Two-line Element Research Articles

GSLP : A GNSS satellite visibility simulation tool

Global Navigation Satellite System (GNSS) currently consists of many global and regional satellite constellations developed by various countries. As a result of presence of multiple constellations, signals from nearly 100 GNSS satellites in space are available for use at any point of time. From any observation point, depending on the location of the point, thus many GNSS satellites would be visible. Prediction of GNSS satellite visibility and their trajectories is important requirement for mission planning. This paper describes a Matlab based utility, GNSS Satellite Look Angle Predictor (GSLP), developed for prediction of GNSS satellite look angles and simulation of trajectories from any point over any time span that takes care of the problems of using the existing tools. The utility uses NORAD Two Line Element (TLE) files as input and visually shows the results along with creating ASCII files those contain the information. The utility currently is usable for GPS, GLONASS, Galileo and NavIC/IRNSS. The concept is successfully implemented, and the results are being used for further research purposes. The utility may be useful for real-time mission planning and GNSS research.

Re-Evaluation Solution Methods for Kepler's Equation of an Elliptical Orbit

An evaluation was achieved by designing a matlab program to solve Kepler’s equation of an elliptical orbit for methods (Newton-Raphson, Danby, Halley and Mikkola). This involves calculating the Eccentric anomaly (E) from mean anomaly (M=0°-360°) for each step and for different values of eccentricities (e=0.1, 0.3, 0.5, 0.7 and 0.9). The results of E were demonstrated that Newton’s- Raphson Danby’s, Halley’s can be used for e between (0-1). Mikkola’s method can be used for e between (0-0.6).The term that added to Danby’s method to obtain the solution of Kepler’s equation is not influence too much on the value of E. The most appropriate initial Gauss value was also determined to be (En=M), this initial value gave a good result for (E) for these methods regardless the value of e to increasing the accuracy of E. After that the orbital elements converting into state vectors within one orbital period within time 50 second, the results demonstrated that all these four methods can be used in semi-circular orbit, but in case of elliptical orbit Danby’s and Halley’s method use only for e ≤ 0.7, Mikkola’s method for e ≤ 0.01 while Newton-Raphson uses for e < 1, which considers more applicable than others to use in semi-circular and elliptical orbit. The results gave a good agreement as compared with the state vectors of Cartosat-2B satellite that available on Two Line Element (TLE).

FIRST RESULTS OF CLARIFYING OF ORBITAL ELEMENTS OF LOW-ORBIT SPACECRAFT USING OBSERVATIONS OF THE RI "MAO" DOPPLER STATION

18 artificial satellites of the Earth, which emit radio signal at a frequency of 430-440 MHz during their flight in the Mykolaiv visibility zone, were found as a result of the searching carried out in the RI MAO. 10 of 18 satel- lites during not less than 7 days each were automatically tracked by the Doppler station created in the RI “MAO”. The frequency of received radio signal was automatically deter- mined as a result of spectral processing of radio signal ampli- tudes registered by the station during satellite tracking. Herewith 5 of 10 satellites emitted non-harmonic broadband signals. The radial velocity of satellites is calculated using the frequency of received radio signals. The obtained values of radial velocity changing in time were used to clarify TLE (Two-Line Element) orbital el- ements of satellites. Initial orbital elements were down- loaded from the space-track.org site. It would be noted that model values of Doppler shift of frequency, obtained using the initial orbital elements, also use for searching radio signals emitted by tracked satellites and received by the station. The regular (mean) and random (standard de- viation) components of the difference (O-C) of measured and model values of radial velocity were calculated. A comparison of the regular and random components of O-C was made, which showed their slight decreasing after clar- ifying orbital elements. In order to improve the accuracy of the orbit determination, it is proposed to upgrade the station's hardware and software in order to reduce synchronizing and frequency determination errors. It is also proposed to use more accurate models as Dop- pler measurements, and the motion of satellite

Study on the Orbit Prediction Errors of Space Objects Based on Historical TLE Data

Two line element (TLE) released by the North American Aerospace Defense Command (NORAD) is widely used by aerospace workers, and the matched SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4) model is used to propagate it. Nevertheless, no corresponding information about its accuracy and covariance is clearly given, thus the application of the TLE data is greatly restricted. In this paper, the determined and predicted orbits are compared to generate the orbit error data, based on the historical TLE data obtained from the Space-Track website and the SGP4/SDP4 model. By dividing different time bins, the fitting coefficients of the variation of orbit prediction error with time are given for each space object, and the characteristics of the error evolution are further discussed for the different types of orbits. The mean analytic model of the orbit prediction error evolution with time is given respectively for the four orbit types of space objects, which provides a valuable reference for extending the application of the TLE data.

