Orbit Determination Using SLR Data for STSAT-2C: Short-arc Analysis
Orbit Determination Using SLR Data for STSAT-2C: Short-arc Analysis
Journal of Astronomy and Space Sciences. 2015. Sep, 32(3): 189-200
Copyright © 2015, The Korean Space Science Society
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received : January 26, 2015
  • Accepted : June 04, 2015
  • Published : September 15, 2015
Export by style
Cited by
About the Authors
Young-Rok, Kim
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
Eunseo, Park
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
Daniel, Kucharski
Space Environment Research Centre, Mount Stromlo Observatory, ACT 2611, Australia
Hyung-Chul, Lim
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea

In this study, we present the results of orbit determination (OD) using satellite laser ranging (SLR) data for the Science and Technology Satellite (STSAT)-2C by a short-arc analysis. For SLR data processing, the NASA/GSFC GEODYN II software with one year (2013/04 – 2014/04) of normal point observations is used. As there is only an extremely small quantity of SLR observations of STSAT-2C and they are sparsely distribution, the selection of the arc length and the estimation intervals for the atmospheric drag coefficients and the empirical acceleration parameters was made on an arc-to-arc basis. For orbit quality assessment, the post-fit residuals of each short-arc and orbit overlaps of arcs are investigated. The OD results show that the weighted root mean square post-fit residuals of short-arcs are less than 1 cm, and the average 1-day orbit overlaps are superior to 50/600/900 m for the radial/cross-track/along-track components. These results demonstrate that OD for STSAT-2C was successfully achieved with cm-level range precision. However its orbit quality did not reach the same level due to the availability of few and sparse measurement conditions. From a mission analysis viewpoint, obtaining the results of OD for STSAT-2C is significant for generating enhanced orbit predictions for more frequent tracking.
The Science and Technology Satellite (STSAT)-2C was developed by the Satellite Technology Research Center (SaTReC) of the Korea Advanced Institute of Science and Technology (KAIST) and launched by Korea’s first launch vehicle, the Korea Space Launch Vehicle (KSLV)-1, on January 30, 2013. The purposes of the STSAT-2C mission are to test the KSLV-1 and develop a small spacecraft ( Kang et al. 2014 ). The STSAT-2C spacecraft is equipped with a laser retro-reflector array for satellite laser ranging (SLR), and has been tracked by the global network of SLR stations (International Laser Ranging Service - ILRS) since March 29, 2013 ( Pearlman et al. 2002 ). SLR is the most precise technique for measuring the distance between a satellite and the tracking station and the ILRS manages operation and data processing of SLR. Fig. 1 illustrates the concept of SLR and Fig. 2 shows the organization of ILRS. In Korea, mobile and stationary systems for SLR tracking have been developed since 2008 by Korea Astronomy and Space Science Institute ( Lim et al. 2010 ; Seo et al. 2010 ; Jo et al. 2011 ; Lim et al. 2011 ; Nah et al. 2013 ). The mobile SLR system development was finished and it delivers adequate ranging observations with a few mm precision ( Park et al. 2012 ; Choi et al. 2014 ). The ILRS associate analysis center is also operated by same institute ( Kim et al. 2012 , 2013b ).
PPT Slide
Lager Image
The concept of satellite laser ranging.
PPT Slide
Lager Image
The organization of International Laser Ranging Service.
