Two-line Element Research Articles

Third Body Perturbation Effect on Low Earth Orbit Satellite (GEOS-17)

Satellite communication systems have become an important element of the global telecommunications infrastructure, providing data, internet access, telephone, and navigation services to billions of people across the world. In this work, the analytical technique for third body perturbation on GEOS-17 orbit satellite computed for a long period At a time interval of 360 days, the dynamic development of Low Orbit is considered for different values of Eccentricity (𝑒 = 0.05, 𝑒 = 0.6, 𝑒 = 0.89). It was accomplished by utilizing the numerical output results from the celestial mechanics' version 1 software program package. Numerical motion simulations were performed using the Celestial Mechanics software program SATORB module (Beutler, 2005) created at the University of Bern's Institute of Astronomy. With input data given by the Two-Line Elements (TLE). Represented by six orbital elements and three Coordinates axis and three acceleration components which were used to solve the equation of motion analytically by variation of parameters equations (VOP) using a technique known as collocation method, also Matlab (2018) is used for analysis and plot the given figures The results indicated that the greatest effect is at highly elliptical orbit (𝑒 = 0.89) for orbital elements, coordinates axis and acceleration components due to orbit propagation and attractions forces.

Geolocation accuracy improvement for NovaSAR-1 imagery acquired through TLE orbit

NovaSAR-1 is a small S-band Synthetic Aperture Radar (SAR) mission mainly for land and maritime applications. Since SAR has side-looking geometry, thus slant and ground range SAR products have geometric distortions. To correct these geometric distortions, orthorectification needs to be done using SAR Rigorous Sensor Model (RSM) algorithm and Digital Elevation Model (DEM). NovaSAR-1 provides the satellite state vectors either through a Global Positioning System (GPS) or through a Two-Line Element (TLE) orbit source. It is observed that, after orthorectification, it shows poor geolocation accuracy (200 m to 9000 m) for the TLE orbit source. In this paper, geolocation accuracy improvement has been done for NovaSAR-1 ground range imagery acquired through TLE orbit source by generating orthorectified products using SAR Rigorous Sensor Model (RSM) algorithm and Ground control point (GCP). After orthorectification, geolocation accuracy of the NovaSAR-1 imagery acquired through TLE orbit source is reduced to less than 10 m.

Gravitational Perturbation Influence on High Altitude Satellite for different Inclination

Satellites have become such a vital part of our daily lives that we take for granted many of their functions, such as global positioning system (GPS) navigation and images of weather systems collected from orbit. In this work, The analytical method for third body perturbation on high Earth orbit satellites was investigated in this study for different inclinations (𝑖 = 1.71, 𝑖 = 5, 𝑖 = 10, 𝑖 = 23, 𝑖 = 25) across two revolution periods computed for short and long periods, Using the program celestial mechanics version 1 module (Beutler 2005) with input data given by the Two-Line Elements (TLE) created at the University of Bern's Institute of Astronomy. To determine the third body perturbation on Earth satellite using the collocation method. By analyzing the variation in the orbital elements, geocentric Coordinates and acceleration components by Matlab 2018, There was no discernible change in the coordinate system or acceleration components, which appeared to be secular in both results, change, and effect of perturbation has greatest point at Geocentric equatorial coordinates combinations. The conclusion indicates that the Moon perturbation has the most significant impact on orbital elements; furthermore, the satellite with increasing altitude has increasing the amount of perturbation.

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.

Simulation of remote sensing satellite motion base on two line element sets for search and rescue at sea.

Nowadays, satellite remote sensing technology has been applied in many fields of socio-economic development, including search and rescue at sea. Systems with the integration of remote sensing satellite technology have made the search and rescue operations faster, more accurate and more efficient. With the search and rescue systems at sea, remote sensing satellite motion simulation is an important task. This helps the authorities to identify and select the appropriate remote sensing satellite image data source to assist in processing and zoning search and rescue at sea. However, in Vietnam, it is difficult to determine the satellite image data source for the search and rescue situations. Therefore, the research team built a remote sensing satellite motion simulation program based on two-line element data. This is the data source that has been used in astronomy research. This program will simulate satellite orbits in real time and at any time. The accuracy evaluation result of satellite orbit simulation have been compared with online remote sensing satellite tracking systems in the world. The research result show that the satellite orbit simulation has ensured accuracy.