Determination of Geostationary Orbits (GEO) Satellite Orbits Using Optical Wide-Field Patrol Network (OWL-Net) Data

In this study, a batch least square estimator that utilizes optical observation data is developed and utilized to determine geostationary orbits (GEO). Through numerical simulations, the effects of error sources, such as clock errors, measurement noise, and the a priori state error, are analyzed. The actual optical tracking data of a GEO satellite, the Communication, Ocean and Meteorological Satellite (COMS), provided by the optical wide-field patrol network (OWL-Net) is used with the developed batch filter for orbit determination. The accuracy of the determined orbit is evaluated by comparison with two-line elements (TLE) and confirmed as proper for the continuous monitoring of GEO objects. Also, the measurement residuals are converged to several arcseconds, corresponding to the OWL-Net performance. Based on these analyses, it is verified that the independent operation of electro-optic space surveillance systems is possible, and the ephemerides of space objects can be obtained.

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.

Machine Learning Approach to Improve Satellite Orbit Prediction Accuracy Using Publicly Available Data

Efficient and high precision orbit prediction is increasingly crucial for improved Space Situational Awareness. Due to the lack of the required information such as space environment conditions and characteristics of Resident Space Objects (RSOs), satellite collisions have happened, partially because that the solely physics-based approaches can fail to achieve the required accuracy for collision avoidance. With the hypothesis that a Machine Learning (ML) approach can learn the underlying pattern of the orbit prediction errors from historical data, in this paper, the Support Vector Machine (SVM) is explored for improving the orbit prediction accuracy. Two publicly available Two-Line Element (TLE) catalog and International Laser Ranging Service (ILRS) catalog are used to validate the proposed ML approach. The position and velocity components of 11 total RSOs maintained at both catalogs are studied. Results of the study demonstrate that the designed dataset structure and SVM model can improve the orbit prediction accuracy with good performance on most cases. The performance on RSOs belonging to different orbit types is analyzed using different sizes of training and testing data. Results of the paper demonstrate the potential of using the proposed ML approach to improve the accuracy of TLE catalog.

Investigation on GEO satellite orbit determination based on CEI measurements of short baselines

Connected-Element Interferometry (CEI) is a technique for measuring the phase delay of difference of Time Of Arrival (TOA) of a downlink radio signal to two antennae on a short baseline. This technique can use an atomic clock for time-frequency transmission and achieve intermediate accuracy angular tracking. Owing to the relatively short length of the baseline, the passive reception mode, and near real-time operation, CEI can be used to continuously monitor the orbit variations of both cooperative and non-cooperative satellites. In this paper, a small-scale CEI system of two orthogonal baselines (75 m × 35 m) is investigated to track a Geostationary Earth Orbit (GEO) Television (TV) satellite at 110·5°E. The phases are extracted from correlation results. The results show that the Root Mean Square (RMS) of the phase fitting residuals, if not calibrated, is within 2° at night and up to 10° in the daytime. After applying the calibration signal, the RMS of the phase fitting residuals in the daytime decreases to the same level at night. Comparing the phase delay with the a priori phase delay using Two-Line-Element (TLE) data, the integer ambiguity is successfully resolved. Finally, a batch algorithm is used to estimate the orbit of the GEO satellite, and the orbit determination accuracy is evaluated using the precise orbits provided by the China National Time Service Centre (NTSC). The results show that the accuracies in the radial direction and the cross-track direction are less than 1 km, and the Three-Dimensional (3D) position accuracy reaches the 2 km order of magnitude.