The main SLR application of STSAT-2C is precise orbit determination (OD). The OD analysis with SLR observations for STSAT-2C can contribute to research on extremely low orbital environments (~300 km) and modeling accuracy assessment by using radial orbit error analysis. Therefore, it is an important issue to secure sufficient SLR tracking data. The SLR tracking statistics during a 12-month follow-up period are presented in Table 1 . The total passes and normal point (NP) observations during the last year are 204 and 2,215, respectively. The acquired amount of NPs is very low and sparse compared to the other laser-tracked low-earth orbiting satellites due to inexact orbit predictions for SLR tracking. For example, in the first week of April 2014 alone, the Jason-2 mission achieved 240 passes and 4,482 NPs. In this light, the SLR tracking for the STSAT-2C can be regarded as extremely sparse measurement conditions. As the STSAT-2C was utilized for successful orbit injection of KSLV-1, it was assigned a highly elliptical orbit (300 km – 1,500 km). While a GPS-based technique is generally used for positioning of non-geodetic satellites, radar-based two-line element (TLE) is utilized for orbit acquisition of STSAT-2C. Thus very poor orbit predictions have been provided for STSAT-2C for SLR tracking. As a result, it can be tracked only when the satellite is in a visible period. SLR tracking and OD using SLR observations are very challenging issues in the SLR community. Although a SLR-based strategy is a baseline for STSAT-2C OD, providing steady results has proved difficult.
ILRS tracking statistics for STSAT-2C (2013/03 - 2014/04).
PPT Slide
Lager Image
NP: normal point.
Lee & Alfriend (2007) pointed out that an inaccurate initial orbit and sparse measurements can result in unstable solutions of orbit estimation. To overcome this problem, various estimation algorithms such as unscented transformation and a particle filter have been suggested by Lee & Alfriend (2007) , Park et al. (2010) , and Kim et al. (2011 , 2014b) . Another way to avoid sparseness is to use a short-arc estimation strategy. Although this approach does not guarantee the best orbit accuracy, it can give the results of orbit estimation and prediction under very sparse measurement conditions. It has been demonstrated that the short-arc approach is very helpful for OD and prediction of low-Earth orbiting (LEO) objects including space debris ( Sang & Bennett 2014 ; Bennett et al. 2015 ). From a practical perspective, the short-arc OD approach in a sparse measurement condition is more advantageous than a new estimation strategy.
Kim et al. (2013a , 2014a) have implemented an orbital analysis for a few arcs of STSAT-2C using a short-arc approach. It has been reported that OD using SLR observations for STSAT-2C can be successfully accomplished despite the very sparse measurement condition. In the current study, almost all passes of one year were included in a short-arc OD strategy and the results were analyzed by post-fit residuals. For some periods, orbit overlaps results are investigated for the orbit quality check. As the estimation intervals of atmospheric drag and empirical acceleration affect the convergence property of OD for STSAT-2C using short-arc, a non-regular daily-based processing strategy with variable estimation intervals is applied. The aim of the current study is to obtain successful OD results for STSAT-2C using SLR short-arcs in order to improve the orbit predictions for SLR tracking. Section 2 summarizes the OD strategy and software settings and Section 3 describes the results of the post-fit residuals and orbit overlaps of short-arc OD. Section 4 gives conclusions.
In this section, the strategy for OD of STSAT-2C using SLR data is summarized. The NASA/GSFC GEODYN II software is used for SLR data processing ( Pavlis et al. 1998 ). The arcs for OD are prepared using a few passes with a minimum number of measurements for the parameter estimation. In this study, the existence of 10 NPs in one arc was adopted as a minimum condition for arc length determination. The final selected arcs for OD are presented in Table 2 . The specific modeling and the estimation parameters are presented in Table 3 . The arc length chosen for the OD was changed by the observation conditions, which originated from the number of NPs and the continuity of passes. The shortest and the longest arc length are 1 and 7 days, respectively. The number of stations used for the analysis also differs for each arc. In Table 2 , some arcs comprised observations from only one station, given that most of the SLR observations for the STSAT-2C were actually obtained by only one station in that period. Generally, such passes must be extended to include the data from other stations, or to be rejected from the OD process. However, to retain as many OD arcs as possible for the study, the short arcs recorded by only one station were included. Short arcs obtained by only one station are commonly accepted for OD of STSAT-2C, and therefore it is reasonable to include these arcs in the analysis.
Summary of the STSAT-2C arcs (2013/03 – 2014/04).
