sensors Article
Optical Tracking Data Validation and Orbit Estimation for Sparse Observations of Satellites by the OWL-Net Jin Choi 1,2 ID , Jung Hyun Jo 1,2, * and Jang-Hyun Park 1 1
2
*
ID
, Hong-Suh Yim 1 , Eun-Jung Choi 1 , Sungki Cho 1
Center for Space Situational Awareness, Korea Astronomy and Space Science Institute, 776, Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Korea;
[email protected] (J.C.);
[email protected] (H.-S.Y.);
[email protected] (E.-J.C.);
[email protected] (S.C.);
[email protected] (J.-H.P.) Astronomy and Space Science Department, University of Science and Technology, 217, Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea Correspondence:
[email protected]; Tel.: +82-42-865-3238
Received: 1 May 2018; Accepted: 5 June 2018; Published: 7 June 2018
Abstract: An Optical Wide-field patroL-Network (OWL-Net) has been developed for maintaining Korean low Earth orbit (LEO) satellites’ orbital ephemeris. The OWL-Net consists of five optical tracking stations. Brightness signals of reflected sunlight of the targets were detected by a charged coupled device (CCD). A chopper system was adopted for fast astrometric data sampling, maximum 50 Hz, within a short observation time. The astrometric accuracy of the optical observation data was validated with precise orbital ephemeris such as Consolidated Prediction File (CPF) data and precise orbit determination result with onboard Global Positioning System (GPS) data from the target satellite. In the optical observation simulation of the OWL-Net for 2017, an average observation span for a single arc of 11 LEO observation targets was about 5 min, while an average optical observation separation time was 5 h. We estimated the position and velocity with an atmospheric drag coefficient of LEO observation targets using a sequential-batch orbit estimation technique after multi-arc batch orbit estimation. Post-fit residuals for the multi-arc batch orbit estimation and sequential-batch orbit estimation were analyzed for the optical measurements and reference orbit (CPF and GPS data). The post-fit residuals with reference show few tens-of-meters errors for in-track direction for multi-arc batch and sequential-batch orbit estimation results. Keywords: CCD; optical telescope; OWL-Net; short-arc; sparse data; orbit estimation
1. Introduction Space Situational Awareness (SSA) aims at detecting and predicting hazardous events by man-made and natural objects through ground-based or space-based sensors [1]. The United States operates the Space Surveillance Network (SSN), which consists of ground-based optical and radar sensors as well as space-based visible satellites [2]. Since 2008, the European Space Agency (ESA) has also implemented an SSA program for Space Surveillance and Tracking, Space Weather, and Near-Earth Objects. The already existing and available national sensors in Europe will be integrated together with newly developed elements [3]. The number of registered unclassified space objects exceeded 19,000 on 16 April 2018 [4]. The Korea Astronomy and Space Science Institute (KASI) has been developing an Optical Wide-field patroL-Network (OWL-Net) as part of the SSA facility of South Korea since 2010. The OWL-Net consists of five optical tracking sensors installed in Mongolia, Morocco, Israel, United States, and South Korea [5]. This global network of telescopes operates as a fully automatic sensor. Sensors 2018, 18, 1868; doi:10.3390/s18061868
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Maintaining orbital ephemeris of 11 South Korean low Earth orbit (LEO) satellites is the top priority goal of the OWL-Net. A key feature of the OWL-Net is a chopper system designed to obtain dense astrometric measurements from single images from a charge-coupled device (CCD) sensor. The chopper rotates to cut a long trail into tens of small ones during the exposure time of the CCD sensor. We could obtain hundreds of astrometric measurements from a few images during a single optical observation chance at an OWL-Net site. The detailed specifications of the OWL-Net are described in the next section. Optical observation data are short and sparse. This means that the observation time interval is much longer than the observation duration, while the observation duration lasts only a few minutes in a single-arc orbit of a satellite. Unlike other ground-based sensors, the optical sensor operates in a passive way to detect reflected sunlight during night time. Therefore, the possible observation times for optical tracking is limited to dawn and dusk for LEO satellites. These short-arc, sparse data can result in unstable solutions of orbit estimation [6]. Instead of a precise orbit estimation process, the short-arc, sparse data can be used to find initial orbit with uncorrelated targets [7]. Kim et al. [8] have described that unscented transformation and a particle filter can be suggested to solve the sparse data problem. An atmospheric drag coefficient estimation with a varying time span was an alternative solution to this problem [9,10]. However, the short-arc orbit determination strategy has been suggested as a more advantageous way for orbit determination and prediction in practical experiments [11]. The short-arc orbit determination study was conducted not only using the single laser tracking sensor but also using the optical tracking sensor [12]. Only two short-arc observation data were used for 2 or 3 days to support subsequent follow-up observations over a few days in Sang and Bennett’s study [12]. In the case of the OWL-Net, the orbit determination process was designed to run on a weekly basis. Genova et al. [13] suggested another estimation strategy for the planetary mission spacecraft BepiColombo on the ESA mission to Mercury. The batch-sequential method was considered for the sequential updating of unmodeled dynamic parameters on behalf of the classic multi-arc method. Besides, improved dynamic parameters resulted in better estimates of the “global parameter”, such as the gravitational coefficient during next step multi-arc estimation. In the case of orbit estimation for LEO satellites with the OWL-Net, basically pre-defined dynamic models are used to estimate only state vectors (position and velocity) of target satellites. In some cases, atmospheric drag models do not fit well with actual in situ due to irregular solar activity. However, orbit determination with a short arc was unstable due to a priori uncertainty [14,15]. Therefore, we suggested a sequential-batch estimation strategy with short-arc, sparse optical observation data from the OWL-Net. The atmospheric drag coefficient was estimated sequentially a priori from the result of the multi-arc batch estimation. The sequential-batch estimation strategy and orbit determination results are described in Section 4. In Section 2, we briefly describe the accuracy of the astrometric measurement from the optical observations of the OWL-Net. The astrometric measurements were compared with outer orbital ephemeris, Consolidated Prediction Format (CPF), and Precise Orbit Determination (POD) with onboard Global Positioning System (GPS) data. In the next section, the short-arc, sparse problem is analyzed for the OWL-Net using simulation data. Then, the sequential-batch estimation strategy is described with orbit determination using the actual astrometric data from the OWL-Net. 2. Astrometric Accuracy of the Optical Tracking Data for the OWL-Net The OWL-Net is a fully automatic optical observation system. The OWL-Net consists of a headquarters and an on-site system. The Head-Quarter (HQ) system is responsible for sending daily schedules and processing orbital information maintenance. The Site Operation System (SOS) in each station operates individual optical tracking systems by a given observation schedule [16]. The optical tracking sensor consists of a 0.5-m telescope with 1.1-degree × 1.1-degree field of view. The pointing accuracy of the mount system is less than 10 arc seconds with a maximum speed of 2 degrees/s2 . The back-end system of the OWL-Net consists of five parts. The imaging sensor is a PL16803 camera model by Finger Lakes Instrumentation LLC (FLI, Lima, NY, USA), which is
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a 4096 × 4096 back-illuminated CCD. The de-rotator compensates for the motion of the alt-az type mount. Blue-Visible-Red-Infrared-Clear (B-V-R-I-C) optical filters are used for photometric observation. Sensors 2018, 18, x of 20 The fourth part is a chopper wheel. The time-tagger system records the opening/closing3time by the rotationBlue-Visible-Red-Infrared-Clear of the chopper wheel [16,17]. A mechanical shutter also exists between the surface of the (B-V-R-I-C) optical filters are used for photometric observation. The CCD and thefourth chopper wheel. part is a chopper wheel. The time-tagger system records the opening/closing time by the the chopper wheel [16,17]. A mechanical also existsthe between thesystem surface points of the to the In rotation the LEOofsatellite optical observation mode of shutter the OWL-Net, mount CCD and the stars chopper wheel.the shutter exposure time (i.e., sidereal tracking). The LEO satellite same background during In the LEO satellite optical observation mode of the OWL-Net, the mount system points to the moves in a direction and speed against the stars on the celestial sphere. Reflected light from LEO same background stars during the shutter exposure time (i.e., sidereal tracking). The LEO satellite satellites creates trailsand on speed the surface CCD sensor. Thesphere. chopper wheellight makes moves in along direction againstof thethe stars on the celestial Reflected fromseveral LEO trails from a single image by chopping the original long trail. The maximum speed of the chopper satellites creates long trails on the surface of the CCD sensor. The chopper wheel makes several trails wheel from imageof bythe chopping the original longbe trail. The maximum speedindividual of the chopper wheel is more is 50 Hz, anda single the speed chopper wheel can reduced to identify small trails 50 Hz, and the speed of the chopper wheel image can be reduced to identify individual trails more easily. Figure 1 shows an optical observation of the CRYOSAT 2 satellitesmall acquired at the Israel easily. 1 shows observation image of the CRYOSAT 2 satellite at the Israel speed. station of theFigure OWL-Net onan1 optical June 2016. The chopper wheel accelerates to aacquired constant rotation station of the OWL-Net on 1 June 2016. The chopper wheel accelerates to a constant rotation speed. Therefore, earlier recorded trails are longer than later ones. Therefore, earlier recorded trails are longer than later ones.
