations, while offering fully transparent uncertainty budgets. Full article

In Global Navigation Satellite System (GNSS)-denied environments, navigation using signals of opportunity (SOP) from Low Earth Orbit (LEO) satellites is considered a feasible alternative. Compared with single-constellation systems, multiple-constellation LEO systems offer improved satellite visibility and geometric diversity, which enhances positioning continuity and accuracy. To allocate weights among heterogeneous observations, prior studies have employed the Helmert variance component estimation (HVCE) method, which iteratively determines relative weight ratios of different observation types through posterior variance estimation. HVCE enables error modeling and weight adjustment without prior noise information but is highly sensitive to outliers, making it vulnerable to their impact. This study proposes a Robust HVCE-based dual-constellation weighted positioning method. The approach integrates prior weighting based on satellite elevation, observation screening based on characteristic slopes, HVCE, and IGG-III robust estimation to achieve dynamic weight adjustment and suppress outliers. Experimental results over a 33.9 km baseline demonstrate that the proposed method attains Two-Dimensional (2D) and Three-Dimensional (3D) positioning accuracies of 12.824 m and 23.230 m, corresponding to improvements of 29% and 16% over conventional HVCE weighting, respectively. It also outperforms single-constellation positioning and equal-weighted fusion, confirming the effectiveness of the proposed approach. Full article

This study aims to enhance Low Earth Orbit (LEO) satellite orbit prediction accuracy. We propose the Precise Orbit Determination with Optimized Perturbations (PODOP) method, considering Earth’s non-spherical gravity, atmospheric drag, etc., and a Long Short-Term Memory (LSTM)-based approach for orbital element time series. Validation shows that PODOP’s 10-day median error is 8.1 km (19% larger than Simplified General Perturbations (SGP4)’s 10.1 km) and LSTM’s 10-day median error is 5.3 km, outperforming SGP4 (48.5 km) and PODOP and improving constellation management and collision prevention. Full article

Space debris is an increasingly severe problem in the space industry. According to projections, the number of satellites will increase from the current 10,000 to 100,000 by 2030, specially in LEO orbits. This significant rise in the number of satellites threatens space sustainability, forcing satellites to perform more maneuvers to avoid impacts or leading to the production of more and more space debris due to collisions (Kessler Syndrome). Consequently, substantial efforts have been made to detect and track space debris, leading to the development of the current catalogs. However, with existing technology, detecting and tracking small debris remains challenging. In order to improve the current system, several proposals of Space-Based Situational Awareness (SBSA) have been made. These proposals involve satellites equipped with telescopes to detect space debris and determine their orbits. Unlike prior works, focused primarily on detection rates, this research aims to quantify their accuracy in orbit determination as a function of observation duration, the number of observers, and sensor precision. The Unscented Kalman Filter (UKF) is employed as the core estimation algorithm, leveraging both simulated single-case analyses and Monte Carlo simulations to evaluate system performance under various configurations and uncertainties. The results indicate that a constellation of at least three observers with high-precision instruments and sub-kilometer positioning accuracy can reliably estimate debris orbits within an observation period of 4–7 min, with the mean error in position and velocity obtained being 2.2–3 km and 3–4 m/s, respectively. These findings offer critical insights for designing future SBSA constellations and optimizing their operational parameters to address the growing challenge of orbital debris. Full article

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

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

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

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

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

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

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