Two-line Element Sets Research Articles

Downlink Analysis of a Low-Earth Orbit Satellite Considering an Airborne Interference Source Moving on Various Trajectory

This paper analyzes low-Earth-orbit (LEO) satellite downlinks when an airborne interference source moves parallel to the satellite trajectory by considering the relative angle differences between the satellites and the interference sources. To make the experimental interference situations more like actual environments, the LEO trajectories are obtained from two-line element set (TLE) data. Airborne interference sources with various altitudes move parallel to the LEO trajectories, and a jamming to signal (J/S) ratio is calculated based on the relative angle differences between the ground station, the LEO satellite, and the interference source. To accurately calculate the J/S ratio, we should apply the sidelobe gain from which the interference signal enters to the ground station antenna. In order to calculate the relative angle difference ψ, the coordinates of the satellite and the interference source are converted from the World Geodetic System 1984 (WGS84) to the ground station-centered east–north-up (ENU) system. The resulting J/S ratio demonstrates that the distance and the relative angle difference ψ between the ground stations, LEO satellite, and airborne interference source appear to be important factors causing changes in the J/S ratio. Among them, the relative angle difference ψ, which determines the sidelobe gain of the ground station antenna, is the most significant factor affecting the J/S ratio variation.

The Steward Observatory LEO Satellite Photometric Survey

The Steward Observatory LEO Satellite Photometric Survey is a comprehensive observational survey to characterize the apparent brightness of the Starlink and OneWeb low Earth orbit satellites and evaluate the potential impact on astronomy. We report the results of over 16,000 independent measurements of nearly 2800 individual satellites. In addition to photometry, we also measured the astrometric position of each satellite and evaluated the accuracy of predicting satellite position with the available two-line element sets. The apparent brightness of a satellite seen in the sky is not constant and depends on the Sun-satellite-observer geometry. To capture this, we designed the survey to create an all-geometries set of measurements to fully characterize the brightness of each population of satellites as seen in the sky. We visualize the data with sky-plots that show the correlation of apparent brightness with on-sky position and relative Sun-satellite-observer geometry. The sky-plots show where in the sky the satellites are brightest. In addition to visual magnitudes, we also present two new metrics: the expected photon flux and the effective albedo. The expected photon flux metric assesses the potential impact on astronomy sensors by predicting the flux for a satellite trail in an image from a theoretical 1 m class telescope and sensor. The effective albedo metric assesses where a satellite is more reflective than baseline, which ties to the physical structure of the satellite and indicates the potential for brightness-reducing design changes. We intend to use this methodology and resulting data to inform the astronomy community about satellite brightness. Observing programs use a variety of telescopes and instruments and look at different parts of the sky. With the expected photon flux metric and a complete all-sky characterization of satellite brightness, observers can evaluate the potential impacts to their projects and possibly avoid the worst effects.

An investigation on space debris of unknown origin using proper elements and neural networks

Proper elements represent a dynamical fingerprint of an object’s inherent state and have been used by small-body taxonomists in characterizing asteroid families. Being linked to the underlying dynamical structure of orbits, Celletti, Pucacco, and Vartolomei have recently adopted these innate orbital parameters for the association of debris from breakup or collision into its parent satellite. Building from this rich astronomical heritage and recent foundations, we introduce an unsupervised learning method—density-based spatial clustering of applications with noise (DBSCAN)—to determine clusters of orbital debris in the space of proper elements. Data is taken from the space-object catalog of trackable Earth-orbiting objects in the form of two-line element sets. Proper elements for debris fragments in low-Earth orbit are computed using an ad hoc numerical scheme, akin to the state-of-the-art Fourier-series-based synthetic method for the asteroid domain. Given the heuristic nature of classical DBSCAN, we investigate the use of neural networks, trained on known families, to augment DBSCAN into a classification problem and apply it to analyst objects of unknown origin.