Figure. 1. Optical observation image of CRYOSAT 2 on 1 June 2016 at the Israel site of the Optical
Figure 1. Optical observation image of CRYOSAT 2 on 1 June 2016 at the Israel site of the Optical Wide-field patroL-Network (OWL-Net). CRYOSAT 2 observed on sidereal tracking at the maximum Wide-field patroL-Network (OWL-Net). 2 observed on sidereal tracking at the maximum chopper speed. The longer trails are theCRYOSAT start of the observation. chopper speed. The longer trails are the start of the observation. The final measurements of the OWL-Net were topo-centric right ascension and declination [17]. The position of each trail was transformed to astrometric positions from physical coordinates on the The final measurements of the OWL-Net were topo-centric right ascension and declination [17]. surface of the CCD by using the corrected angular coordinates of stars in the same image. The World The position of each trail (WCS) was transformed to astrometric from physical coordinates on the Coordinates System solution tool was used with thepositions General Star Catalogue (GSC) 1.2 [18]. surface of the CCD using the corrected coordinates stars in recorded the sametime image. The World After the by coordinate correction, theangular angular position of theoftrails and set were matched by the(WCS) rate of change of each Thisthe was done in Star consideration of the physical Coordinates System solution tool measurement. was used with General Catalogue (GSC) 1.2 [18]. acceleration motion ofcorrection, the chopperthe wheel. However, someoferrors occurred this process After the coordinate angular position the trails andduring recorded time set were because of false detection or software problems [19]. The errors could make problems for the matched by the rate of change of each measurement. This was done in consideration of the physical matching of time and metric data. In that case, the erroneous matching affects the accuracy and acceleration motion the estimation. chopper wheel. However, errorsusing occurred during this process precision of theoforbit We also calibrated some these errors the rate of angular rate afterbecause of false normal detection software problems The errors could forobservation the matching of data or processing. Figure 2 shows[19]. the angular rate (pixels permake second)problems of the optical formetric CRYOSAT 2 using thecase, OWL-Net in Israel. The elevation angle of the CRYOSAT 2 from ground of the time and data. In that the erroneous matching affects accuracy andthe precision was also shown understand the geometric condition the optical As the elevation orbit estimation. We to also calibrated these errors usingofthe rate ofobservation. angular rate after normal data angle was increased, the angular rates were also increased. However, the angular rates for each small processing. Figure 2 shows the angular rate (pixels per second) of the optical observation for CRYOSAT
2 using the OWL-Net in Israel. The elevation angle of CRYOSAT 2 from the ground was also shown to understand the geometric condition of the optical observation. As the elevation angle was increased,
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the angular rates were also increased. However, the angular rates for each small trail in a single trail a single shot werewithin maintained small fluctuations. thatof the rate of the angular shotinwere maintained smallwithin fluctuations. This meansThis thatmeans the rate the angular rates is rates is almost consistent in the single shot. The whole optical observation dataset in this study was almost consistent in the single shot. The whole optical observation dataset in this study was manually manually again. confirmedconfirmed again.
Figure 2. 2.Angular Angularrate rate(pixels/second) (pixels/second)and andpointing pointingelevation elevation(degree) (degree)for for11 11shots shotsin inone oneobservation observation Figure set for CRYOSAT 2. The observation was performed at the OWL-Net in Israel. The angular rates set for CRYOSAT 2. The observation was performed at the OWL-Net in Israel. The angular rates in in a a single shot had similar values. The angular rates are proportional with the elevation angle of the single shot had similar values. The angular rates are proportional with the elevation angle of the satellite from from the the ground. ground. satellite
The errors errors of of the the matching matching of of time time and andmetric metricdata dataresulted resulted irregular irregular errors errors in in the the position position of of the the The satellite or or the the time time slip slip in in the optical measurements. measurements. In In the the case case of of orbit orbit estimation estimation with with multi-arc multi-arc satellite observation, the the errors errors result result in in bigger bigger precision precision errors errors of the estimated orbit. However, However, the the orbit orbit observation, estimator diverged diverged from from the the short-arc short-arc optical optical observation observation without without the the calibration calibration of of the the matching matching of of estimator time and metric data. Furthermore, time slip error growth occurred in the in-track direction error time and metric data. Furthermore, time slip error growth occurred in the in-track direction error of of the estimated orbit. The estimated parameters suchasasposition, position,velocity, velocity,and and atmospheric atmospheric drag drag the estimated orbit. The estimated parameters such coefficient had had bigger bigger errors errors compared compared with with the the results results of of precise precise orbit orbit estimation estimation using using SLR SLR (Satellite (Satellite coefficient Laser Ranging) Ranging) or or GPS GPS data. data. Laser We conducted conducted calibration calibration and and validation validation processes processes for for the the optical optical observation observation of of LEO LEO satellites satellites We during the the development development and and test test phase phase of of the the OWL-Net. OWL-Net. The Thetarget targetLEO LEOsatellites satelliteswere wereCRYOSAT CRYOSAT 22 during and KOMPSAT KOMPSAT 5. 5. CRYOSAT CRYOSAT 22 was was developed developed for for monitoring monitoring changes changes in in the the thickness thickness of of the the ice ice on on and the Earth. Earth. The Theaverage averagealtitude altitudeof ofCRYOSAT CRYOSAT22isisabout about720 720km kmwith with88 88degrees degreesof oforbital orbitalinclination. inclination. the CRYOSAT 22 was a good validation validation target with enough enough brightness brightness and and observation observation chances chances for for the the CRYOSAT OWL-Net with with aa non-Sun-synchronous non-Sun-synchronous orbit. orbit. KOMPSAT KOMPSAT 55 was was selected selected as as aa validation validation observation observation OWL-Net target among among Korean Korean LEO LEO satellites. satellites. ItItisisoperational operationalon onaaSun-Synchronous Sun-SynchronousOrbit Orbit(SSO). (SSO).KOMPSAT KOMPSAT target was bright bright enough enough to detect using the telescope of the OWL-Net. Detailed Detailed orbital orbital and and physical physical 55 was characteristics of of the the two two LEO LEO satellites satellites are are described in Table 1. characteristics Table 1. Orbital and physical characteristics of low Earth orbit (LEO) targets. Table 1. Orbital and physical characteristics of low Earth orbit (LEO) targets.
Name Name
NORADID ID NORAD
CRYOSAT 22 CRYOSAT
36508 36508
KOMPSAT 5
KOMPSAT 5
39227
39227
OrbitalInformation Information Orbital
altitude: altitude:720 720km km inclination:88 88degrees degrees inclination: non-Sun-synchronous non-Sun-synchronous altitude: 550 km altitude: 550 km inclination: 97.6 degrees inclination: 97.6 degrees Sun-synchronous Sun-synchronous
Launch Mass Launch Mass
Size Size
720 kg 720 kg
4.6 m m× 2.3 m m 4.6 × 2.3
1400 kg
3.7 m × 2.6 m 3.7 m × 2.6 m
1400 kg
We selected two sets of observation data for two separate weeks for CRYOSAT 2 and KOMPSAT We selected two sets of observation data for two separate weeks for CRYOSAT 2 and KOMPSAT 5. Table 2 shows the summary of the successful optical observation for CRYOSAT 2 and KOMPSAT 5. Table 2 shows the summary of the successful optical observation for CRYOSAT 2 and KOMPSAT 5. We obtained observations in Israel, the United States, and Korea. Due to weather conditions and 5. We obtained observations in Israel, the United States, and Korea. Due to weather conditions and system maintenance, the Mongolia and Morocco stations were not used. The observation duration system maintenance, the Mongolia and Morocco stations were not used. The observation duration indicates the time between the first and last observation point of each observation chance. The average indicates the time between the first and last observation point of each observation chance. The observation duration was 2.4 min. The observation duration and number of shots counted were for average observation duration was 2.4 min. The observation duration and number of shots counted were for successful observations only. The total numbers of observation points for CRYOSAT 2 were 1929 and 1041 for weeks 1 and 2, respectively. In the case of KOMPSAT 5, the total numbers of
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successful observations only. The total numbers of observation points for CRYOSAT 2 were 1929 and 1041 for weeks 1 and 2, respectively. In the case of KOMPSAT 5, the total numbers of observation points were 1058 and 1255 for weeks 1 and 2. The falsely detected points were neglected and some observation points were not detected due to brightness or unknown reasons. Figure 3 shows the three-dimensional (3D) orbit of CRYOSAT 2 and KOMPSAT 5 when the optical observations were performed. In the case of the week 1 observation of CRYOSAT 2, the optical observation was performed at a single station in Israel. The CRYOSAT 2 and KOMPSAT 5 optical observation data from the OWL-Net were compared with CPF and POD with onboard GPS data, respectively, taking the maneuvers into account. During the selected observation span, we confirmed that there were no maneuvers for CRYOSAT 2 and KOMPSAT 5. CRYOSAT 2 is one of the satellite laser ranging (SLR) observation target satellites. In the case of the SLR satellites, satellite predictions for laser tracking were provided in a CPF file via the International Laser Ranging Service (ILRS) webpage [20]. Generally, the accuracy of a CPF is a few tens of meters, which is more accurate than public Two Line Elements (TLEs) [21]. KOMPSAT 5 has a dual-frequency IGOR GPS receiver which is carried to obtain accurate positioning for synthetic aperture radar (SAR) missions [22]. The accuracy of the GPS receiver is within a few centimeters. In the case of the CPF file, it included a 7-day prediction and was provided on a daily schedule. It indicated that a single CPF file could be used as a comparison file for 7 days of observation. However, we used the first day prediction only for each CPF file. It was concerned with the accuracy of prediction for the CPF file. The difference between the CPF file on other days had grown over time. We used 2-day prediction data from a single CPF file as a comparison when there was no CPF file for that day. Table 2. Summary of optical observation results for validating astrometric angular accuracy. The week number was used to separate the observation data by week for orbit determination. The observation duration and number of shots were counted for the successfully achieved optical observations. Satellite
Week Number
Site
Date (yyyy-mm-dd)
Observation Duration (minute)
Number of Shot
Number of Point
1
Israel Israel Israel Israel Israel
2016-06-01 2016-06-02 2016-06-03 2016-06-05 2016-06-06
0.9 1.0 1.1 1.1 1.0
5 3 5 4 4
355 346 429 385 409
2
Korea Israel USA Israel USA
2017-08-26 2017-08-27 2017-08-28 2017-08-30 2017-09-02
1.6 3.2 0.8 4.1 4.5
5 3 3 11 4
146 81 106 516 192
1
Korea USA USA USA Israel USA Israel
2017-11-09 2017-11-10 2017-11-10 2017-11-11 2017-11-11 2017-11-13 2017-11-15
0.5 6.1 0.05 4.5 3.2 4.4 5.1
2 5 1 13 5 7 6
70 201 43 323 96 157 168
2
Korea USA USA Israel USA Israel Israel Korea Israel
2017-12-06 2017-12-08 2017-12-08 2017-12-08 2017-12-09 2017-12-09 2017-12-12 2017-12-12 2017-12-12
0.9 4.6 0.05 5.5 1.0 0.8 0.04 0.8 5.6
3 9 1 9 4 3 1 2 10
127 237 41 263 163 77 36 58 253
CRYOSAT 2
KOMPSAT 5
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Figure 3. The three-dimensional and KOMPSAT KOMPSAT55when whenthe theoptical optical Figure 2. The three-dimensional(3D) (3D) orbit orbit of of CRYOSAT CRYOSAT 22 and observations were performed by the OWL-Net. In Earth-Centered Fixed frame, the positions observations were performed by the OWL-Net. In Earth-Centered Fixed frame, the positions of theof the OWL-Net are marked marked with with the thenames namesof ofthe thecountries countriesininwhich whichthey theywere wereinstalled. installed. The OWL-Net stations stations are The 3D3D orbitorbit of CRYOSAT 2 and KOMPSAT 5 are presented of CRYOSAT 2 and KOMPSAT 5 are presentedasascolored coloredarcs. arcs.
