Search Results (39)

Designing Low Earth Orbit (LEO) constellations for the continuous, collaborative observation of space objects in MEO/GEO is a complex optimization task, frequently limited by prohibitive computational costs. This study introduces an efficient surrogate-based framework to overcome this challenge. Our approach integrates Optimized Latin Hypercube Sampling (OLHS) with a Radial Basis Function (RBF) model to minimize the required number of satellites. In a comprehensive case study targeting 18 diverse space objects—including communication satellites in GEO (e.g., EUTELSAT, ANIK) and navigation satellites in MEO/IGSO from GPS, Galileo, and BeiDou constellations—the method proved highly effective and scalable. It successfully designed a 208-satellite Walker constellation that provides 100% continuous coverage over a 36-h period. Furthermore, the design ensures that each target is simultaneously observed by at least three satellites at all times. A key finding is the method’s remarkable efficiency and scalability: the optimal solution for this larger problem was found using only 46 high-fidelity function evaluations, maintaining a computational time that was 5–8 times faster than traditional global optimization algorithms. This research demonstrates that surrogate-assisted optimization can drastically lower the computational barrier in constellation design, offering a powerful tool for building cost-effective and robust Space Situational Awareness (SSA) systems. Full article

We study a class of circular restricted planar Newtonian four-body problems in which three masses are positioned at the vertices of a Lagrange equilateral triangle configuration, each mass revolving around the center of mass in circular orbits. Assuming that the value of the fourth mass is negligibly small (i.e., it does not perturb the motion of the other three masses, though its own motion is influenced by them), we use variational minimization methods to prove the existence of noncollision periodic solutions with some fixed winding numbers. These noncollision solutions exist for both equal and unequal mass values for the three bodies located at the vertices of the Lagrange equilateral configuration. Full article

The 4-body equations of motion are derived in our previously published paper. Here we prove the existence–uniqueness of a periodic solution by applying the fixed-point method for a suitable introduced operator. To apply the fixed-point theorem, we need to derive appropriate analytical inequalities for the right-hand sides of the equations that ensure that the operator for periodic solutions maps the set of periodic functions into itself. In this way, we prove the existence of the Bohr–Sommerfeld orbits for the 4-body problem in the relativistic case. That allows us to estimate the minimal distances between the electrons on the first and second Bohr–Sommerfeld stationary states. A natural example of such a problem is the Lithium atom, which has three electrons orbiting the nucleus. Full article

Signal-of-Opportunity (SOP) positioning based on Low-Earth-Orbit (LEO) constellations has gradually become a research hotspot. Due to their large quantity, wide spectral coverage, and strong signal power, LEO satellite SOP positioning exhibits robust anti-jamming capabilities. However, no in-depth studies have been conducted on their anti-jamming performance, particularly regarding the most common type of interference faced by ground receivers—Periodic Frequency Modulation (PFM) interference. Due to the significant differences in signal characteristics between LEO satellite downlink signals and those of Global Navigation Satellite Systems (GNSSs) based on Medium-Earth-Orbit (MEO) or Geostationary-Earth-Orbit (GEO) satellites, traditional interference suppression techniques cannot be directly applied. This paper proposes a Signal Adaptive Iterative Optimization Resampling (SAIOR) algorithm, which leverages the periodicity of PFM jamming signals and the characteristics of LEO constellation signals. The algorithm enhances the concentration of jamming energy by appropriately resampling the data, thereby reducing the overlap between LEO satellite signals and interference. This approach effectively minimizes the damage to the desired signal during anti-jamming processing. Simulation and experimental results demonstrate that, compared to traditional algorithms, this method can effectively eliminates single/multiple-component PFM interference, improve the interference suppression performance under the conditions of narrow bandwidth and high signal power, and holds a high application value in LEO satellite SOP positioning. Full article