PPT Slide
Lager Image
NP: normal point.
Details of models and estimation parameters for STSAT-2C orbit determination.
PPT Slide
Lager Image
LRA: laser retro-reflector array, NP: normal point.
The estimation frequency of the parameters such as the drag coefficients and the empirical acceleration coefficients can affect the precision of the OD for LEO satellites. For Starlette, 24 hour and 12 hour intervals are used for drag coefficient estimation ( Lejba et al. 2007 ; Lejba & Schillak 2011 ). Jeon et al. (2011) and Jagoda & Rutkowska (2013) use 8 hours and 7 days for the OD of Starlette. Lejba & Schilliak (2011) demonstrated that more frequent estimation of the empirical acceleration parameters can improve the precision of the post-fit residuals of Starlette and Stella. However, in very sparse measurement conditions, convergence of estimation by the least-squares batch cannot be guaranteed if the number of estimation parameters increases. For the sparse data distribution of STSAT-2C some arcs necessitate the use of only specific intervals for convergence. Improvement of the tracking geometry by expanding the arc length is an alternative except for the cases where the observed arcs of orbit are separated by large time-gaps. In this study, a suitable selection strategy of the estimation intervals is therefore accomplished for every arc including a tuning process. Five different intervals are used for the drag coefficient estimation: 6, 8, 12, 24, and 48 hours. For the empirical acceleration coefficients 5 estimation intervals are applied: 8, 12, 24, 48, and 72 hours. In order to achieve stable convergence, the empirical acceleration coefficient are not estimated for several arcs. Generally, empirical acceleration parameters are estimated to compensate incomplete modeling errors of LEO satellites. However, in the present study, they are used as tuning parameters due to very sparse measurements. As a consequence, different OD strategies were utilized for each arc in order to overcome the inconsistent conditions created by the sparse measurements of STSAT-2C.
To eliminate outlying range residuals, a 7.0 sigma editing strategy is applied; in contrast the common sigma criterion in the analysis of LAGEOS and ETALON observations is 3.0 or 3.5 ( Kim et al. 2013b ). The relatively large sigma editing value is used to prevent failure of least-squares estimation due to a lack of observations. The center of the offset correction of the laser retro-reflector array for STSAT-2C applied in the OD analysis is given at the ILRS web page and is presented in Table 3 . As the OD characteristics and results for STSAT-2C are very sensitive to the initial conditions and to the estimation configuration, an extensive iterative process including manual tuning was required to find the prior initial values and for proper selection of the estimation parameters. The prior value of the initial orbit was first obtained from the predicted orbits by the KAIST prediction center (KAI), the main provider of STSAT-2C orbit predictions. Due to the low accuracy of the TLE-based KAI’s prediction, manual tuning was performed to reduce errors at the first iteration of the OD analysis. The successfully determined orbital parameters of the first arc are used as the initial conditions for the consecutive arc.
In this section, the OD results and the orbit quality assessments are investigated. The post-fit residuals, which show how well the estimated orbit fits the SLR measurements, and orbit overlaps, which demonstrate the quality and the consistency of the determined orbits, are presented.
- 3.1 Post-fit Rsiduals
For STSAT-2C, the determined weighted root mean square (RMS) values of the post-fit residuals for 2013 and 2014 are 0.60 and 0.70 cm, respectively. The results are presented in Table 4 and Fig. 3 . Table 4 shows the post-fit residuals and the coefficient estimation intervals for STSAT-2C OD. The weighted RMS of the post-fit residuals for most arcs is less than 1 cm. Fig. 3 shows the residuals of the weighted measurement residuals according to the day of the year from January 1, 2013. Fig. 4 and Table 5 show the residuals of each station for the total period. Fig. 4 displays the station residual precision of STSAT-2C OD. In Table 5 , the mean measurement residual (weighted RMS) for each station and its observation-weighting are summarized. These residuals do not indicate the absolute precision of stations because each station has a different weight value by observation-weighting sigma (σ) and the number of observations is quite unbalanced. The value of σ is determined by the tracking performance of each station. First, ILRS core stations, which have a stable NP quality and a long-term tracking history, have σ=1. Next, the weighting σ of other stations is assigned as 1, 4, or 10 according to the ILRS station quality report. If the observation-weighting value is above 1 for a station, SLR data of that station are underweighted in OD as much as the amount of the σ-value. Fig. 5 shows the effects of drag estimation frequency through the results of the post-fit residuals. Except some arcs that have no converged results, 8 hour-based results generally show better precision than 24 hour-based results. However, this also shows that the 8 hour-based strategy for drag coefficient estimation sometimes fails to obtain converged results. This is attributed to the sparse measurement condition of STSAT-2C giving an unstable estimation solution due to the increased number of estimation parameters.