POD onboard position information of the KOMPSAT 5 was provided using POD withwith onboard GPSGPS datadata position information of the KOMPSAT 5 was provided using thethe SP3 SP3 format. This information was not prediction data but in situ measurements. However, some data format. This information was not prediction data but in situ measurements. However, some data were were lacking for both of the observation weeks for KOMPSAT 5 with the OWL-Net. The second lacking for both of the observation weeks for KOMPSAT 5 with the OWL-Net. The second observation observation time for week 1 for KOMPSAT 5 lacked the POD with onboard GPS data. Therefore, we time for week 1 for KOMPSAT 5 lacked the POD with onboard GPS data. Therefore, we could not could not make the comparison for the second observation data of week 1 for KOMPSAT 5. make theThe comparison for the second observation data of week 1 for KOMPSAT 5. ephemeris data was converted into identical frames as the optical observation data in The ephemeris data was observation converted into identical frames as the optical observation consideration of the optical models. The CPF and onboard POD with GPS data data were in consideration of the optical observation models. The CPF and onboard POD with GPS data were provided as a rectangular coordinates forms in Earth-Centered Fixed. Therefore, we converted CPF provided as awith rectangular coordinates forms in Earth-Centered Fixed. we converted and POD onboard GPS data to topo-centric angular coordinates in anTherefore, Earth-Centered Inertial CPFcoordinate and PODframe with at onboard GPS the data to topo-centric angular an Earth-Centered J2000.0 with location information of eachcoordinates site for each in observation set. The Inertial coordinate frame at also J2000.0 with theThe location information each site for optical each observation observation models were considered. light travel time fromofsatellite to the telescope Themodels annual were aberration effects were also [23]. Equations (1) and to (2)the describe set. was The corrected. observation also considered. The corrected light travel time from satellite optical light travel time and annual aberration effect,effects respectively [24]. corrected In Equation (2),Equations α is the true right(2) telescope was corrected. The annual aberration were also [23]. (1) and ascension, ́ is the observed right ascension, δ is the true declination, is the observed declination, describe light travel time and annual aberration effect, respectively [24]. In Equation (2), α is the true is the trueα´ obliquity of date,right and ascension, is the geocentric longitude of the Sun in the ecliptic declination, plane. right ascension, is the observed δ is the true declination, δ´ is the observed
ε T is the true obliquity of date, and ω is the geocentric longitude of the Sun in the range from satellite to optical telescope R ecliptic plane. light travel time t =
light travel time (t) =
speed of light c
range from satellite to optical telescope (R) speed of light(c)
(1)
(1)
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α = ́
20.5 cos ́ cos
cos
+ sin ́ sin
(2) 20.5(cos α´ cos ω cos cos ε T + sin α´ sin ω ) α = α´ − tan cos cos sin δ = 20.5 cos cos δ´ ́ sin + cos ́ sin sin (2) ´ ´ ´ ´ δ = δ − 20.5 cos ω cos ωT tan ε T cos δ − sin α´ sin δ + cos α´ sin δ sin ω The residual observation-calculated (O-C) difference is shown in the time sequence in Figure 4. The residual observation-calculated (O-C) difference is shown in the time sequence in Figure 4. For CRYOSAT 2, the upper graph in Figure 4 is the residual between the observation and the For CRYOSAT 2, the upper graph in Figure 4 is the residual between the observation and the comparison from the observation on 1 June 2016. The optical observation was performed for five comparison from the observation on 1 June 2016. The optical observation was performed for five shots shots in one observation chance. We obtained tens of optical observation points from each shot. There in one observation chance. We obtained tens of optical observation points from each shot. There were were irregular patterns in each single shot. The pattern was caused by temporal shaking of the mount irregular patterns in each single shot. The pattern was caused by temporal shaking of the mount by by wind or photometric error. The upper graph is for first date results in the lower graph. The lower wind or photometric error. The upper graph is for first date results in the lower graph. The lower graph shows the residual for the first week for CRYOSAT 2 in Table 2. In this week, we obtained five graph shows the residual for the first week for CRYOSAT 2 in Table 2. In this week, we obtained five optical observation chances at the Israel site. The widths of difference were changed from 10 to 25 arc optical observation chances at the Israel site. The widths of difference were changed from 10 to 25 arc seconds, caused by the weather conditions and time-synchronization accuracy. seconds, caused by the weather conditions and time-synchronization accuracy.
Figure4.3.Residual Residualobservation-calculated observation-calculated (O-C) (O-C) difference between the Figure the optical optical observation observationdata datafrom from theOWL-Net OWL-Netand andcomparison comparison Consolidated Prediction File (CPF) data CRYOSAT 1 June the Consolidated Prediction File (CPF) data for for CRYOSAT 2 on21on June 2016. 2016. The observation was performed by the OWL-Net at the Israel site. The upper graph shows the The observation was performed by the OWL-Net at the Israel site. The upper graph shows the residual residual 1 June 2016. was one optical observation chance with five lower graph for 1 June for 2016. There wasThere one optical observation chance with five shots. Theshots. lowerThe graph shows the shows the residual 2016 to 6for June 2016 for CRYOSAT 2. residual from 1 Junefrom 2016 1toJune 6 June 2016 CRYOSAT 2.
Figure55shows showsthe theO-C O-Cdifference difference for for the rest of the three Figure three optical opticalobservation observationsets setsfor forCRYOSAT CRYOSAT 2 and KOMPSAT 5. The first graph is for the result of the observation in week 2 for CRYOSAT 2. The2. 2 and KOMPSAT The first graph is for the result of the observation in week 2 for CRYOSAT width of the differences is similar to the result for week 1 in 1Figure 4. However, the widths of the The width of the differences is similar to the result for week in Figure 4. However, the widths of differences forfor KOMPSAT 5 in thethesecond the differences KOMPSAT 5 in secondand andthird thirdgraph graphare arebigger biggerthan thanthe thedifferences differencesfor for CRYOSAT2.2.The Theoptical opticalobservation observationerrors errors were were caused caused by by the the seeing CRYOSAT seeing condition condition for forthe theweather weatherand and time-synchronization accuracy. In particular, the optical tracking system measured two-dimensional time-synchronization accuracy. In particular, the optical tracking system measured two-dimensional
metric data on the celestial field. Therefore, the optical observation errors were increased with the satellite on a lower altitude.
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metric data on the celestial field. Therefore, the optical observation errors were increased with the 8 of 21 altitude.
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4. Residual O-C difference between the optical observation data from the OWL-Net and the Figure 5. comparison CPF data for CRYOSAT CRYOSAT 22 in in August August 2017 2017 for for the first first graph. The second and third graphs show the difference between the optical observation data from the OWL-Net and onboard Global Positioning System (GPS) data. The The optical optical observation observation data data for for KOMPSAT 5 was performed in November 2017, respectively. TheThe maximum difference for KOMPSAT 5 was bigger November 2017 2017and andDecember December 2017, respectively. maximum difference for KOMPSAT 5 was than the result CRYOSAT 2. bigger than thefor result for CRYOSAT 2.