Long-Term Orbital Lifetime Prediction of Highly Eccentric Orbits: A Statistical Approach

This paper concentrates on the long-term orbital lifetime prediction of highly eccentric orbits (HEOs) based on two-line element sets via a statistical approach. Due to the significantly different evolution characteristics of low- and high-inclination HEOs induced by different orbital resonances, two area-to-mass estimation methods are proposed, respectively. The resonance phenomena encountered in the HEO region strongly affect the orbital evolution and cause high sensitivity. Therefore, a statistical approach is adopted to handle these effects and correctly estimate low-inclination HEO lifetime. We use the Monte Carlo method and kernel-density estimation to calculate the probability distribution of the orbital lifetime. Finally, the performance of the method is assessed by the actual orbital lifetimes of space objects that reentered from HEOs in the past 50 years. The results indicate that our statistical approach can improve the orbital lifetime prediction accuracy to a large extent, especially for the low-inclination HEOs. If a relative error of 15% is adopted as the error tolerance, compared with the traditional method based on a single orbital propagation, our statistical method can increase the success rate from 40% to more than 70%. For the high-inclination HEOs, the objects with a relative error below 15% account for more than 90%.

Studies of Satellite Position Measurements of LEO CubeSat to Identify the Motion Mode Relative to Its Center of Mass

This paper addresses the possibility of reconstructing motion relative to the center of mass of a low Earth orbit (LEO) nanosatellite of the CubeSat 3U standard using satellite position measurements (Two-Line Element Set (TLE)). This kind of task needs to be performed in the case where it is not possible to establish radio communication with the nanosatellite after it is launched into orbit. Therefore, it is important for the nanosatellite developers to develop some understanding of what is going on with the nanosatellite in order to be able to analyze the current situation after deployment. The study was carried out on the example of the aerodynamically stabilized SamSat-218D nanosatellite developed by the professors and students of Samara National Research University. SamSat-218D was launched into a near-circular orbit with an average altitude of 486 km on April 2016 during the first launch campaign from the Vostochny cosmodrome. Knowledge of CubeSat aerodynamics allows estimating the nature of its possible motion relative to the CubeSat center of mass by ballistic coefficient changes, evaluated with the use of satellite position measurements. The analysis showed that SamSat-218D performed spatial rotation with an angular velocity of more than two degree per second and had not stabilized aerodynamically by 2 March 2022, when it entered the atmosphere and was destroyed.

Orbital kinematics of conjuncting objects in Low-Earth Orbit and opportunities for autonomous observations

As satellites and debris continue to proliferate in Low Earth Orbit (LEO), collision avoidance maneuvers are becoming routine for operational spacecraft, causing increasingly discontinuous operations. Despite the congested environment, collisions are still very unlikely events and most satellites would never actually need to maneuver during their lifetime. Maneuvers are currently performed far more than necessary because of the limited accuracy of the tracking data used for assessing collision risks, which leads to overestimates. A little explored solution is to equip satellites with sensors that enable them, whenever at risk of collision, to autonomously track the hazardous objects and refine their positional knowledge before making a maneuver decision. Unlike what is possible from ground, satellites can collect data and estimate the collision risk even shortly before a potential collision (e.g., one orbit before), improving the final prediction accuracy and reducing false alarm rates. Moreover, while most surveillance data is currently obtained through ground-based sensors, space-based observations can provide unique information as they do not suffer from atmospheric issues (e.g., diffractions, aberrations). Here, the feasibility of observing hazardous objects directly from at-risk satellites before potential collisions is corroborated by demonstrating that objects in LEO usually pass close together several times before the closest approach, providing short observation opportunities. A thorough characterization of these observing windows is performed by reconstructing and analyzing the trajectory evolution for thousands of historical conjunction events, starting from Two-Line Element (TLE) sets and using a Simplified General Perturbations 4 model (SGP4) for the propagation. Statistical analysis is performed to assess the average number and duration of the observation opportunities, the relative distances and velocities involved, and other relevant features. Results show that a satellite with a detection range of 500 km would be able in more than 80% of the cases to observe a high-risk object twice and for at least 10 s before the potential collision.