Evaluation of Satellite\u2019s Point-Ahead Angle Derived from TLE for Laser Communication

Advances in lasers, optics and electronics for Satellite’s optical communication are opening the possibility of very high performance near Earth space links with data rate up to several Gbps. Being the divergence of the laser beam typically of tens of murad, an extremely high precision pointing is needed to correctly establish and maintain data optical link. In particular, the relative motion between the satellite and the ground station shall be accurately evaluated to estimate how to correct pointing angles for future orbital locations. This correction is made via a point-ahead mirror (PAM) mechanism, which deviates the laser beam by an angle called point-ahead angle (PAA). The purpose of this paper is evaluate the possibility of accurately estimate the point-ahead angle in advance using the two-line elements sets for the orbiting satellite, which are available before the ground station overpass. The study evaluated TLE-based orbital evolution of Sentinel-6 satellite, comparing the results with the high precision data obtained by laser ranging from the crustal dynamics data information system (CDDIS). The maximum error observed between the estimated and measured point-ahead angles was less than 1murad, demonstrating the possibility of this point-ahead correction technique for LEO orbiting satellites.

Orbit Estimation for Spacecraft Based on Intermittent Measurements: An Event-Triggered UKF Approach

This article addresses a problem of spacecraft orbit estimation with measurement transmission restrictions through an event-triggered state estimation approach. Specifically, we consider the scenario that the ground station communicates with the spacecraft through multiple channels and each channel decides whether or not to transmit the measurements to the spacecraft based on separate deterministic event-triggering conditions. Considering $J_2$ perturbations, an event-triggered unscented Kalman filter-based state estimation algorithm is designed on the basis of a model of orbit dynamics and a measurement model of the ground station. The performance of the estimator is evaluated based on real-time two-line element data. The obtained results indicate that the proposed algorithm can achieve satisfactory estimation performance at reduced measurement transmission rates.

Simplified Approach to Detect Satellite Maneuvers Using TLE Data and Simplified Perturbation Model Utilizing Orbital Element Variation

In this study, an algorithm to identify the maneuvers of a satellite is developed by comparing the Keplerian elements acquired from the two-line elements (TLEs) and Keplerian elements propagated from simplified perturbation models. TLEs contain a specific set of orbital elements, whereas the simplified perturbation models are used to propagate the state vectors at a given time. By comparing the corresponding Keplerian elements derived from both methods, a satellite’s maneuver is identified. This article provides an outline of the working methodology and efficacy of the method. The function of this approach is evaluated in two case studies, i.e., TOPEX/Poseidon and Envisat, whose maneuver histories are available. The same method is implemented to identify the station-keeping maneuvers for TDRS-3, whose maneuver history is not available. Results derived from the analysis indicate that maneuvers with a magnitude of even as low as cm/s are detected when the detection parameters are calibrated properly.

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.

The stare and chase observation strategy at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald: From concept to implementation

A sustainable use of the outer space becomes imperative for preserving current operational missions and enabling the placement of new space-based technology in the outer space safely. The uncontrolled growing number of resident space objects (RSO) increases the likelihood of close conjunctions and therefore collisions that will populate the space environment even more. To prevent such situations, orbit catalogues of RSO are built and maintained, which are used to assess the collision risk between RSO. In order to keep the catalogues up-to-date, a worldwide ground-based infrastructure is used to collect observations coming from different observation techniques.The current study focuses on the so-called stare and chase observation strategy using an active and passive-optical system. The final aim is to correct the pointing of the telescope so that the target will be within the field of view of the laser beam, thus enabling the acquisition of laser ranges. By doing so, objects with poor ephemerides, available e.g. from Two Line Elements (TLE), will not pose a problem anymore for the rather small field of view of the laser beam. The system gathers both angular and range measurements, which can be used for an immediate orbit determination, or improvement, that will enhance the accuracy of the predictions helping other stations to acquire the target faster and permitting the station to repeat the procedure once more.The development of the observation strategy is particularized for the Zimmerwald Laser and Astrometry Telescope (ZIMLAT), located at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald (SwissOGS), Switzerland. Likewise, all the implemented algorithms were tested using real measurements from ZIMLAT and the tracking camera.

Reverse Engineering of Perturbations in the Orbital Decay Environment from Nanosatellite Two-Line Elements

The two leading perturbations acting on satellites in the orbital decay region of low Earth orbit are gravitational nonsphericity of the Earth and atmospheric drag. A detailed understanding of their properties is required to accurately predict satellite dynamics, such as the orbital lifetime. However, there is still room to improve current perturbation models in this region, especially for the atmosphere. The purpose of this paper is 1) to develop a simple method to reverse engineer the leading perturbations from two-line elements (TLEs), and 2) to apply the method to the 2017 Re-Entry Satellite with Gossamer Aeroshell and GPS/Iridium (EGG) nanosatellite mission as a case study. Because of the low ballistic coefficient of EGG and its low orbital altitude, flight was highly affected by both aerodynamic and geopotential effects. Secular and long-periodic effects are extracted via linearized perturbation theory. The results show that EGG acted as a low-cost passive multiphysics sensor for several phenomena, including the changing solar flux, the diurnal atmospheric bulge, rotating winds, and the zonal geopotential. For example, the second zonal geopotential harmonic coefficient is estimated to within 0.008%. To the authors’ knowledge, this is the first study to produce estimates of both atmospheric and geopotential perturbations via TLEs from a single satellite.