To mitigate the limited accuracy of the Simplified General Perturbations 4 (SGP4) model in predicting medium-orbit satellite trajectories, we propose an enhanced methodology integrating deep learning with traditional algorithms. The developed BiLSTM-TS forecasting framework comprises a Bidirectional Long Short-Term Memory (BiLSTM) network, trend analysis module (T), and seasonal decomposition module (S). This architecture effectively captures sequential dependencies, trend variations, and periodic patterns within time series data, thereby improving prediction interpretability. In our experimental validation, we chose Beidou-2 M6 (C14), GSAT0203 (GALILEO 7), and the Global Positioning System (GPS) satellite named GPS BIIR-13 (PRN 02) as representative satellites. Satellite position data derived from conventional orbital models were input into the BiLSTM-TS framework for statistical learning to predict orbital deviations. These predicted errors were subsequently combined with SGP4 model outputs obtained through Two-Line Element set (TLE) data analysis to minimize overall trajectory inaccuracies. Using BeiDou-2 M6 (C14) as a case study, results indicated that the BiLSTM-TS implementation achieved significant error reduction; mean-squared error along the X-axis was reduced to 0.0309 km², with mean absolute error of 0.1245 km, and maximum absolute error was constrained to 0.4448 km. Full article

We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A $(2k+1)$-periodic orbit $\{{\beta }_1<{\beta }_2<\cdots <{\beta }_{2k+1}\}$, ($k\ge 3$) is called second minimal for the map f, if $2k-1$ is a minimal period of ${f|}_{[{\beta }_1,{\beta }_{2k+1}]}$ in the Sharkovski ordering. Full classification of second minimal orbits is presented in terms of cyclic permutations and directed graphs of transitions. It is proved that second minimal odd orbits either have a Stefan-type structure like minimal odd orbits or one of the $4k-3$ types, each characterized with unique cyclic permutations and directed graphs of transitions with an accuracy up to the inverses. The new concept of second minimal orbits and its classification have an important application towards an understanding of the universal structure of the distribution of the periodic windows in the bifurcation diagram generated by the chaotic dynamics of nonlinear maps on the interval. Full article

The Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP) satellite has been continuously providing global environmental data records (EDRs) for more than one decade since its launch in 2011. Recently, the VIIRS EDRs of cloud features have been reprocessed using unified and consistent algorithm for selected periods to minimize or remove the inconsistencies due to different versions of retrieval algorithms as well as input VIIRS sensor data records (SDRs) adopted by different periods of operational EDRs. This study conducts the first simultaneous quality and accuracy assessment of reprocessed Cloud Top Height (CTH) and Cloud Base Height (CBH) products against both the operational VIIRS EDRs and corresponding cloud height measurements from the active sensors of NASA’s CloudSat-CALIPSO system. In general, the reprocessed CTH and CBH EDRs show strong similarities and correlations with CloudSat-CALIPSOs, with coefficients of determination (${\mathrm{R}}^2$) reaching 0.82 and 0.77, respectively. Additionally, the reprocessed VIIRS cloud height products demonstrate significant improvements in retrieving high-altitude clouds and in sensitivity to cloud height dynamics. It outperforms the operational product in capturing very high CTHs exceeding 15 km and exhibits CBH probability patterns more closely aligned with CloudSat-CALIPSO measurements. This preliminary assessment enhances data applicability of remote sensing products for atmospheric and climate research, allowing for more accurate cloud measurements and advancing environmental monitoring efforts. Full article

A continuous adaptive stabilization technique for the unstable period-1 orbit of the fractional difference logistic map is presented in this paper. An impulse-based control technique without short oscillatory transients right after the control impulse is designed for the fractional map with a long memory horizon. However, it appears that the coordinate of the unstable period-1 orbit may drift due to the continuous application of the impulse-based control scheme. An adaptive scheme capable of tracking the drifting coordinate of the unstable period-1 orbit is designed and validated by a number of computational experiments. The proposed control scheme is minimally invasive compared to the continuous feedback control as it preserves the model of the system while requiring only a series of sparse, small, instantaneous control impulses to achieve continuous adaptive stabilization of the unstable period-1 orbit of the fractional difference logistic map. Full article