Generating realistic two-line element sets for notional space vehicles and constellations

As space becomes increasingly populated with new satellites and systems, modeling and simulation of existing and future systems becomes more important. The two-line element set has been the standard format for sharing data about a satellite’s orbit since the 1960s, and well-developed algorithms can predict the future location of satellites based on these data. In order to simulate potential future systems, especially when mixed with existing systems, data must be generated to represent the desired orbits. We present a means to create two-line element sets with parameters that closely resemble real satellite behavior and rely on a novel approach to calculate the mean motion for even greater accuracy.

Analysis on Propagation Accuracy of Deep-Space TLE Objects Affected by Solar/Lunar Orbit Calculation

Two Line Element set (TLE) is a widely used catalog data of space objects, consequently its propagation accuracy and error characteristic became one of the concerned problems in space debris research. TLEs should be propagated with the compatible SGP4/SDP4 (Simplified General Perturbations 4/Simplified Deep Space 4) model. For a deep-space object, SGP4/SDP4 model includes J2,J3, J4 zonal perturbations, solar/lunar third-body perturbation, and an extra treatment for 12 h/24 h orbit resonance problem. In regard to third-body perturbation, the SGP4/SDP4 model describes solar/lunar orbit, with a set of time-varying elements, as a simple two-body mean motion, of which there would be 2∘–3∘ solar/lunar position error after a 10 d extrapolation. A modest accuracy solar/lunar orbit model has been chosen to provide a more precise position estimation at the TLE element epoch. Due to the difference between solar/lunar motion complexity, the lunar is directly modeled by its true anomaly function, while the solar is modeled by the two-body mean motion. The result that approximately 1′–2′ for the solar position and 15′–20′ for the lunar position is achieved for a 10 d extrapolation. The laser ranging satellite Etalon 1 and Galileo 23 were taken as examples to show that the evolution of position accuracy of the TLEs could have an abnormal change during the propagation, while an “improved” TLE with solar/lunar orbit correction will have better performance.

Systematic TLE data improvement by neural network for most cataloged resident space objects

Two-line element sets (TLE) released by the 18th Space Control Squadron are the most complete source of information for space situational awareness in the public domain. They are used in a wide range of contexts that include navigation of nanosatellites and ground communication. However, the TLE data are known for having significant bias and errors. Predicting the bias of TLE can be a way to correct them automatically and hence optimize the systems that rely on them at low cost, for instance for reentry calculations and mission analysis. This paper shows the performance of a neural network trained on more than 4500 inactive resident space objects (RSO) on 10 months of orbital data, on all types of orbits. It is shown that the state vector errors are corrected by at least 40% for 70% of the TLE and that the residual error distributions are well described by a Student’s t-distribution for which covariance elements are defined consistently. The performance of the trained neural network are shown to be similar for multiple active satellites.

The regional nanosatellite constellation modelling formation by a piggyback launch from different spaceports

The roadmap for constructing a regional nanosatellite constellation using the piggyback launch according to Chinese provider information has developed. For nanosatellite constellation formation to a specific purpose, it is necessary to analyse existing constellation operated similar tasks. Therefore, the software module for the Spire Global constellation orbital construction analysis was developed. The construction of Spire Global nanosatellites constellation based on orbital parameters database in the two-line element set format, satellite constellation databases and the developer site was analysed. A launch from the International Space Station and a piggyback launch were used for constellation formation. Nanosatellite deployment schemes, orbital parameters and flight parameters are investigated launches from the Taiyuan and Jiuquan Satellite Launch Centers with orbit inclination about 90°, that best correspond to the passes over Minsk (ϕ = 53°54′27″ N, λ = 27°33′52″ E) are analysed. The method of nanosatellite orbit preflight prediction at a passing launch has been developed. It involves a finding the nanosatellite state vector in the first flight day and at the time of constellation mission operate start. The launch time, satellite launch center coordinates, launch vehicle type, orbit inclination and altitude (period) are used in the method. In addition, the launch history and the satellite motion dynamics analysis on similar orbits is carried out. It was found that five launches are enough to organise a regional nanosatellite constellation with average radio visibility interruption time of at least 36 min with a maximum value of 85 min.

