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

Shin, Bumjoon; Lee, Eunji; Park, Sang-Young

doi:10.5140/jass.2019.36.3.169

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

Journal of astronomy and space sciences, v.36 no.3, 2019년, pp.169 - 180

Shin, Bumjoon (Department of Astronomy, Yonsei University) , Lee, Eunji (Department of Astronomy, Yonsei University) , Park, Sang-Young (Department of Astronomy, Yonsei University)

Abstract ▼ AI-Helper

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.

주제어

표/그림 (21)

그림 Fig. 1. Flowchart of the batch least squares estimator.
표 Table 1. Simulation environment for verifcation of batch least squares algorithm
그림 Fig. 2. Position error of Monte Carlo simulation and covariance ellipsoid.
그림 Fig. 3. Correlation of orbit determination accuracy with respect to arc length with large noise.
표 Table 2. Simulation environments for all kinds of error analysis
그림 Fig. 4. Correlation of orbit determination accuracy with respect to noise level, with arc length of 7,200 and 72,000 seconds (log scale).
그림 Fig. 5. Correlation of orbit determination accuracy with respect to arc length with a fixed number of observation data points.
그림 Fig. 6. Correlation of orbit determination accuracy with respect to observation interval.
그림 Fig. 7. Correlation of OD accuracy with respect to a priori uncertainty for LEO and GEO satellites. OD, orbit determination; LEO, low earth orbit; GEO, geostationary orbits.
그림 Fig. 8. Positional accuracy without the a priori covariance matrix (upper) and with the matrix (lower).
그림 Fig. 9. Positional accuracy according to the a priori covariance matrix with fixed a priori error of 50 km and 50 m/s (upper: case 3-1) and 150 km and 150 m/s (lower: case 3-2) in position and velocity.
그림 Fig. 10. Positional accuracy according to the a priori error with fixed a priori covariance of 100 km and 100 m/s (upper: case 4-1) and 150 km and 150 m/s (lower: case 4-2) in position and velocity.
그림 Fig. 11. Correlation of orbit determination accuracy with respect to the measurement noise.
그림 Fig. 12. Orbit determination accuracy respect to the clock errors (case 5: clock offset, case 6: clock mismatch).
표 Table 3. Confguration of the OD for COMS using OWL-Net data
그림 Fig. 13. Overlap analysis for TLE of COMS by propagation. TLE, two-line elements; COMS, Communication, Ocean and Meteorological Satellite.
그림 Fig. 14. Measurement residuals evaluated by two-line elements (left: whole data, right: except irregular data).
그림 Fig. 15. Post-ft residuals of Communication, Ocean and Meteorological Satellite (left: 2-hour arc, right: 7-hour arc).
표 Table 4. Comparison of OD results to TLE in the form of topocentric RTN coordinates
표 Table 5. Comparison of OD results to TLE in the form of Keplerian elements
그림 Fig. 16. Position and velocity differences of OD results for COMS compared to TLE for 24 hours in topocentric RTN coordinates (left: 2-hour solution, right: 7-hour solution). OD, orbit determination; COMS, Communication, Ocean and Meteorological Satellite; TLE, two-line elements; RTN, radial-transversenormal.

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제안 방법

In this section, Monte Carlo simulation with varying noise levels was carried out to analyze the effects of observation noise on the OD accuracy. Note that the noise was set from 1 to 100 arcseconds, unlike the actual value of several arcseconds, for characteristics analysis.
In this study, we have developed and verified a batch least square estimator which utilizes optical observation data to determine the orbits of GEO objects. The characteristics of the observation error sources and OD results were analyzed by numerical simulations using pseudo-optical observation data.
In this study, orbit determination (OD) software employing a batch filter is developed to independently operate a space surveillance system. Moreover, this software generates pseudo-optical observation data to examine the effects of the arc length, observation intervals, clock errors, noise, and a priori uncertainty on the accuracy of the OD for a GEO satellite. It is significant that the optical observation data for a domestic geostationary satellite taken from OWL-Net is analyzed using the developed software.
The target orbital elements, dynamics model, and estimation options applied to the batch filter are indicated in Table 2. The OD accuracy was evaluated by comparing the estimated states to the reference states.
The accuracy of the OD for the GEO satellite was analyzed using various observation intervals, with the condition of a fixed arc length of 7,200 seconds and a noise level varying from 1 to 20 arcseconds. The accuracy of the OD tends to increase as the observation interval is shortened (Fig.

대상 데이터

The optical wide-field patrol network (OWL-Net) is the first Korean optical surveillance system of space objects, constructed to protect space assets by tracking and monitoring domestic satellites. The system was developed by the Korea Astronomy and Space Science Institute (KASI), and makes use of five observatories in Korea, Mongolia, Morocco, Israel, and the USA. Measurement data composed of topocentric right ascension and declination is extracted from the image pixel coordinates (Park et al.