Statistical analysis of the O-C difference comparison was performed for two LEO satellites, CRYOSAT 2 and and KOMPSAT KOMPSAT 5,5,with withthe theoptical opticalobservation observation data 2 weeks. In Figure 6, left the box left data forfor 2 weeks. In Figure 6, the box whisker plot comparison is andifference O-C difference analysis for CRYOSAT 2 and theimage right shows image and and whisker plot comparison is an O-C analysis for CRYOSAT 2 and the right shows thefor same for KOMPSAT 5. For box and plot, whisker plot, the “x” the mean the same KOMPSAT 5. For each boxeach and whisker the “x” locates thelocates mean value. The value. mean The mean differences for right ascension for CRYOSAT wereand −0.41 andarc −0.16 arc seconds, while the differences for right ascension for CRYOSAT 2 were 2−0.41 −0.16 seconds, while the mean mean differences for declination for CRYOSAT 2 were 3.0 2.0 andarc 2.0seconds. arc seconds. absolute values for differences for declination for CRYOSAT 2 were 3.0 and The The absolute values for the the differences of declination were larger than those for right ascension. In the case of KOMPSAT 5, the mean differences of right ascension were −4.1 and −3.9 arc seconds and the mean differences of
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differences of declination were larger than those for right ascension. In the case of KOMPSAT 5, the mean differences of right ascension were −4.1 and −3.9 arc seconds and the mean differences of declination declination were were 1.2 1.2 and and 1.2 1.2 arc arc seconds. seconds. The The box box shape shape for for the the bottom bottom and and top top was was made made with with the the first seconds. However, first and and third third quartiles. quartiles. The The height height of of each each box box is is smaller smaller than than 55 arc arc seconds. However, the the widths widths between between whiskers whiskers is is almost almost 20 20 arc arc seconds. seconds. The The boxes boxes and and whiskers whiskers are are symmetrical symmetrical with with aa similar similar median median and and mean mean value. value. Even Even the the maximum maximum O-C O-C difference difference for for right right ascension ascension in in Figure Figure 55 is is almost almost 40 6. This 40 arc arc seconds. seconds. However, However, these these results results are are neglected neglected as as outliers outliers in in Figure Figure 6. This indicates indicates that that the the outliers are of negligible value for statistical analysis of the accuracy of the optical observation results outliers are of negligible value for statistical analysis of the accuracy of the optical observation results of of the the OWL-Net. OWL-Net.
Figure Figure 5. 6. Box Boxand andwhisker whiskerplot plotcomparison comparison for forthe the1-week 1-weekO-C O-Cdifference difference between between optical optical observation observation data and precise orbit ephemeris (CPF and Precise Orbit Determination (POD) with onboard GPS data and precise orbit ephemeris (CPF and Precise Orbit Determination (POD) with onboard GPS data) data) for CRYOSAT 2 and KOMPSAT 5. The left graph for CRYOSAT 2 was the result of the for CRYOSAT 2 and KOMPSAT 5. The left graph for CRYOSAT 2 was the result of the comparison comparison with CPF for 2 weeks in 2016 and 2017. The optical observation for KOMPSAT 5 in the with CPF for 2 weeks in 2016 and 2017. The optical observation for KOMPSAT 5 in the right-side graph right-side graphwith werePOD compared with POD with onboard GPS data. were compared with onboard GPS data.
There are two comparisons of the historical optical tracking system for SSA with the OWL-Net. There are two comparisons of the historical optical tracking system for SSA with the OWL-Net. The Baker-Nunn camera is the first-generation optical tracking network for LEO satellites and their The Baker-Nunn camera is the first-generation optical tracking network for LEO satellites and their launch vehicles. The along-track metric accuracy of a single Baker-Nunn camera is about 2 arc launch vehicles. The along-track metric accuracy of a single Baker-Nunn camera is about 2 arc seconds seconds in stationary mode with Very Large Frequency (VLF) signals time keeping [25]. The Bakerin stationary mode with Very Large Frequency (VLF) signals time keeping [25]. The Baker-Nunn Nunn camera was replaced by Ground-Based Electro-Optical Deep Space Surveillance (GEODSS) camera was replaced by Ground-Based Electro-Optical Deep Space Surveillance (GEODSS) [26]. [26]. The GEODSS is a dedicated optical sensor for observing deep space objects as part of the SSN. The GEODSS is a dedicated optical sensor for observing deep space objects as part of the SSN. The sidereal metric observation accuracy of the GEODSS is 4–6 arc seconds. The accuracy of its time The sidereal metric observation accuracy of the GEODSS is 4–6 arc seconds. The accuracy of its time synch is within 0.001 s [27]. There is another optical tracking sensor contributing to the SSN. The synch is within 0.001 s [27]. There is another optical tracking sensor contributing to the SSN. The Maui Maui Space Surveillance System (MSSS) consists of multiple assets capable of providing highly Space Surveillance System (MSSS) consists of multiple assets capable of providing highly accurate accurate optical observations for missiles or satellites. In the case of the 1.6-m Advanced Electrooptical observations for missiles or satellites. In the case of the 1.6-m Advanced Electro-Optical System Optical System (AEOS), the accuracy of metric data varied from 2 arc seconds to more than 10 arc (AEOS), the accuracy of metric data varied from 2 arc seconds to more than 10 arc seconds for the seconds for the LAGEOS 2 satellite. The altitude of LAGEOS 2 is about 1300 km. The Raven telescope LAGEOS 2 satellite. The altitude of LAGEOS 2 is about 1300 km. The Raven telescope has 0.4-m has 0.4-m optics to operate with higher accuracy ballistics or rate-track methods. The Root-Meanoptics to operate with higher accuracy ballistics or rate-track methods. The Root-Mean-Square (RMS) Square (RMS) pointing error magnitude is 2.2 arc seconds for the GPS optical observation compared pointing error magnitude is 2.2 arc seconds for the GPS optical observation compared to the true GPS to the true GPS ephemeris [28]. ephemeris [28]. 3. 3. Characteristics Characteristics of of the the Optical Optical Observation Observation Data Data with with the the OWL-Net: OWL-Net: Dense Dense Data Data in in Short Short Arc Arc between between Sparse Sparse Observation Observation Chances Chances The be implemented implemented by by satisfying satisfying three three constraints: constraints: site The optical optical observations observations of of satellites satellites can can be site elevation angle, Sun elevation angle, and lighting condition. In the case of the OWL-Net, the site elevation angle, Sun elevation angle, and lighting condition. In the case of the OWL-Net, the site elevation degrees. ThisThis means thatthat system tracks the target satellite when when the target elevation angle angleisisset settoto1515 degrees. means system tracks the target satellite the satellite is 15 degrees aboveabove the ground. TheThe SunSun elevation angle is issetsetatat−12 target satellite is 15 degrees the ground. elevation angle −12degrees degreesat at the the astronomical twilight level. The penumbra and direct sunlight is considered as the lighting condition. astronomical twilight level. The penumbra and direct sunlight is considered as the lighting condition. Observation Observation time time span span of of the the LEO LEO satellite satellite with with the the OWL-Net OWL-Net is is limited limited to to dawn dawn and and dusk. dusk. Even Even if if prior constraints are satisfied, the read-out time of the CCD sensor and telescope pointing time are prior constraints are satisfied, the read-out time of the CCD sensor and telescope pointing time are also schedule. also considered considered in in the the actual actual observation observation schedule.
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Figure 77 shows shows the the example example of of the the optical optical observation observation schedule Figure schedule during during aa single single night night and and the the optical observation observation constraints. constraints. We defined each each observation observation chance optical We defined chance as as “Action” “Action” (A1, (A1, A2, A2, etc.) etc.) and and eachshot shot as as “Shot” “Shot” (S1, (S1, S2, S2, etc.), each LEO each etc.), respectively. respectively. Generally, Generally, each LEO optical optical observation observation target target had had one one or two actions per night for each OWL-Net site. The length of each action and the number of shots or two actions per night for each OWL-Net site. The length of each action and the number of shots are are dependent on optical the optical observation conditions as previously we previously described. dependent on the observation conditions as we described.
Figure Constraints of of the the observable observable time: time: Sun Sun Figure 7.6. Optical Optical observation observation schedule schedule of of the the OWL-Net. OWL-Net. Constraints elevation angle (astronomical twilight, − 12 degrees), target satellite elevation angle, and lighting elevation angle (astronomical twilight, −12 degrees), target satellite elevation angle, and lighting condition observable time span (A1, A2,A2, etc.), several shots (S1, condition(penumbra (penumbraand anddirect directSun). Sun).During Duringthe the observable time span (A1, etc.), several shots S2, etc.) could be achieved with charge-coupled device (CCD) readout and mount moving time. (S1, S2, etc.) could be achieved with charge-coupled device (CCD) readout and mount moving time.