Real-time processing pipeline for automatic streak detection in astronomical images implemented in a multi-GPU system

Abstract Detecting and tracking objects in low Earth orbit is an increasingly important task. Telescope observations contribute to its accomplishment, and telescope imagers produce a large amount of data for this task. Thus, it is convenient to use fast computer-aided processes to analyze it. Telescopes tracking at the sidereal rate usually detect these objects in their imagers as streaks, their lengths depending on the exposure time and the slant range to the object. We have developed a processing pipeline to automatically detect streaks in astronomical images in real time (i.e., faster than the images are produced) by a graphics processing unit parallel processing system. After the detection stage, streak photometric information is obtained, and object candidate identification is provided through matches with a two-line element set database. The system has been tested on a large set of images, consisting of two hours of observation time, from the Tomo-e Gozen camera of the 105 cm Schmidt telescope at Kiso Observatory in Japan. Streaks were automatically detected in approximately 0.5% of the images. The process detected streaks down to a minimum apparent magnitude of +11.3 and matched the streaks with objects from the space-track catalog in 78% of the cases. We believe that this processing pipeline can be instrumental in detecting new objects and tracking existing ones when processing speed is important, for instance, when a short handover time is required between follow-up observation stations, or when there is a large number of images to process. This study will contribute to consolidating optical observations as an effective way to control and alleviate the space debris problem.

Study of the Two-Line Element Accuracy by 1U CubeSat with a GPS Receiver.

There is a common practice to calculate orbital trajectories of space objects like satellites and space debris using Two-Line Element Sets (TLEs). However, TLEs provide rather coarse parameters for fine orbit computation and their precision varies with age of their issue and position of the satellite. The paper evaluates such induced position determination error using the comparison of a position calculated from TLE data for a small CubeSat class satellite and a position obtained from the on-board custom GPS receiver that is a part of such satellite payload. The analyses of the impact of satellite position at the orbit, i.e., a dependency of position error on satellite geographical latitude, and impact of the ageing of TLE data in frame of position and velocity vector were made. There was shown that use of TLE data can bring some significant errors in calculation of predicted satellite position which can affect performance and efficiency of some related tasks like steering the ground station antenna for communication with the satellite or planning the satellites operations namely for the classes of small and amateur satellites.

TLE outlier detection based on expectation maximization algorithm

The most widely-used data for civilian Space Situational Awareness are the Two-Line Element sets (TLEs) provided by the USSTRATCOM. TLEs play critical roles in space monitoring and analysis activities, and are also used in many applications requiring position information of space objects. However, TLEs suffer from uneven data quality, and it is usually necessary to perform outlier or anomaly detections before utilizing these ephemerides. There are many such procedures available in the published literature, and thresholds are usually obtained through simulations or from experiences, which lacks theoretical soundness and thus is inflexible to use. A new filter based on the Expectation Maximization (EM) algorithm is proposed to ease some restrictions, in which outlier thresholds are determined based on the variances estimated in the polynomial regression and prediction, which makes the new filter theoretically sound and more flexible to use. The new filter can be applied to detect outliers in TLEs of objects in any orbital regions, under various space environments, and enduring different operations such as orbit maneuvers. Multiple experiments are presented to demonstrate the effectiveness of the proposed filter to detect outliers of different magnitudes in TLEs. Simulated outliers in the mean motion and eccentricity with the relative magnitude ≥ 5 × 10 - 3 are almost 100% detected, 74% – 98% of outliers in the inclination with the relative magnitude = 0.01 are detected, and 37% – 68% of those with the relative magnitude 5 × 10 - 3 detected. In addition, sequences can be more accurately identified, which help detect outliers in different sequences, making the proposed filter more applicable to complex situations.