Space event detection method based on cluster analysis of satellite historical orbital data

A new method of detecting space events using satellite two-line element (TLE) histories is proposed. Anomalous data segments in the TLE-derived time series of a specific orbital element is detected to locate space events. After data preprocessing, a series of equal-length data segments are extracted from the time series and converted into a data form that is uniformly sampled in the time domain. Anomaly detection is achieved by clustering the data segments using a one-dimensional self-organizing map. After the clustering operation, the same type of data segments are grouped together and different types of data segments are divided into different groups. Thus, the type of space event and the associated orbital anomaly pattern can be obtained simultaneously. Space event detection results of typical active satellites show that the proposed method can accurately avoid false detections while maintaining a high detection rate. By comparing detection results of different clustering granularities, the ability to obtain detailed information of space events is also proved.

A numerical approach to the problem of angles-only initial relative orbit determination in low earth orbit

A practical and effective numerical method is presented, aiming at solving the problem of initial relative orbit determination using solely line-of-sight measurements. The proposed approach exploits the small discrepancies which can be observed between a linear and a more advanced relative motion model. The method consists in systematically performing a series of least-squares adjustments at varying intersatellite distances in the vicinity of a family of collinear solutions coming from the linear theory. The solution presenting the smallest fitting residuals is then selected. The investigations specifically focus on the rendezvous in low Earth near-circular orbit with a noncooperative target. The objective is to determine the relative state of the formation using only bearing observations when the spacecraft are separated by a few dozen kilometers without any a priori additional information. The method is validated with flight data coming from the ARGON (2012) and AVANTI (2016) experiments. Both cases demonstrate that an observation time span of a few maneuver-free orbits is enough to compute a solution which can compete with Two-Line Elements in terms of accuracy.

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.

Linear Model for Reentry Time Prediction of Spacecraft in Low-Eccentricity, Low Earth Orbits

A linear model and associated algorithm for the time prediction of uncontrolled atmospheric reentries is presented for spacecraft in low-eccentricity, near-circular low Earth orbits, specifically at altitudes of 300 km and lower. The primary objective of the present research was to develop a comparatively high-accuracy reentry time prediction algorithm by reducing the complexity of the dynamics model, spacecraft physical model, and the overall computation methodology. As opposed to contemporary higher-fidelity prediction methods, reentry trajectories within the presented model are propagated with reduced three-degree-of-freedom equations of motion. In addition to two-line element data for initial orbit conditions, a solar-cycle-independent pseudo-exponential atmospheric density model with variable inverse scale height is used, coupled with coarse estimates for spacecraft aerodynamic characteristics and shape. The algorithm requires the execution of a series of parametric simulations to determine the reentry time for variations in spacecraft aerodynamic coefficients and drag reference area. When implemented, the linear model yields a mean time prediction accuracy deviation of less than 8 h approximately 5 days before reentry as shown by analysis of the Tiangong-1 reentry, as well as 5 additional example reentry cases from 1979 to 2018. All cases were selected to demonstrate the algorithm’s ability to deliver accurate reentry time predictions for spacecraft with varying physical size and mass, and reentering during different periods of solar cycle activity.

Nowcast and forecast of galactic cosmic ray (GCR) and solar energetic particle (SEP) fluxes in magnetosphere and ionosphere – Extension of WASAVIES to Earth orbit

Real-time estimation of cosmic-ray fluxes on satellite orbits is one of the greatest challenges in space weather research. Therefore, we develop a system for nowcasting and forecasting the galactic cosmic ray (GCR) and solar energetic particle (SEP) fluxes at any location in the magnetosphere and ionosphere during ground-level enhancement (GLE) events. It is an extended version of the WArning System for AVIation Exposure to SEP (WASAVIES), which can determine event profiles by using real-time data of the count rates of several neutron monitors (NMs) at the ground level and high-energy proton fluxes observed by Geostationary Operational Environmental Satellites (GOES) satellites. The extended version, called WASAVIES-EO, can calculate the GCR and SEP fluxes outside a satellite based on its two-line element (TLE) data. Moreover, organ absorbed-dose and dose-equivalent rates of astronauts in the International Space Station (ISS) can be estimated using the system, considering its shielding effect. The accuracy of WASAVIES-EO was validated based on the dose rates measured in ISS, as well as based on high-energy proton fluxes observed by POES satellites during large GLEs that have occurred in the 21st century. Agreement between the nowcast and forecast dose rates in ISS, especially in terms of their temporal structures, indicates the usefulness of the developed system for future mission operations.