The optical optical tracking tracking simulation simulation with the OWL-Net was performed The performed to to analyze analyze the the length length of of the the arcand and interval interval between between the the optical optical observation chance under the optical arc optical tracking tracking condition condition for for the the OWL-Net. The Korean LEO satellites. TheThe average altitude fromfrom the OWL-Net. The simulation simulationtargets targetswere were1111South South Korean LEO satellites. average altitude ground waswas 730 km. Except for one the other have circular orbits. Among the 11 targets, the ground 730 km. Except fortarget, one target, the targets other targets have circular orbits. Among the 11 eight targets designed to have a to Sun-synchronous orbit (SSO). The(SSO). target satellites in satellites SSO revisit targets, eightwere targets were designed have a Sun-synchronous orbit The target in the same atlocation the same hourlocal every dayevery [29].day The[29]. optical chance can be SSO revisitlocation the same at local the same hour Theobservation optical observation chance reduced for thefor LEO in SSO.inThe was performed for onefor year 2017. can be reduced thesatellites LEO satellites SSO.simulation The simulation was performed oneduring year during However, we did consider the the weather conditions and abnormal conditions 2017. However, we not did not consider weather conditions and abnormal conditionsofofthe thesystem systemor or maintenance of the system. As an example, the Mongolia site had been down for a few months due maintenance of the system. As an example, the Mongolia site had been down for a few months due to to the temperature operating hardwaresystems. systems.InInthe thedevelopment development and and testing testing phase of the lowlow temperature forfor operating hardware of the the OWL-Net, we we faced faced many many abnormal abnormal situations situations which OWL-Net, which forced forced us us to to improve improve the the hardware hardware or or software software ofthe thesystem. system.In Inaddition, addition,we weachieved achievedobservations observationsofof a bright launch vehicle a system in of a bright launch vehicle forfor a system testtest in the the early phases of development the development of OWL-Net. the OWL-Net. early phases of the of the Figure88shows showsthe the results of the optical observation simulation the OWL-Net. The length mean Figure results of the optical observation simulation of theofOWL-Net. The mean length of the arc (arc-length) for a single optical observation chance is about 4 min. Except for KITSAT of the arc (arc-length) for a single optical observation chance is about 4 min. Except for KITSAT 1, 1, the maximum time optical observationdoes doesnot notexceed exceed10 10min. min. The The average average period the maximum time of of thethe optical observation period of of orbit orbit for 12 LEO satellites is 100 min; therefore, the mean arc-length for optical observation is only 4–5% for 12 LEO satellites is 100 min; therefore, the mean arc-length for optical observation is only 4–5% of of the entire entire orbit. orbit. On On the the other other hand, hand, the the mean mean value value of of the the interval interval between between the the the optical optical observation observation chancesisisabout about 400 min. maximum interval of LEO ninesatellites LEO satellites This chances 400 min. TheThe maximum interval of nine exceedsexceeds 800 min.800 Thismin. indicates indicates that the optical observation using the OWL-Net for 12 LEO satellites can be performed for that the optical observation using the OWL-Net for 12 LEO satellites can be performed for 4 min 4 min per four revolutions. However, in reality, some sites can be shut down due to weather per four revolutions. However, in reality, some sites can be shut down due to weather conditions conditions or maintenance. shown cases in selected cases in Table 2, weable were ablethe to or maintenance. Practically, Practically, as shown inasselected in Table 2, we were only to only perform perform the optical observation five times per week for CRYOSAT 2. The lower whiskers of the lower optical observation five times per week for CRYOSAT 2. The lower whiskers of the lower graph in graph in Figure 8 mean that thewas satellite was observed simultaneously with relatively close stations. Figure 8 mean that the satellite observed simultaneously with relatively close stations. The optical optical observation observation from from the the OWL-Net OWL-Net was was performed performed in The in aa very very short short duration duration with with sparse sparse intervals of the observation chance, but the observation data in the single shot was also dense. intervals of the observation chance, but the observation data in the single shot was also dense. These These high-rateoptical opticalobservation observation data be achieved with the chopper system as we previously high-rate data cancan be achieved with the chopper system as we previously described. described. Vallado et al. [30]that considered that several hundred points observation per arc comprised Vallado et al. [30] considered several hundred observation per arcpoints comprised “dense” data “dense” data with the SSN sensor. The regular observation points of the SSN were achieved, with the SSN sensor. The regular observation points of the SSN were achieved, averaging three points averaging three points per arc. The OWL-Net’s high-rate, dense optical observations can help to make per arc. The OWL-Net’s high-rate, dense optical observations can help to make orbital estimations orbital estimations more stable with the short-arc optical observations. more stable with the short-arc optical observations.
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Figure chances for for 11 11 LEO LEO targets targets Figure 7. 8.Statistics Statisticsof ofthe thelength length of ofthe thearc arc and and interval interval between between observation observation chances of the OWL-Net and CRYOSAT 2 from the optical observation simulation for 2017. The mean value of the OWL-Net and CRYOSAT 2 from the optical observation simulation for 2017. The mean value of of lengths of the arc (arc-length) did not exceed 4 min, whereas the mean value of intervals between lengths of the arc (arc-length) did not exceed 4 min, whereas the mean value of intervals between the the optical observation chance about optical observation chance waswas about 400 400 min.min.
4. Observation Data Data of of the the OWL-Net OWL-Net 4. Short-Arc Short-Arc Orbit Orbit Estimation Estimation with with the the Optical Optical Observation The estimation is is aa typical typical orbit orbit determination determination method. method. Another Another The batch batch least-squares least-squares (BLS) (BLS) orbit orbit estimation orbit estimation method, the sequential filtering orbit estimation, is more flexible and able to provide orbit estimation method, the sequential filtering orbit estimation, is more flexible and able to provide aa fast for sequentially sequentially added added observations. observations. These methods have have advantages advantages and and fast response response for These two two methods disadvantages for measurement processing, computing power, divergence, and the influence of disadvantages for measurement processing, computing power, divergence, and the influencebad of data, etc. The BLSBLS orbit estimation needs more computing speed bad data, etc. The orbit estimation needs more computingpower powerand andhas hasaaslower slower response response speed than data are are sparse sparse and and noisy, noisy,the theBLS BLSorbit orbit than the the sequential sequential filtering. filtering. However, However, when when the the observation observation data estimation can be a more suitable answer for stable orbit estimation results [31]. estimation can be a more suitable answer for stable orbit estimation results [31]. The andPPbeing beingdetermined determined The BLS BLS orbit orbit estimation estimation solution solution is is described described as as Equation Equation (3), (3), with with x and aa priori [32]. Here, and P denote a state deviation vector and covariance, respectively. Theorbit BLS priori [32]. Here, x and P denote a state deviation vector and covariance, respectively. The BLS orbit estimator thiswas study was developed with a numerical orbit propagator usingperturbation the special estimator in thisin study developed with a numerical orbit propagator using the special perturbation (SP) method [33]. (SP) method [33]. (3) = + + ̅ , = + xek = ( H T W H + W k )−1 ( H T Wy + W k x k ), P = ( H T W H + W k )−1 (3) In the case of the optical tracking observation, the angle-only measurements, right ascension and In the case of the optical tracking observation, the angle-only measurements, right ascension declination, are acquired without the range information. The OWL-Net is a ground-based optical and declination, are acquired without the range information. The OWL-Net is a ground-based sensor; therefore, a topo-centric environment condition was considered for the observation model. optical sensor; therefore, a topo-centric environment condition was with considered for the observation The measurements for satellites from the OWL-Net were corrected the coordinates of stars in model. The measurements for satellites from the OWL-Net were corrected with the coordinates J2000.0 [18]. Therefore, the same coordinate system was used in the orbit estimation program. In of stars in J2000.0 [18]. Therefore, thethe same coordinate was used in the orbit Equation (4), the observation model for optical trackingsystem observation is described. The estimation range from program. In Equation (4), the observation model for the optical observation is described. ground-based optical tracking sensor to target satellite, , was tracking calculated with the initial orbital The range from ground-based optical tracking sensor to target satellite, r, was calculated with the information. initial orbital information. −1 r2 , , δ = = sin−1 r3 (4) (4) α == tan r1 r The due to to the the irregular irregular The modeling modeling of of the perturbation by the atmospheric drag has errors due variation is calculated calculated using using the the variation of of the atmosphere. In In Equation Equation (5), (5), the the atmospheric density, density, ρ,, is atmosphere changed by by the the atmosphere models. models. Cd denotes denotes the the atmospheric atmospheric drag drag coefficient, which can be changed physical physical characteristics characteristics of of space space objects. objects. In In the the case case of plate, the atmospheric drag coefficient is 2.2. However, the satellites can have complicated shapes, with the exception of some geodesy satellites. To overcome the error of the atmospheric drag density models and the variation of the effective area , by forcing the atmospheric perturbation, the atmospheric drag coefficient or ballistic coefficient,
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However, the satellites can have complicated shapes, with the exception of some geodesy satellites. To overcome the error of the atmospheric drag density models and the variation of the effective area d A20 Sensors 2018, 18, of by forcing thex atmospheric perturbation, the atmospheric drag coefficient or ballistic coefficient,12Cm , can be estimated. In this study, we estimated the atmospheric drag coefficient with the position and can be estimated. In this study, wethe estimated theof atmospheric drag coefficient with position and vector of the satellite to overcome sparseness the optical observation dataset forthe 7 days. vector of the satellite to overcome the sparseness of the optical observation dataset for 7 days. → → 11Cd A 2 v rel a drag = (5) (5) = − 2 m ρvrel |→ |v rel || 2
The coefficient could be be found with various intervals. The Theestimation estimationofofthe theatmospheric atmosphericdrag drag coefficient could found with various intervals. frequency of theofestimation of theofatmospheric drag drag coefficient affected the accuracy of the The frequency the estimation the atmospheric coefficient affected the accuracy of orbit the estimation resultsresults [8,9,34,35]. The atmospheric drag coefficient was estimated at intervals of 1, 2,of8, orbit estimation [8,9,34,35]. The atmospheric drag coefficient was estimated at intervals 12, 24 and h in 24 theh research. In general, more more frequent drag drag coefficient estimations improve orbit 1, 2,and 8, 12, in the research. In general, frequent coefficient estimations improve orbit estimation precision. theof case of orbit estimation the OWL-Net, the optical observation estimation precision. In theIn case orbit estimation with with the OWL-Net, the optical observation data data too were too sparse a single was too to short to estimate the atmospheric drag coefficient were sparse and a and single actionaction was too short estimate the atmospheric drag coefficient within a fixed time interval. This is because optical observation events cannot occur repeatedly at awithin fixed time interval. This is because optical observation events cannot occur repeatedly at regular regular intervals and cycles. the other too-short optical observationscan can result result in intervals and cycles. On theOnother hand,hand, too-short arc arc optical observations in filter filter divergence or or inaccurate inaccurate orbit orbit estimation results [36]. divergence [36]. Accordingly, Accordingly, we we sequentially sequentiallyestimated estimatedthe the atmosphericdrag dragcoefficient coefficient for for each single action with atmospheric with short-arc short-arc BLS BLSorbit orbitestimations estimationsaapriori priorifrom from theestimated estimatedorbital orbital parameter parameter by multi-arc multi-arc BLS the BLS orbit orbitestimation estimationresults. results. InFigure Figure9,9,the thesequential-batch sequential-batch least-squares least-squares orbit In orbit estimation estimationisisdescribed. described.First, First,multi-arc multi-arcbatch batch least-squares orbit estimation is performed using the optical observation data for 7 days in accordance least-squares orbit estimation is performed using the optical observation data for 7 days in with the orbit determination strategy of the OWL-Net system. The position and position velocity information accordance with the orbit determination strategy of the OWL-Net system. The and velocity from TLE was employed before this step. Afterthis that,step. the short-arc batch orbitleast-squares estimations information from TLE was employed before After that, theleast-squares short-arc batch for each single short-arc action is conducted sequentially with the re-estimation of the position andof orbit estimations for each single short-arc action is conducted sequentially with the re-estimation velocity andand thevelocity atmospheric drag coefficient.drag The coefficient. estimation result from the multi-arc batch orbit the position and the atmospheric The estimation result from the multiestimation is used a priori for the first short-arc batch least-squares orbit estimation. By the second arc batch orbit estimation is used a priori for the first short-arc batch least-squares orbit estimation. step re-estimating atmosphericthe drag coefficient drag of each single short-arc, variation of the By theofsecond step ofthe re-estimating atmospheric coefficient of each the single short-arc, the atmospheric drag coefficient can be achieved. variation of the atmospheric drag coefficient can be achieved.