The Michelson interferometer for global high-resolution thermospheric imaging (MIGHTI) aboard the NASA ionospheric connection (ICON) satellite offers extensive atmospheric wind field data for mid-latitude regions and has recently released its version 5 (v05) data. We conducted a comprehensive comparison and validation of MIGHTI v05 level 2.2 data for the period from December 2019 to October 2022, covering all MIGHTI data in orbit. In a comparison of raw wind speeds, MIGHTI demonstrates good agreement with the ground-based Fabry–Pérot interferometer (FPI), meteor radars, and the space-borne instrument TIMED Doppler interferometer (TIDI). However, some differences still exist. Comparisons with meteor radars revealed differences attributable to observational altitude, day–night variations, and latitude distribution. Below 100 km, MIGHTI and meteor radar exhibit excellent consistency (r = 0.819 for zonal and r = 0.782 for meridional winds). Day–night differences are minimal, with closer amplitude values observed at night. MIGHTI shows stronger correlations with low-latitude meteor radar, with coefficients of 0.859 (zonal) and 0.891 (meridional) at Ledong. The meridional wind correlation is better in low-latitude regions, in contrast to mid-latitudes. Similar observations were made in a comparison with FPI, emphasizing the need for caution when considering the meridional wind component of MIGHTI at observational boundaries (~40 °N). In addition to comparing raw wind speed data, we analyzed the amplitude of fluctuations extracted by MIGHTI and TIDI by employing the least squares method to extract planetary waves. The results indicate that both TIDI and MIGHTI observe the same fluctuation events, but TIDI extracts larger fluctuation amplitudes than MIGHTI. Finally, we present, for the first time, the spatial structure of a five-day wave that occurred in March 2020. Full article

Multipath effects can significantly reduce the accuracy of GNSS precise positioning. Traditional methods, such as sidereal filtering and grid-based approaches, attempt to model and mitigate these errors by leveraging the spatial autocorrelation of multipath based on residuals. However, these methods can only approximately handle spatial autocorrelation data, limiting their effectiveness. This study investigates the spatial cross-correlation of residuals between various GNSS frequency bands, analyzes their covariance function parameters, and evaluates the impact of constellation shifts on long-term multipath mitigation. Based on this, a simplified autocorrelation-based approach utilizing unified covariance parameters for multipath mitigation is proposed, with its efficacy assessed for both short- and long-term applications. The study demonstrates the correlation of multipath effects across various GPS and Galileo frequencies, including GPS L1/L2/L5 and Galileo E1/E5a/E5b/E5ab/E6, by analyzing correlation coefficients. A strong correlation (greater than 0.8) is observed between residuals of closely spaced frequencies, such as E5b and E5ab, despite their frequency differences. Additionally, the covariance parameters of the residuals are found to be consistent across all frequencies for a baseline, suggesting that unified parameters can be applied effectively for spatial autocorrelation-based multipath mitigation without sacrificing performance. The orbit shifts of certain GPS satellites, particularly G02, G20, and G21, result in significant changes in orbital parameters and satellite tracks, reducing the effectiveness of long-term multipath mitigation. However, the impact of GPS orbit shifts can be minimized through periodic model updates or by integrating GPS and Galileo modeling. In experiments, the LSC correction strategy based on a GPS/Galileo combination, utilizing unified parameters, outperforms the grid method based on the GPS/Galileo combination, improving the mean residual variance elimination rate by 11.3% for GPS L1 and 11.4% for Galileo E1. These improvements remain consistent, with rates of 11.3% and 15.7%, respectively, even on DOY 365, which is 327 days after the modeling data were collected. Full article

This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and show that, for four equal masses organized in a linear configuration, these solutions are the minimizers of the action functional. Additionally, we employ numerical experiments using Poincaré sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors, crucial for further studies in multi-body problems. Full article

The significance of detecting faint and diminutive space targets cannot be overstated, as it underpins the preservation of Earth’s orbital environment’s safety and long-term sustainability. Founded by the different response characteristics between targets and backgrounds to aberrations, this paper proposes a novel aberration modulation correlation method (AMCM) for dim and small space target detection. By meticulously manipulating the light path using a wavefront corrector via a modulation signal, the target brightness will fluctuate periodically, while the background brightness remains essentially constant. Benefited by the strong correlation between targets’ characteristic changes and the modulation signal, dim and small targets can be effectively detected. Rigorous simulations and practical experiments have validated the remarkable efficacy of AMCM. Compared to conventional algorithms, AMCM boasts a substantial enhancement in the signal-to-noise ratio (SNR) detection limit from 5 to approximately 2, with an area under the precision–recall curve of 0.9396, underscoring its ability to accurately identify targets while minimizing false positives. In essence, AMCM offers an effective method for detecting dim and small space targets and is also conveniently integrated into other passive target detection systems. Full article