데이터처리

The statistical validity of the algorithm can be verified by confirming the consistency between the covariance matrix and practical OD estimation results from a Monte Carlo simulation. The Monte Carlo simulation was conducted 1,000 times using a priori state error corresponding to the a priori covariance and pseudo-observations with Gaussian errors reflecting observation noise. The verification was conducted for GEO, similar to previous research where the same process was used for LEO (Lee et al.
In this study, we have developed and verified a batch least square estimator which utilizes optical observation data to determine the orbits of GEO objects. The characteristics of the observation error sources and OD results were analyzed by numerical simulations using pseudo-optical observation data. Furthermore, the developed batch filter was applied to OD for a GEO satellite, COMS, using real observation data from OWL-Net and the results were compared with TLE.
A covariance matrix calculated through a batch filter indicates the accuracy of the derived estimation results based on a system model and the observation quality. The statistical validity of the algorithm can be verified by confirming the consistency between the covariance matrix and practical OD estimation results from a Monte Carlo simulation. The Monte Carlo simulation was conducted 1,000 times using a priori state error corresponding to the a priori covariance and pseudo-observations with Gaussian errors reflecting observation noise.

이론/모형

Although sequential estimation is better suited to realtime monitoring compared to a batch-type estimator, the batch-type estimator is more accurate and robust (Crassidis & Junkins 2011). Considering the objective of this study, to obtain accurate orbit solution for long-time prediction, and the process of the optical tracking system where the measurement data is extracted from optical images after observations, the batch least squares method was employed in this work. The batch least squares is the simplest method of estimating epoch states using a set of observed data over a period.
In this study, the batch estimator was developed in the Matlab environment employing the General Mission Analysis Tool (GMAT) as the dynamics model. GMAT was developed and released for public use by NASA, and the force models and numerical integrator in the software have been verified and applied to practical mission analysis (Hughes et al.

성능/효과

9 exhibits the position error of case 3, which is within tens of kilometers with the covariance of under 100 km, even though the noise increases. A position error of larger than hundreds of kilometers was found when the covariance matrix implied 1,000 km in both sub-cases, and the dependence on the noise increased as the a priori error was increased. Fig.
The analytic results verified that the accuracy of the OD improves as the arc length is increased and the observation interval is shortened and that it is more efficient to adjust the arc length to get a more precise orbit solution. Also, it was confirmed that the a priori covariance prevents the scatter of the OD results for a GEO satellite from the a priori guess, even with low measurement quality. Regarding observation noise, the error in the OD was proportional to the level of noise and the derived values were consistent with the geometric estimation.
The observation residuals converged to a few arcseconds, which is close to the known value of the observation quality of OWL-Net. The OD accuracy was evaluated by comparison to TLE, which has an accuracy of several tens of kilometers, and the OD accuracy was found to be about 15 km and 1 km in the short and long arc cases, respectively.
The OD property analysis using pseudo-observation data was carried out in terms of arc length (number of observation data points), observation intervals, a priori uncertainty, measurement noise, and clock errors. The analytic results verified that the accuracy of the OD improves as the arc length is increased and the observation interval is shortened and that it is more efficient to adjust the arc length to get a more precise orbit solution. Also, it was confirmed that the a priori covariance prevents the scatter of the OD results for a GEO satellite from the a priori guess, even with low measurement quality.
Table 5 presents the differences between the OD results and TLE in the form of the orbital elements. The differences in the semi-major axis, eccentricity, and inclination decrease considerably as the arc length increases: the relative errors vary from 0.1% to 0.004% for the semi-major axis, more than 800% to 30% for the eccentricity, and from 27% to 0.2% for the inclination. The true longitude, which is typically applied in equatorial and circular orbits, however, had a relative error of under 0.
16 shows the differences in position and velocity in topocentric RTN coordinates. The prediction accuracy of the long arc solution was 20 times better than that of the short arc solution; the positional differences were hundreds of kilometers in the short arc cases and about 20 km in the long arc case for a day. Considering the field of view of OWL-Net, which is 1.
1 degrees at about four hours after the observations started. The residuals correspond to a position error of several kilometers, which coincides with the overlap analysis, and it is thus confirmed that TLE has several kilometers of position accuracy.
4. The result shows that the accuracy of the OD significantly improves as the arc length increases; when the arc length was 10 times longer, the accuracy of the position and velocity improved by a factor of 100 or higher. For example, the position error was 5 km when the level of noise was 5 arc-seconds and the arc length was 7,200 seconds, and that error became 20 m when the level of noise was same but arc length was increased to 72,000 seconds.
The results of the Monte Carlo simulation show that 99% of the OD estimation results fall within a 3σ error range estimated by the covariance ellipsoid.
Through these analyses, it is confirmed that the a priori covariance is significant in the OD for GEO, especially when the measurement quality is poor. Therefore, an appropriate a priori covariance matrix based on the actual reliability of the a priori state vector must be applied to obtain more accurate OD results.
Through this study, it was confirmed that appropriate observation weights based on the quality of observation data and an a priori covariance matrix based on the reliability of a priori states are important for obtaining more precise orbit solutions. The clock error which can be involved in the practical observation data from OWL-Net must be corrected.
Contrary to the previous analysis, the number of observation data points was maintained in the range of 1,700–1,790 by adjusting the observation interval as the arc length was varied. Using a consistent number of observations, the position errors were on the order of hundreds of kilometers and hundreds of meters for arc lengths of 250 and 10,000 seconds, respectively, and the velocity errors were 2.18 and 0.04 m/s for these are lengths (Fig. 5). This shows that the accuracy of OD tends to improve with increase in the observation arc length, which occurs because more dynamical information about the orbit is provided by a longer time of observation.

참고문헌 (13)

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상세보기
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