Figure8.9.Sequential-batch Sequential-batchorbit orbitestimation estimationdiagram. diagram.In In multi-arc batch orbit estimation step, Figure thethe multi-arc batch orbit estimation step, the the position and velocity vectors and the single atmospheric drag coefficient are estimated by optical position and velocity vectors and the single atmospheric drag coefficient estimated by optical observationdata data epochs. epochs. After After that, that, batch batch orbit orbit estimations estimations for observation for single single short-arcs short-arcs are areconducted conductedby by sequentiallyestimating estimating the the atmospheric atmospheric drag drag coefficient. coefficient. The sequentially The position, position, velocity, velocity,and andcovariance covariancewere were propagated to to the the next next short short arcs arcs with propagated with results results from fromthe thepresent presentshort-arc short-arcbatch batchorbit orbitestimation. estimation.
For the first multi-arc BLS orbit estimation, the position and velocity are calculated a priori with TLE in Equation (6). We selected TLE in consideration of backward propagation. TLE information was well fitted to the actual orbit within 1 or 2 days before the epoch of TLE [37]. The atmospheric drag coefficient for the first step was 2.2, which is a well-known arbitrary constant. =
, , ,
,
,
TLE
= 2.2
(6)
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For the first multi-arc BLS orbit estimation, the position and velocity are calculated a priori with TLE in Equation (6). We selected TLE in consideration of backward propagation. TLE information was well fitted to the actual orbit within 1 or 2 days before the epoch of TLE [37]. The atmospheric drag coefficient for the first step was 2.2, which is a well-known arbitrary constant. Xinitial = x, y, z, v x , vy , vz f rom TLE (CD = 2.2)
(6)
The estimated orbit parameter from the multi-arc BLS orbit estimation, X0 , P0 , was determined before the single short-arc BLS orbit estimation for the first optical observation, Action 1. The estimated orbit parameters, X1 , P1 , for the first short-arc action, Action 1, were propagated to the first optical observation point of the next short-arc action, Action 2. X 0 n +1 = Φ ( t n +1 , t n ) X n P0 n+1 = Φ(tn+1 , tn ) Pn Φ T (tn+1 , tn
(7)
The propagated state vector and covariance, X 0 1 , P0 1 , were used for the next short-arc BLS orbit estimation a priori in Equation (7). Finally, we obtained the estimated position and velocity, [ X1 , P1 ], [ X2 , P2 ], . . . [ Xn , Pn ], and the estimated atmospheric drag coefficients, CD_1 , CD_2 , . . . CD_n , for each single short-arc optical observation data point. The BLS orbit estimator was developed for sequential-batch type orbit estimation. MATLAB software was used to build it. Table 3 shows the dynamic models and estimator specification. To overcome the truncation error in the calculation of high-order term geopotential perturbation (up to 60 × 60), the recursive computation of Legendre polynomials technique was applied [38]. We selected the Jacchia-Bowman 2008 (JB2008) atmosphere model to calculate the atmosphere density. The JB2008 model is an effective model to calculate the atmosphere density for irregular solar activity [39]. The shape of the estimated satellite was assumed to be a simple sphere model. The estimator was developed in a weighted BLS type. TLEs were collected a priori using a space-track website. Table 3. The batch least-squares orbit estimator setup and dynamic models to calculate perturbations. The Jacchia-Bowman 2008 model was used as the atmospheric drag model to reduce the error of models by irregular solar activity.
Dynamic models
Estimator
Earth‘s gravity
EGM2008 (70 × 70)
Planetary Atmospheric drag SRP
Sun and Moon, planets JB2008, spherical shape spherical shape
Integrator Filter A priori
RKF7(8) Weighted batch least-squares TLE
Pavlis et al. [40] Kuga and Carrara [38] Standish et al. [41] Bowman et al. [39]
Long et al. [33] www.space-track.org [42]
We considered four perturbations to describe the orbits of CRYOSAT 2 and KOMPSAT 5. The perturbations for space objects in Earth orbit have different scales by an altitude of the space objects [31]. The main perturbations were considered for this study. Relatively small scale perturbations like relativity and albedo were neglected. In particular, we focused on the atmospheric drag perturbation in this study because it varied due to not only the altitude of space objects but also the status of the atmosphere. The error by modeling of the atmosphere presented as the variation of the atmospheric drag coefficient. The measurement residuals of multi-arc batch least-squares orbit estimation and sequential-batch least-squares orbit estimation are shown in Figure 10. The target satellite was CRYOSAT 2. The optical observation was performed using the OWL-Net at the Israel site from 1 June to 6 June 2016. The upper graph shows the measurement residuals for multi-arc BLS orbit estimation results. Both right ascension
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(blue cross) and declination (green cross) are within 15 arc seconds. The lower five graphs show the measurement residuals for the result of short-arc orbit estimation with five short-arc optical observations. Each of the optical observation durations was within 40–70 s. Single short-arc BLS Sensorsestimation 2018, 18, x was also successfully performed. The measurement residuals for short-arc BLS14orbit of 20 orbit estimation were similar to the multi-arc BLS orbit estimation results.
Figure Measurementresiduals residualsofofthe themulti-arc multi-arcbatch batchleast-squares least-squares orbit orbit estimation estimation results results (upper) (upper) Figure 10. 9. Measurement and short-arc batch least-squares orbit estimation results (lower) the optical and five fivesingle single short-arc batch least-squares orbit estimation resultswith (lower) with observation the optical using the OWL-Net at the Israel site The optical observation was peformed from observation using the OWL-Net at for theCRYOSAT Israel site 2.for CRYOSAT 2. The optical observation was1 June 2016 to 6 June 2016. Each short-arc optical observation was performed in 40–70 s. (blue cross: peformed from 1 June 2016 to 6 June 2016. Each short-arc optical observation was performed in 40–70 right ascension, green cross: declination). s. (blue cross: right ascension, green cross: declination).