Mining Two-Line Element Data to Detect Orbital Maneuver for Satellite

Data clustering analysis is proposed to detect the orbital maneuvers of satellites at different scales. In this study, the unsupervised classification methods of K-means, hierarchical, and fuzzy C-means clustering are used to handle the two-line element (TLE) historical data. The K-means-based contour map method is applied to the characteristic variable selection and cluster number determination. The TLE data of large-, medium-, and small-scale orbital maneuvers are clustered by the aforementioned three methods. Through a series of numerical experiments, it is found that for different scales of orbital maneuvers, the clustering methods have different performances and that they can essentially fulfill the functional requirements of orbital detection. By data mining, the orbital maneuvers of the remote sensing satellites “YAOGAN-9”, “TIANHUI-1”, and “Envisat” can be easily detected, which will provide useful information for further orbital supervision and prediction.

AN OPEN SOURCE WEB-GIS BASED PRECISE SATELLITE TRACKING AND VISUALISATION TOOL USING TWO LINE ELEMENT DATA

Abstract. Accurate monitoring of satellites plays a pivotal role in analysing critical mission specific parameters for estimating orbital position uncertainties. An appropriate database management system (DBMS) at the software end, could prove its potential as a convenient solution over the existing file based two line element (TLE) data structure. The current web-based satellite tracking systems, such as n2yo, satview, and satflare, are unable to provide location-based satellite monitoring. Moreover, the users need to zoom into the displayed world map for obtaining information of the satellites that are currently over the respective area. Also, satellite searching is a cumbersome task in these web-based systems. In this research work, a systematic approach has been utilised to develop a generic open-source Web-GIS based tool for addressing the aforementioned issues. This tool incorporates a PostgreSQL database for storing the parsed TLE data which are freely available on the CelesTrak (NORAD) repository. Our choice of selecting PostgreSQL as a backend DB is primarily due to its open source and scalable properties compared to other resource intensive databases. Using suitable python libraries (e.g. Skyfield and Orbit-Predictor), the position and velocity at any point of time can be accurately estimated. For this purpose, the tool has been tested on several cities for displaying location-based satellite tracking that includes different types of space-objects.

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.

DOPPLER STATION FOR ORBITAL TRACKING OF LOW-ORBIT SPACECRAFTS BY THEIR RADIO BEACON SIGNALS

A ground station of orbital tracking of low-orbit spacecrafts has been developed and tested in the RI "Mykolaiv Astronomical Observatory". The station uses the Doppler shift of frequencies of signals radiated by spacecraft radio beacons for their orbital tracking. The station consists of: 1) 10-section antenna with a circular directional diagram and the operating frequency band 400-450 MHz, 2) electronic unit of connection of the antenna sections to a receiver, 3) the SDR-receiver used USB receiver of terrestrial digital TV and radio (“DVB-T+DAB+FM”), 4) personal computer. Software of the station includes the free program HDSDR for SDR-receiver control, as well as an antenna direction control program, a program for determining a frequency of a signal, emitted by satellite radio beacon and received by the station, and a program for clarifying elements of satellite's orbit using the measured values of the frequency.The NORAD ID of a satellite and a frequency of the signal emitted by its radio beacon should be set to clarify the satellite orbit. The antenna direction control program download current TLE (Two Line Elements) orbital elements of the satellite from the space-track.org site using the satellite’s ID. These elements are used by the program to calculate, as functions of time, the values of range, azimuth and elevation angle of the satellite relative to the station. The program determines then the moments of the connections of the necessary antenna sections to the receiver, and performs these connections in the automatic mode, which provides continuous tracking of the satellite during its passage in the zone of direct radio visibility of the station. Simultaneous recording of the received radio signal is performed by the HDSDR program in wav-files. The program of determining a frequency of satellite radio beacon signal analyzes the records and automatically detects the radio beacon signal and determines its frequency. The initial orbital elements obtained from the space-track site are clarified according to the measured values of the frequency using the program developed by V.A.Yamnitsky.The report presents the results of the station test, which include an estimation of internal errors of the orbital elements determining of tracked satellites.A network of stations similar to the one considered in the report could be used to orbital tracking of low-orbit spacecrafts equipped with radio beacons.