Improved orbit predictions using two-line elements through error pattern mining and transferring

As the sole orbit data source of space objects for public access, the NORAD catalog provides the basic orbital information in the form of two-line element (TLE) for various space tasks. But the accuracy of orbit prediction (OP) using TLE with the analytical Simplified General Perturbations-4 (SGP4) propagator drops quickly with time, especially for low orbits, significantly limiting the capability of TLEs for advanced space situational awareness (SSA) applications. To enhance the TLE performance over long-duration OP, this paper proposes a data-driven method for improved TLE-based orbit predictions through mining and transferring the orbit error patterns. Two state-of-the-art learning methods, the gradient boosting decision tree (GBDT) and convolutional neural networks (CNN), are applied to model the underlying error patterns, and then the learned models are used as an error corrector to modify the future orbit predictions. Experimental results demonstrate that the time-varying orbit error patterns in the past can be captured by the developed learning framework. As a result, the accuracy of orbit predictions over the future 14 days can be improved by more than 75% in the along-track direction and 90% in the cross-track and radial directions, when the model-predicted errors are used. It also shows that the error pattern learning and application process is computationally efficient, and it could be implemented for near real-time applications. This study demonstrates the promising potential of machine learning (ML)/deep learning (DL) for enhanced SSA capability with the publicly available TLEs.

Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis

We describe the phase space structures related to the semi-major axis of Molniya-like satellites subject to tesseral and lunisolar resonances. In particular, the questions answered in this contribution are: (1) we study the indirect interplay of the critical inclination resonance on the semi-geosynchronous resonance using a hierarchy of more realistic dynamical systems, thus discussing the dynamics beyond the integrable approximation. By introducing ad hoc tractable models averaged over fast angles, (2) we numerically demarcate the hyperbolic structures organising the long-term dynamics via fast Lyapunov indicators cartography. Based on the publicly available two-line elements space orbital data, (3) we identify two satellites, namely Molniya 1-69 and Molniya 1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. Finally, (4) the computations of their associated dynamical maps highlight that the spacecraft are trapped within the hyperbolic tangle. This research therefore reports evidence of actual artificial satellites in the near-Earth environment whose dynamics are ruled by hyperbolic manifolds and resonant mechanisms. The tools, formalism and methodologies we present are exportable to other region of space subject to similar commensurabilities as the geosynchronous region.

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.

Tuning of NASA Standard Breakup Model for Fragmentation Events Modelling

The continuous growth of space debris motivates the development and the improvement of tools that support the monitoring of a more and more congested space environment. Satellite breakup models play a key role to predict and analyze orbital debris evolution, and the NASA Standard Breakup Model represents a widely used reference, with current activities relevant to its evolution and improvements especially towards fragmentation of small mass spacecraft. From an operational perspective, an important point for fragmentation modelling concerns the tuning of the breakup model to achieve consistency with orbital data of observed fragments. In this framework, this paper proposes an iterative approach to estimate the model inputs, and in particular, the parents’ masses involved in a collision event. The iterative logic exploits the knowledge of Two Line Elements (TLE) of the fragments at some time after the event to adjust the input parameters of the breakup model with the objective of obtaining the same number of real fragments within a certain tolerance. Atmospheric re-entry is accounted for. As a result, the breakup model outputs a set of fragments whose statistical distribution, in terms of number and size, is consistent with the catalogued ones. The iterative approach is demonstrated for two different scenarios (i.e., catastrophic collision and non-catastrophic collision) using numerical simulations. Then, it is also applied to a real collision event.

Space Debris Tracking with the Poisson Labeled Multi-Bernoulli Filter.

This paper presents a Bayesian filter based solution to the Space Object (SO) tracking problem using simulated optical telescopic observations. The presented solution utilizes the Probabilistic Admissible Region (PAR) approach, which is an orbital admissible region that adheres to the assumption of independence between newborn targets and surviving SOs. These SOs obey physical energy constraints in terms of orbital semi-major axis length and eccentricity within a range of orbits of interest. In this article, Low Earth Orbit (LEO) SOs are considered. The solution also adopts the Partially Uniform Birth (PUB) intensity, which generates uniformly distributed births in the sensor field of view. The measurement update then generates a particle SO distribution. In this work, a Poisson Labeled Multi-Bernoulli (PLMB) multi-target tracking filter is proposed, using the PUB intensity model for the multi-target birth density, and a PAR for the spatial density to determine the initial orbits of SOs. Experiments are demonstrated using simulated SO trajectories created from real Two-Line Element data, with simulated measurements from twelve telescopes located in observatories, which form part of the Falcon telescope network. Optimal Sub-Pattern Assignment (OSPA) and CLEAR MOT metrics demonstrate encouraging multi-SO tracking results even under very low numbers of observations per SO pass.