measurementresiduals residualsofof multi-arc batch least-squares estimation and sequentialThe measurement multi-arc batch least-squares orbitorbit estimation and sequential-batch batch least-squares orbit estimation forsets four of CRYOSAT 2 and KOMPSAT 5 observations are least-squares orbit estimation for four of sets CRYOSAT 2 and KOMPSAT 5 observations are shown shown box and whisker in Figure 11 (blue: right ascension, orange: declination).The The outliers as box as and whisker plots plots in Figure 11 (blue: right ascension, orange: declination). those graphs. graphs. In were neglected in those In general, general, the the residuals residuals from from the results using multi-arc orbit estimation were more stable than the residuals from the results using single short-arc orbit estimation. The residuals residualsfor forKOMPSAT KOMPSAT5 were 5 were bigger more unstable the results of CRYOSAT The bigger andand more unstable thanthan the results of CRYOSAT 2. The2.mean mean values of the residuals of the multi-arc observations show variation smaller variation than the mean values of the residuals of the multi-arc observations show smaller than the mean values of values of the observations. short-arc observations. mean of most residuals do not exceed 5 arc the short-arc However,However, the mean the values of values most residuals do not exceed 5 arc seconds. seconds. Post-fit residuals for CRYOSAT 2 and KOMPSAT 5 orbit estimation results are shown in Table 4. residuals forroot-mean-squares CRYOSAT 2 and KOMPSAT 5 orbit estimation are shown in Table This Post-fit table also lists the error of the results of orbit results estimation. The detailed 4. This tableinformation also lists theisroot-mean-squares error the resultsresiduals of orbit were estimation. The for detailed observation summarized in Table 2. of The post-fit calculated both observation information is summarized in Table The post-fit residuals were both right ascension and declination. There were some2.result deficiencies due to the calculated number offor actions. rightpost-fit ascension and declination. were some result deficiencies duetotothe theresults number ofshort-arc actions. The residuals for multi-arcThere BLS orbit estimation results were similar from The post-fit residualsSome for multi-arc BLS orbit estimation results similar the results from shortBLS orbit estimation. of post-fit residuals were bigger thanwere others for thetosame week and satellite. arcthat BLScase, orbitthe estimation. Some of post-fit residualslarger wereirregular bigger than others the sameinweek and In optical observation data presented errors as wefor described Section 2. satellite. In that the optical data presented irregular2 for errors we reason. described The residuals forcase, KOMPSAT 5 areobservation relatively bigger than thoselarger of CRYOSAT the as same in Section 2. The residuals for KOMPSAT 5 are relatively bigger than those of CRYOSAT 2 for the same reason. The estimated atmospheric drag coefficients are shown in Table 4. In general, the atmospheric drag coefficient was fixed at 2.2 as we described earlier. However, the estimated atmospheric drag coefficient value can be reduced or increased by inaccurate values of a given mass or effective area of a satellite for orbit estimation. On the other hand, the estimated atmospheric drag also can be varied due to the error of the atmosphere model. The atmospheric drag coefficient for multi-arc observation was estimated with the optical observation data from the first point of the first short-arc observation to the last point of the last short-arc data. This indicated that the estimated atmospheric drag coefficient was an average value for 1 week. In another example, we used single short-arc data points
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Figure 11. Measurement residuals of multi-arc batch least-squares orbit estimation results and short-arc Figureleast-squares 10. Measurement ofresults multi-arc least-squares orbit estimation shortbatch orbit residuals estimation for batch CRYOSAT 2 and KOMPSAT 5 (blue:results right and ascension, arc batch least-squares estimation results for 2 of and (blue: right orange: declination). Theorbit outliers were neglected. TheCRYOSAT mean values theKOMPSAT residuals of5the multi-arc ascension, orange: declination). The outliers were neglected. The mean values of the residuals of the observations show smaller variation than the mean values of the short-arc observations. The mean multi-arc observations smaller variation than the mean values of the short-arc observations. The values of most residualsshow do not exceed 5 arc seconds. mean values of most residuals do not exceed 5 arc seconds.
The estimated atmospheric drag coefficients are shown in Table 4. In general, the atmospheric Table 4. Post-fit residuals (Root-Mean-Square (RMS), arc seconds) of multi-arc and short-arc batch drag coefficient was fixed at 2.2 as we described earlier. However, the estimated atmospheric drag least-squares (BLS) orbit estimation results for CRYOSAT 2 and KOMPSAT 5 (right ascension (R.A.), coefficient value can be reduced or increased by inaccurate values of a given mass or effective area of declination (Dec.)). The short-arc BLS orbit estimation results were similar to the multi-arc BLS orbit a satellite for orbit estimation. On the other hand, the estimated atmospheric drag also can be varied for multi-arc and short-arc BLS estimation results. The estimated atmospheric drag coefficients ( due to the error of the atmosphere model. The atmospheric drag coefficient for multi-arc observation orbit estimations for CRYOSAT 2 and KOMPSAT 5 are described. was estimated with the optical observation data from the first point of the first short-arc observation to RMS Multdata. Short Short Short Short Short drag Shortcoefficient Short theSatellite last point Week of the last short-arc This Short indicated thatShort the estimated atmospheric Number (``) i-arc -arc1 -arc2 -arc3 -arc4 -arc5 -arc6 -arc7 -arc8 -arc9 was an average value for 1 week. In another example, we used single short-arc data points to estimate R.A. 2.86 3.18 3.48 2.57 2.51 2.20 the atmospheric1 drag coefficient The atmospheric drag- coefficients for Dec. 1.80for each 2.75 short-arc. 1.09 1.45 estimated 1.76 1.45 - the CRYOS 1.882 1.885 1.892 1.889 1.910 1.886 short arc were average values only for single short arcs. AT 2
KOMPS AT 5
2
R.A. Dec.
1
R.A. Dec.
2.73 1.65 1.984 4.2 2.57 2.656
4.81 1.18 1.979 4.26 2.66 2.641
1.52 1.30 1.972 4.68 3.75 2.641
2.45 1.59 1.979 2.42 1.76 2.640
2.31 2.06 1.956 3.75 1.95 2.632
2.03 1.12 1.973 3.71 1.87 2.633
2.31 2.49 2.648
4.66 3.49 2.660
-
-
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Table 4. Post-fit residuals (Root-Mean-Square (RMS), arc seconds) of multi-arc and short-arc batch least-squares (BLS) orbit estimation results for CRYOSAT 2 and KOMPSAT 5 (right ascension (R.A.), declination (Dec.)). The short-arc BLS orbit estimation results were similar to the multi-arc BLS orbit estimation results. The estimated atmospheric drag coefficients (CD ) for multi-arc and short-arc BLS orbit estimations for CRYOSAT 2 and KOMPSAT 5 are described. Satellite
Week Number 1
CRYOSAT 2 2
1 KOMPSAT 5 2
RMS (“)
Multiarc
Shortarc1
Shortarc2
Shortarc3
Shortarc4
Shortarc5
Shortarc6
Shortarc7
Shortarc8
Shortarc9
R.A. Dec. CD R.A. Dec. CD
2.86 1.80 1.882 2.73 1.65 1.984
3.18 2.75 1.885 4.81 1.18 1.979
3.48 1.09 1.892 1.52 1.30 1.972
2.57 1.45 1.889 2.45 1.59 1.979
2.51 1.76 1.910 2.31 2.06 1.956
2.20 1.45 1.886 2.03 1.12 1.973
-
-
-
-
R.A. Dec. CD R.A. Dec. CD
4.2 2.57 2.656 4.03 2.29 2.852
4.26 2.66 2.641 4.39 1.98 2.840
4.68 3.75 2.641 4.17 2.36 2.839
2.42 1.76 2.640 2.09 2.32 2.837
3.75 1.95 2.632 3.55 2.39 2.839
3.71 1.87 2.633 3.04 1.89 2.847
2.31 2.49 2.648 1.64 3.37 2.851
4.66 3.49 2.660 6.85 2.81 2.849
7.25 2.28 2.850
3.75 1.80 2.855
CRYOSAT 2 and KOMPSAT 5 were selected as the calibration and validation targets for the OWL-Net at the first observation test phase due to their provided precise ephemeris. As previously described in Section 2, CPF and onboard GPS data were provided. The provided ephemeris was used as a reference for comparing the estimated orbits. The post-fit residuals with reference orbit for CRYOSAT 2 and KOMPSAT 5 were analyzed for the estimated results of the multi-arc and short-arc BLS orbit estimations, respectively. In the case of the short-arc BLS orbit estimation, the estimated orbits were propagated from the epoch of each short arc to the epoch of the next short arc. Table 5 shows the post-fit residuals with reference results in the radial, in-track, and cross-track (RIC) frame. Comparison results for multi-arc and short-arc approaches were similar to each other for the RIC frame. Table 5. Post-fit residuals (meter) with reference of multi-arc and short-arc batch least-squares (BLS) orbit estimation results for CRYOSAT 2 and KOMPSAT 5. The references are CPF and onboard GPS data for CRYOSAT 2 and KOMPSAT 5, respectively. The post-fit residuals for short-arc BLS orbit estimation were calculated with propagation from the epoch for each short arc to the epoch of the next short arc.
Satellite
Week Number
CRYOSAT 2 KOMPSAT 5
Multi-Arc
Short-Arc with Integration
Radial (m)
In-Track (m)
Cross-Track (m)
Radial (m)
In-Track (m)
Cross-Track (m)
1 2
21.03 11.13
85.94 40.67
57.02 5.25
21.19 11.45
86.09 39.44
55.84 5.68
1 2
4.14 5.05
13.83 21.52
8.28 4.15
4.54 5.30
17.24 21.77
8.07 3.78
The post-fit residuals with reference show the accuracy of the estimated orbits of CRYOSAT 2 and KOMPSAT 5 with the optical observation data from the OWL-Net. The in-track direction error was bigger than the radial and cross-track direction errors. The errors of week 1 of CRYOSAT 2 were twice as large as the errors of week 2. In particular, the cross-track error was almost 10 times greater than the results of week 1. Both multi-arc and short-arc approaches were shown to have the same results. In the case of week 1, we employed the observation data using the OWL-Net in Israel only. In addition, the observations for each short arc were performed within 30 min on either side of midnight in Coordinated Universal Time (UTC). On the other hand, for week 2 of CRYOSAT 2, we obtained observations with the OWL-Net in Korea, Israel, and the United States.