PPT Slide
Lager Image
Measurement residuals of STSAT-2C orbit determination (2013-2014).
PPT Slide
Lager Image
Measurement residuals of each station (2013-2014).
The post-fit residuals and coefficient estimation intervals for STSAT-2C orbit determination.
PPT Slide
Lager Image
WRMS: weighted root mean square.
Measurement residuals of each station.
PPT Slide
Lager Image
σ: observation-weighting sigma, WRMS: weighted root mean square.
PPT Slide
Lager Image
Effects of drag estimation frequency.
- 3.2 Orbit Overlaps
Although the overlapped periods are generally arranged consecutively, we could not find continuous overlapping periods among the sparse arcs for STSAT-2C. Therefore, we extracted a few discrete overlapped periods using several arcs as shown in Tables 6 and 7 . For the orbit overlaps, one arc is selected among the previously determined arcs presented in Table 4 . The other arc is newly determined using a day close to the first arc. To include more periods, the two orbit overlap concept displayed in Fig. 6 is utilized in the section. In the first case, the new arc is included in the previous arc, and in the second case, the two arcs have a common period in the middle of the arcs. The details of the arcs’ orbit overlaps and their post-fit residuals are presented in Table 6 . The post-fit residuals (RMS) for all arcs’ overlaps are maintained at less than 1 cm.
Arcs for orbit overlaps of STSAT-2C orbit determination (2013-2014).
PPT Slide
Lager Image
RMS: root mean square.
Orbit overlaps results of STSAT-2C orbit determination (2013-2014).
PPT Slide
Lager Image
WRMS: weighted root mean square, NP: normal point.
PPT Slide
Lager Image
Concept of orbit overlaps.
Table 7 shows the overlapped periods and their overlap results for STSAT-2C OD. The first and the last 12 hours of the overlapped periods are eliminated and each period is selected to have a minimum of one day’s overlap. The differences in the overlapped orbits are displayed with the radial, along-track, and cross-track directions. The orbit overlaps results show values varying from 1 m to 1 km. While the post-fit residuals show small differences between two overlapped arcs, the orbit overlaps yield larger variations. This inconsistency is one of the drawbacks of SLR-based OD using sparse range observations. This is a result of orbit-fits in the OD process being performed by using only few short arcs. To avoid this situation, continuous and frequent SLR tracking is essential for STSAT-2C. The differences for the radial direction have relatively small values, less than 50 m. The differences for the along-track and cross-track directions are under 600 m and 900 m, respectively. Figs. 7 and 8 show the differences in the overlapped orbits according to the day of the year in the radial direction. Each overlapped period has its own characteristics in each direction without consistent trends. The along-track and cross-track produce widely different values according to the time. Therefore, we can infer that OD for STSAT-2C using SLR data has shortcomings in the robustness of the along-track and cross-track directions. As the unstable conditions for OD of the STSAT-2C lead to inconsistent accuracy of the orbit overlaps, improvement of the sparse measurements is needed to improve the reliability of the orbit analysis.
PPT Slide
Lager Image
Orbit overlap results (overlapped arcs 1 – 7).