Recurrent neural network model to predict re-entry trajectories of uncontrolled space objects

This paper proposes a novel sequence-to-sequence recurrent neural network model to predict re-entry trajectories of uncontrolled space objects. The epoch and altitude information of the objects from two-line element data were interpolated to equally spaced data and were used as inputs to the model. More than 200 datasets from five different objects with already known re-entry times were used as the training set for the model. Test datasets being not used for training, were chosen to validate the model’s performance. To assess the performance, the model predictions were compared with the ground-truth data of the test objects and with predictions from the Inter-Agency Space Debris Coordination re-entry campaign, in which space agencies from various countries had participated. The results indicate that the proposed approach is highly suitable for re-entry prediction compared to classical dynamics-based approaches, despite the small quantity of training data.

Real‐Time Thermospheric Density Estimation via Radar and GPS Tracking Data Assimilation

AbstractAs the number of man‐made Earth‐orbiting objects increases, satellite operators need enhanced space traffic management capabilities to ensure safe space operations. For objects in Low Earth orbit, orbit determination and prediction require accurate estimates of the local thermospheric density. In previous work, the estimation of thermospheric densities using two‐line element data and a reduced‐order model for the upper atmosphere was demonstrated. In this study we demonstrate an approach for density estimation using radar and GPS tracking data. For this, we assimilate the tracking data in a dynamic reduced‐order density model using a Kalman filter by simultaneously estimating the orbits and global density. We used the radar range and range rate measurements of 20 objects and the GPS position measurements of 10 commercial satellites. The estimated density was validated against accurate SWARM density data and compared with NRLMSISE‐00, JB2008, and two‐line element (TLE)‐estimated densities. We found that the estimated densities are significantly more accurate than NRLMSISE‐00 and JB2008 densities. In particular, using the GPS data of 10 satellites, we obtain density estimates with a daily 1‐σ error of only 5% compared to 14% and 22% for empirical models and 10% for TLE‐estimated density. These accurate density estimates can be used to improve orbit determination and the use of real‐time tracking data would enable real‐time density estimation.

A nanosatellite task scheduling framework to improve mission value using fuzzy constraints

Task scheduling is an effective approach to increase the value of a satellite mission, which leads to improved resource management and quality of service. This work improves the energy prediction model and a task scheduling formulation, expressed in integer programming to maximize the number of tasks performed in nanosatellite missions. A realistic battery model is introduced in the formulation to extend battery lifetime. This is achieved by a disjunctive program that makes battery charge and discharge more efficient. Furthermore, fuzzy constraints are designed to limit the current rates (for charge and discharge) and the depth of discharge for battery lifetime preservation. Each battery access is penalized in the objective function, thereby stimulating energy consumption to match energy input. For simulation purposes, the varying power input was based on two-line element data of the CubeSat FloripaSat-I, operating in an orbit with J2 perturbation and an attitude that keeps one face of the nanosatellite towards the Earth for the entire orbit, similar to a remote sensing mission. The effectiveness of the task-scheduling methodology was shown by means of simulated experiments of representative scenarios. With the improvements proposed here, a robust and realistic framework for optimal offline scheduling of nanosatellite missions is achieved.

Atmospheric reentry hemisphere prediction for prograde orbits using logical disjunction

A unique logic-based algorithm for atmospheric reentry hemisphere prediction is presented for spacecraft in low-eccentricity, prograde low Earth orbits at altitudes of 300 km and lower. Using two-line element (TLE) data for initial orbit conditions, coupled with coarse estimates for spacecraft aerodynamic characteristics, the algorithm relies on logical disjunction operations based on a dual analysis of histogram and two-weighted Gaussian probability density function (PDF) fits of predicted reentry latitude data. The algorithm requires the execution of a series of parametric simulations to determine the reentry hemisphere for variations in spacecraft aerodynamic coefficients and drag reference area. When implemented, the algorithm yields accurate hemisphere predictions on average 15 days from reentry as demonstrated by historical reentry cases from 1979 to 2018. All reentry cases were selected to demonstrate the algorithm’s ability to deliver accurate reentry hemisphere predictions for spacecraft with varying physical size and mass, and reentering during different periods of solar cycle activity.