Autonomous Spacecraft Orbit Determination from Incident Light Intensity via Eclipse Transient Timing

Autonomous orbit determination methods requiring minimal hardware, computational power, and external reference are desirable for small, low-cost spacecraft, or as a backup on larger craft. This paper presents a set of methods for orbit identification and estimation using only scalar measurements of the incident sunlight intensity, which should be available to most spacecraft without the need for additional dedicated hardware. By using these data to time the duration and transients of eclipse, a spacecraft may maintain a provided orbital estimate or develop a new orbital estimate from scratch. The presented methods use a novel sun-referenced orbit parameter conversion to identify candidate orbits, and an unscented Kalman filter based on the simplified general perturbations model and an atmosphere-corrected eclipse transient model to refine estimates and identify the correct candidate. These navigation methods are tested against public two-line element set data and are shown to provide continuous position estimates with an orbit-averaged error typically on the order of several kilometers in a variety of low-Earth-orbit geometries. So long as the spacecraft is in an eclipsing orbit about a known body, the algorithms described herein can provide orbital state estimates even to satellites without dedicated navigation hardware or external tracking.

Разработка геоинформационной методики и экспериментальные исследования по кросс-калибровке целевой аппаратуры дистанционного зондирования Земли космических аппаратов серии «Канопус-В»

Cross-calibration of the Earth’s remote sensing payload is an addition to the traditionally used flight calibration. It consists of homogeneous terrain regions` image acquiring with a calibrated and reference apparatus and comparing the measured values of the spectral radiance. When selecting references for cross-calibration, the main requirements are the proximity of the spatial resolution and spectral channels of the satellite payload, as well as the observation conditions. Remote sensing spacecrafts Sentinel-2A / 2B and Landsat 8 were selected asreferences. An algorithm was developed to search for intersections of Earth remote sensing satellites ground tracks, which enables finding the parts of the Earth’s surface observed from satellites involved in calibration at a time difference not exceeding 30 minutes. Prediction of satellite paths is carried out using the analytical propagation model SGP4, and two-line element sets of orbital parameters (TLE) taken from open sources. Using the obtained intersection points of propagated ground tracks, the Kanopus-V grouping survey was planned and the corresponding materials by foreign systems were obtained. Basing on them, spectral radiance values obtained by calibrating satellites were compared showing the result of less than 10 % discrepancy.

Irradiation Flux Modelling for Thermal–Electrical Simulation of CubeSats: Orbit, Attitude and Radiation Integration

During satellite development, engineers need to simulate and understand the satellite’s behavior in orbit and minimize failures or inadequate satellite operation. In this sense, one crucial assessment is the irradiance field, which impacts, for example, the power generation through the photovoltaic cells, as well as rules the satellite’s thermal conditions. This good practice is also valid for CubeSat projects. This paper presents a numerical tool to explore typical irradiation scenarios for CubeSat missions by combining state-of-the-art models. Such a tool can provide the input estimation for software and hardware in the loop analysis for a given initial condition and predict it along with the satellite’s lifespan. Three main models will be considered to estimate the irradiation flux over a CubeSat, namely an orbit, an attitude, and a radiation source model, including solar, albedo, and infrared emitted by the Earth. A case study illustrating the tool’s abilities is presented for a typical CubeSats’ two-line element set (TLE) and five attitudes. Finally, a possible application of the tool as an input to a CubeSat task-scheduling is introduced. The results show that the complete model’s use has considerable differences from the simplified models sometimes used in the literature.