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It was shown that using single-site tracking data causes incorrect orbit estimation results, especially for the cross-track direction. In the case of the post-fit residuals with reference for KOMPSAT 5, the width of errors for the RIC frame was smaller than the post-fit residuals for CRYOSAT 2. We used CPF and POD with onboard GPS data for comparison with CRYOSAT 2 and KOMPSAT 5, respectively. In consideration of the offering accuracy of both references, the results of the KOMPSAT 5 were more reliable. When the space object was 600–2000 km above the ground, 1 arc second could be converted into 3–10 m. For the O-C difference in Section 2, the average O-C differences of KOMPSAT 5 were 3.5 and 1.2 arc seconds for right ascension and declination, respectively. The post-fit residuals with reference to the multi-arc BLS orbit estimation results were similar to the short-arc BLS orbit estimation results. The multi-arc BLS orbit estimations were performed with whole short-arc sets. However, the short-arc BLS orbit estimations only used single short-arc data points to estimate the orbit and the atmospheric drag coefficient. Therefore, the errors could be increased the estimated orbits with the short arc for a few minutes were propagated 17 toofthe Sensors 2018,because 18, x 20 next optical observation dataset. The prediction predictionerrors errorswith withreference referencewere wereanalyzed analyzedfor forCRYOSAT CRYOSAT 2 and KOMPSAT in Figure 2 and KOMPSAT 5 in5 Figure 12. 12.the In the of KOMPSAT 5, there was a maneuver eventone oneday dayafter afterthe theoptical optical observations observations of In casecase of KOMPSAT 5, there was a maneuver event in-track direction errors between POD with onboard GPS data the week 1 case. After one day, the in-track and the prediction were dramatically dramatically increased to 10 10 km. km. We confirmed the maneuver event by other. The multi-arc BLS orbit estimation results were comparing several consecutive TLEs with each other. used to make predictions for 77 days. days. This was followed by a basic policy for the operation of the OWL-Net. The with thethe consecutive TLEs were alsoalso compared withwith CPF and Thepropagated propagatedorbits orbits with consecutive TLEs were compared CPFPOD and with with onboard GPS GPS data.data. The The in-track direction prediction errors showed POD onboard in-track direction prediction errors showeda amaximum maximum2.2 2.2 km km of vibration. Occasionally, Occasionally, the the maximum maximum in-track in-track direction direction error error was was increased increased to 5–6 km for KOMPSAT vibration. KOMPSAT 5. The The in-track in-track direction direction errors errors were were dominant dominant in in the the 7-day 7-day prediction prediction error for CRYOSAT 2 and KOMPSAT 5.5.The Themaximum maximumin-track in-trackdirection direction errors from multi-arc orbit estimations KOMPSAT errors from thethe multi-arc BLSBLS orbit estimations did did not not exceed 1 km for both satellites. exceed 1 km for both satellites.
Figure 12. Prediction error for 7 days days after after multi-arc multi-arc batch least-squares orbit estimation using 2 weeks 11. Prediction of data and 1 week of data for for KOMPSAT 5 (c).5 In for KOMPSAT 5, there data for forCRYOSAT CRYOSAT2 2(a,b) (a,b) and 1 week of data KOMPSAT (c).one In case one case for KOMPSAT 5, was maneuver event event one day observation. The maximum prediction errors of two therea was a maneuver oneafter day the afteroptical the optical observation. The maximum prediction errors of satellites did not 1 km1for days. two satellites didexceed not exceed km7 for 7 days.
directly proportional proportional to the the astrometric astrometric scale scale errors. errors. The range The range scale errors were not directly between the observer observer and KOMPSAT KOMPSAT 55 varied varied from from 550 550 to 2000 km within a single optical observation between chance. The in-track direction error of 1 km can be converted to the astrometric scale error from 1.75 with the the range range variation. variation. The field-of-view (FOV) of the OWL-Net to 6.25 arc minutes in accordance with minutes. Another point of view for the in-track in-track error is time time synchronization. synchronization. The speed of is 66 arc minutes. KOMPSAT 5 is 7.6 km per second. KOMPSAT 5 orbits 1 km in about 130 ms. The recorded time scale KOMPSAT 5 is 7.6 km per second. KOMPSAT 5 orbits 1 km millisecond. Therefore, of the OWL-Net is one millisecond. Therefore, KOMPSAT KOMPSAT 55 and CRYOSAT 2 can be tracked with enough accuracy of time and telescope pointing prediction for the subsequent 7 days with the orbit using the the OWL-Net. OWL-Net. estimation results using 5. Discussion and Conclusions The OWL-Net, the optical tracking network for SSA, is undergoing a testing phase in 2018. We performed calibration and validation for the optical observation performance using the OWL-Net for two selected LEO satellites, CRYOSAT 2 and KOMPSAT 5. The mean astrometric accuracy for right
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5. Discussion and Conclusions The OWL-Net, the optical tracking network for SSA, is undergoing a testing phase in 2018. We performed calibration and validation for the optical observation performance using the OWL-Net for two selected LEO satellites, CRYOSAT 2 and KOMPSAT 5. The mean astrometric accuracy for right ascension and declination was within 5 arc seconds. The optical observation data for CRYOSAT 2 was compared with the CPF file. The reference orbit to which the optical observation data of KOMPSAT 5 was compared was POD with onboard GPS data in a normal situation. Occasionally, the astrometric error jumped to 40 arc seconds. The time synchronization was suspected to be a main error source. Because the optical observation data from the OWL-Net is very dense due to the chopper, maximum 50 Hz, some errors were neglected during the orbit estimation process. The overall mismatching of time and position information caused large errors of accuracy for orbit estimation and filter divergence. The critical reasons for the mismatching of time and position information were false and mis-detections of trails. The detection parameters of the CCD sensor can affect the detection rate of the trails and the precision of the astrometry. In this study, we mainly considered the calibration of the matching of time and position. The mismatching problem was successfully corrected using the assessment of the angular rate of the satellites. We did not use any orbital information to correct the mismatching error. Even though the optical observation data from the OWL-Net is very dense, it is generated within a very short duration of a few minutes. In addition, the optical observation chances are sparse. We performed the optical observation simulation for the OWL-Net to analyze the short-arc and sparse condition problems for 2017 with consecutive TLEs. The average observation duration for a single optical observation time is 4 min, while the average optical observation time span is 400 min. This sparse problem is more serious with actual weather conditions. Sometimes we failed to make an optical observation for over 10 days for a single LEO satellite. Additional optical stations or collaboration with other sensors could be a solution for this issue. In particular, the stations in the Southern Hemisphere of the Earth are good for simultaneous observation in a single orbit of a LEO satellite with the OWL-Net stations in the Northern Hemisphere. The orbit estimation filter was divergent or the estimation results were not reliable due to the short duration of the optical observation data. In addition, the sparseness of the optical observation data limited frequent estimation for the atmospheric drag coefficient. Therefore, we adopted the sequential-batch least-squares orbit estimation strategy for more frequent estimations of the atmospheric drag coefficient. The orbit estimation test was performed with the optical observation data during 1 week for CRYOSAT 2 and KOMPSAT 5. The sequential-batch type orbit estimation strategy was tested to estimate the atmospheric drag coefficient frequently using dense and sparse optical observation data. The batch orbit estimation for short arcs was performed a priori using the results of the multi-arc batch orbit estimation. The estimated orbit with each short-arc optical observation data point was propagated to the start point of the next short arc. From this estimation strategy, the short-arc batch estimations were conducted without filter divergence. The short-arc batch orbit estimations results show similar post-fit residual values to those of the multi-arc batch orbit estimation, as shown in Table 3. The post-fit residuals with reference orbit from CPF and POD with onboard GPS data also have similar results to those of the multi-arc and short-arc batch orbit estimations in Table 4. In this study, the atmospheric drag coefficient was re-estimated for each short-arc-based estimated value from the multi-arc orbit estimation. The atmospheric drag coefficient variations for CRYOSAT 2 and KOMPSAT 5 were confirmed. The variations of the atmospheric drag coefficient can be simply confirmed using the TLE data. The orbital information from TLE is a mean value from the orbit estimation using the last few days from the epoch of each TLE. Therefore, variation of the ballistic coefficients from the TLE has similar sensitivity. However, the variation of the atmospheric perturbation calculated with the estimated atmospheric drag coefficients for short arcs shows a similar tendency with ballistic coefficients from TLEs.
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The orbit prediction performance of the estimated orbit with the OWL-Net was confirmed with the reference orbits. The in-track direction errors did not exceed 1 km for 7 days. The purpose of determining the orbit of LEO satellites using the OWL-Net is to maintain the orbital information of Korean LEO satellites. Therefore, orbit estimation should provide accurate orbit information for tracking LEO satellites. Generally, TLEs are used to track space objects but may present errors within a few kilometers. In this light, the orbit estimation results in this study can support more accurate optical observations than TLEs for the OWL-Net. Author Contributions: Conceptualization, J.C. and J.H.J.; Methodology, J.C.; Software, J.C and J.H.J.; Validation, J.C.; Formal Analysis, J.C.; Resources, H.-S.Y.; Writing-Original Draft Preparation, J.C.; Writing-Review & Editing, J.H.J. and S.K.; Visualization, J.C.; Project Administration, J.-H.P.; Funding Acquisition, E.-J.C. and S.J. Funding: This study was supported by KASI (Korea Astronomy and Space Science Institute) grant 2018-1-854-00 (Project: OWL-NET operation and application). Acknowledgments: Authors express sincere appreciation to colleagues for the development, maintenance and operation of the OWL-Net system: Dong-Goo Roh, Myung-Jin Kim, Sooyoung Kim, Sun-Youp Park, Maru Park, Young-Ho Bae, Youngsik Park, Houng-Kyu Moon, Jae-Hyuk Kim, Aeri Kim and Young-Jun Choi. Conflicts of Interest: The authors declare no conflict of interest.
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