The low Earth orbit (LEO) satellite internet network (LEO-SIN) has become a heated issue for the next generation of mobile communications, serving as a crucial means to achieve global wide-area broadband coverage and, especially, mobile phone directly to satellite cell (MPDTSC) communication. The ultra-high-speed movement of LEO satellites relative to the Earth results in serious Doppler effects, leading to signal de-synchronization at the user end (UE), and relative high-speed motion leading to frequent satellite handovers. Satellite ephemeris, which indicates the satellite’s position, has the potential to determine the position of the transmit (Tx) within the LEO-SIN, thereby enhancing the reliability and efficiency of satellite communication. The adoption of ephemeris in the LEO-SIN has met some new challenges: (1) how UEs can acquire ephemerides before signal synchronization is complete, (2) how to minimize the frequency of ephemeris broadcasting, and (3) how to decrease the overhead of ephemeris broadcasting. To address the above challenges, this paper proposes a method for extrapolating the LEO-SIN orbit based on multi-satellite ephemeris coordination (MSEC) and the multi-stream fractional autoregressive integrated moving average (MS-FARIMA). First, a multi-factor global error analysis model for ephemeris-extrapolation error is established, which decomposes it into three types; namely, random error (RE), trending error (TE), and periodic error (PE), with a focus on increasing the extrapolation accuracy by improving RE and TE. Second, RE is eliminated by utilizing the ephemerides from multiple satellites received at the same UE at the same time, as well as multiple ephemerides from the same satellite at different times. Subsequently, we propose a new FARIMA algorithm with the innovation of a multi-stream data time-series forecast (TSF), which effectively improves ephemeris extrapolation errors. Finally, the simulation results show that the proposed method reduces ephemeris extrapolation errors by 33.5% compared to existing methods, which also contributes to a performance enhancement in the Doppler frequency offset (DFO) estimation of MPDTSC. Full article

A novel station-keeping strategy leveraging periodic revolutions of homeomorphic orbits in the Elliptic Restricted Three-Body Problem within the pulsating frame is presented. A systemic approach founded on arc-length continuation is presented for the discovery, computation, and classification of periodic revolutions that morph from their traditional circular restricted three-body counterparts to build an a priori dataset. The dataset is comprehensive in covering all possible geometric architectures of the restricted problem. Shape similarity is quantified using Hausdorff distance and works as a filter for the station-keeping algorithm in relation to appropriate target conditions. Finally, an efficient scheme to quantify impulsive orbit maintenance maneuvers that minimize the total fuel cost is presented. The proposed approach is salient in its generic applicability across any elliptic three-body system and any periodic orbit family. Finally, average annual station-keeping costs using the described methodology are quantified for selected “orbits of interest” in the cis-lunar and the Sun–Earth systems. The robustness and efficacy of the approach instill confidence in its applicability for realistic mission design scenarios. Full article

Background: During blow-out fracture surgery, restoration of the orbital volume and rigid implant fixation are essential. The migration of an implant is a concern of most surgeons. The purpose of this study was to introduce a simple idea of molding and fixing an orbital implant. Methods: In the tongue-in-groove method, an incision of about 2 mm was made on the edge of the implant and it was bent to form a slot. A hole was made in the center of the implant for fitting a bone hook, and the implant was firmly fit into the remaining intact bone. Before and after surgery, computed tomography (CT) was used to evaluate changes in the orbital volume and the location of the implant. Statistically significant restoration of the orbital volume was confirmed on postoperative CT. Results: Compared with the unaffected orbital volume, the affected orbital volume was increased from 87.06 ± 7.92% before surgery to 96.14 ± 6.11% after surgery (p < 0.001). There was one case of implant migration during follow-up. However, the degree of movement was not severe, and there were no events during the follow-up period. Conclusions: The tongue-in-groove technique offers advantages, such as easy fixation of the implant, with minimal trauma to the surrounding tissues. In addition, the method offers advantages, such as being easy to learn, requiring little time for trimming the implant, and being relatively low cost. Therefore, it can be one of the options for implant fixation. Full article