Debris cloud of India anti-satellite test to Microsat-R satellite

Understanding the motion of debris cloud produced by the anti-satellite test can help us to know the danger of these tests. This study presents the orbit status of 57 fragments observed by the CelesTrak and presented in the NORAD Two-Line Element Sets of India Anti-Satellite Test. There are 10 of these observed fragments have altitudes of the apogee larger than 1000.0km, the maximum one is 1725.7km. We also numerical calculated the number of debris, the results show that the number of debris with the diameter larger than 0.2m is 14, the number of debris with the diameter larger than 0.01m is 6587, and the number of debris with the diameter larger than 0.001m is 7.22×105. The results of the secondary collision of the debris will produced more fragments in the space. The life time of the fragments depends on the initial orbit parameters and the sizes of the debris.

Serendipitous detection and size estimation of space debris using a survey zenith-pointing telescope

The size distribution of space debris constitutes an important input to risk analysis for current and future space missions. In preparation for future observations with the zenith-pointing 4-m International Liquid Mirror Telescope (ILMT), the 1.3-m Devasthal Fast Optical Telescope (DFOT) was used to gain experience with zenith-pointing observations and, serendipitously, to detect, identify and characterize orbital debris. Observational data were acquired on 11 nights in May 2015 using a 2048 × 2048-pixel CCD detector operating in time-delay integration mode. Thirteen debris streaks were detected, mostly during dawn and twilight. All were identified by correlation with available two-line element sets. By modelling each of the objects as a diffuse-specular Lambertian sphere with an albedo ρ= 0.175, their effective diameters were estimated from the observed apparent magnitudes, altitudes, velocities and solar phase angles. Seven objects were found to be in low Earth orbits and five in mid-Earth or geo-transfer orbits. The apparent Gaia magnitudes of the identified objects range from 5.6 to 12.0 and their estimated effective diameters from 0.8 to 7.6 m. The detection size limit of DFOT is found to be 50 cm for objects orbiting at an altitude of 1000 km. Images from the future ILMT photometric survey are expected to provide detections of space debris having diameters as small as 5 cm at this altitude.

Maneuver Detection Method Based on Probability Distribution Fitting of the Prediction Error

This paper presents a method for detecting historical orbital maneuvers from satellite two-line element sets. Maneuvers are detected by comparing a published state of a specific orbital parameter with a prediction state and analyzing the prediction error between them. Probability distributions of the prediction error associated with different prediction times are fitted first using sample data generated from the satellite two-line element set. The threshold for detecting outliers in the published time series of the orbital parameter is derived based on the fitting result. Subsequently, the method for deriving historical maneuvering information is designed, which ensures that a maneuver is identified by multiple consecutive outliers instead of an isolated outlier in the published time series, thereby eliminating noise interference. Maneuver detection results on typical active satellites show that the proposed method can detect historical maneuvers accurately while maintaining a low false detection rate. When the number of two-line elements for a satellite is insufficient to obtain a good detection result, a preliminary analysis proves that it is feasible to improve the detection rate by borrowing data from a nearby satellite, as long as the two satellites have similar probability distributions of the prediction error.

Optimising filtering of two-line element sets to increase re-entry prediction accuracy for GTO objects

Predicting re-entry epoch of space objects enables managing the risk to ground population. Predictions are particularly difficult for objects in highly-elliptical orbits, and important for objects with components that can survive re-entry, e.g. rocket bodies (R/Bs). This paper presents a methodology to filter two-line element sets (TLEs) to facilitate accurate re-entry prediction of such objects. Difficulties in using TLEs for precise analyses are highlighted and a set of filters that identifies erroneous element sets is developed. The filter settings are optimised using an artificially generated TLE time series. Optimisation results are verified on real TLEs by analysing the automatically found outliers for exemplar R/Bs. Based on a study of 96 historical re-entries, it is shown that TLE filtering is necessary on all orbital elements that are being used in a given analysis in order to avoid considerably inaccurate results.