Physics and human-based information fusion for improved resident space object tracking

Maintaining a catalog of Resident Space Objects (RSOs) can be cast in a typical Bayesian multi-object estimation problem, where the various sources of uncertainty in the problem – the orbital mechanics, the kinematic states of the identified objects, the data sources, etc. – are modeled as random variables with associated probability distributions. In the context of Space Situational Awareness, however, the information available to a space analyst on many uncertain components is scarce, preventing their appropriate modeling with a random variable and thus their exploitation in a RSO tracking algorithm. A typical example are human-based data sources such as Two-Line Elements (TLEs), which are publicly available but lack any statistical description of their accuracy. In this paper, we propose the first exploitation of uncertain variables in a RSO tracking problem, allowing for a representation of the uncertain components reflecting the information available to the space analyst, however scarce, and nothing more. In particular, we show that a human-based data source and a physics-based data source can be embedded in a unified and rigorous Bayesian estimator in order to track a RSO. We illustrate this concept on a scenario where real TLEs queried from the U.S. Strategic Command are fused with realistically simulated radar observations in order to track a Low-Earth Orbit satellite.

Historical-orbital-data-based method for monitoring the operational status of satellites in low Earth orbit

A method is developed for monitoring the operational status of satellites in low Earth orbit (LEO) based on their historical two-line element (TLE) data. In this method, whether the satellite still has the maneuverability to maintain the orbital altitude is used as the criteria for judging the operational status, the whole judgment process includes two steps. The first step is to design a specialized algorithm to detect orbit maintenance maneuvers from the satellite's TLE time-history. The algorithm uses abnormal data segments of the TLE derived semi-major axis time series to identify the orbit maintenance maneuver, and various measures are taken to eliminate the noise interference and to ensure the detection accuracy. The second step is to use the detected maneuvering history to determine the current operational status of the satellite. In this step, the statistical technique is used to get the temporal regularity of the satellite to implement orbit maintenance maneuvers and the allowable range of the natural variation of the semi-major axis, so then the criteria for determining the satellite operational status is developed. Analysis of typical LEO satellites indicates that this method can accurately determine the current operational status of the satellite and provide an approximate estimation interval of the satellite retiring time, which is of practical value.

Diagnosing low earth orbit satellite anomalies using NOAA-15 electron data associated with geomagnetic perturbations

A satellite placed in space is constantly affected by the space environment, resulting in various impacts from temporary faults to permanent failures depending on factors such as satellite orbit, solar and geomagnetic activities, satellite local time, and satellite construction material. Anomaly events commonly occur during periods of high geomagnetic activity that also trigger plasma variation in the low Earth orbit (LEO) environment. In this study, we diagnosed anomalies in LEO satellites using electron data from the Medium Energy Proton and Electron Detector onboard the National Oceanic and Atmospheric Administration (NOAA)-15 satellite. In addition, we analyzed the fluctuation of electron flux in association with geomagnetic disturbances 3 days before and after the anomaly day. We selected 20 LEO anomaly cases registered in the Satellite News Digest database for the years 2000–2008. Satellite local time, an important parameter for anomaly diagnosis, was determined using propagated two-line element data in the SGP4 simplified general perturbation model to calculate the longitude of the ascending node of the satellite through the position and velocity vectors. The results showed that the majority of LEO satellite anomalies are linked to low-energy electron fluxes of 30–100 keV and magnetic perturbations that had a higher correlation coefficient (~ 90%) on the day of the anomaly. The mean local time calculation for the anomaly day with respect to the nighttime migration of energetic electrons revealed that the majority of anomalies (65%) occurred on the night side of Earth during the dusk-to-dawn sector of magnetic local time.