PPT Slide
Lager Image
Orbit overlap results (overlapped arcs 8 – 14).
In this study, orbit determination (OD) for the STSAT-2C satellite using SLR observations was successfully accomplished by a short-arc approach. OD using SLR normal point (NP) observations over one year was performed by the NASA/GSFC GEODYN II software. Variable estimation intervals for the atmospheric drag coefficients and the empirical acceleration parameters and a non-regular daily-based strategy are applied because the inaccuracy of TLE-based predictions for the STSAT-2C leads to very sparse measurement conditions. The prior value of the initial orbit was obtained from the previous TLE-based predictions through an iterative manual tuning. For the orbit quality assessment, the post-fit residuals and orbit overlaps are analyzed. The weighted root mean square values of the post-fit residuals are at a precision level of under 1 cm. The radial precision of the overlaps shows 50 m accuracy. The precision of the along-track and cross-track directions is less than 600 m and 900 m, respectively. Although the post-fit residuals of STSAT-2C OD have a cm-level precision, the orbit overlap results imply that the 3D orbit accuracy is at the m-level or km-level. This indicates that the lack of SLR observations in STSAT-2C leads to the large difference between OD precision and accuracy. To overcome this inconsistency due to sparse measurement conditions, more SLR measurements through improved orbit predictions are urgently needed. In this sense, the OD for STSAT-2C based on the SLR data is a significant step towards better precision of the orbit prediction. The study of STSAT-2C orbits under sufficient SLR observations would validate the dynamic and measurement modeling accuracy in 300-1,500 km environments.
The authors deeply appreciate the STSAT-2C mission operation and SLR support of the Satellite Technology Research Center (SaTReC) at the Korea Advanced Institute of Science and Technology (KAIST). The authors also gratefully acknowledge the International Laser Ranging Service (ILRS) network for the support and acquisition of the SLR observations. This work was supported by KASI through the SLR system development program for space geodesy funded by the Ministry of Science, ICT & Future Planning (MSIP).
Altamimi Z , Collilieux X , Legrand J , Garayt B , Boucher C 2007 ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters J. Geophys. Res. 112 B09401 -    DOI : 10.1029/2007JB004949
Altamimi Z , Collilieux X , Métivier L 2011 ITRF2008: an improved solution of the international terrestrial reference frame J. Geodesy 85 457 - 473    DOI : 10.1007/s00190-011-0444-4
Bennett JC , Sang J , Smith C , Zhang K 2015 An analysis of very shortarc orbit determination for low-Earth objects using sparse optical and laser tracking data Adv. Space Res. 55 617 - 629    DOI : 10.1016/j.asr.2014.10.020
Choi MS , Lim HC , Choi EJ , Park E , Yu SY 2014 Performance analysis of the first Korean satellite laser ranging system J. Astron. Space Sci. 31 225 - 233    DOI : 10.5140/JASS.2014.31.3.225
Hedin AE 1991 Extension of the MSIS Thermosphere model into the middle and lower atmosphere J. Geophys. Res. 96 1159 - 1172    DOI : 10.1029/90JA02125
Jagoda M , Rutkowska M 2013 Estimation of the Love and Shida numbers: h2, l2, using SLR data for the low satellites Adv. Space Res. 52 633 - 638    DOI : 10.1016/j.asr.2013.04.018
Jeon HS , Cho S , Kwak YS , Chung JK , Park JU 2011 Mass density of the upper atmosphere derived from Starlette's Precise Orbit Determination with Satellite Laser Ranging Astrophys. Space Sci. 332 341 - 351    DOI : 10.1007/s10509-010-0528-2
Jo JH , Park IK , Lim HC , Seo YK , Yim HS 2011 The design concept of the first mobile satellite laser ranging system (ARGO-M) in Korea J. Astron. Space Sci. 28 93 - 102    DOI : 10.5140/JASS.2011.28.1.093
Kang KI , Lim CW , Shin HJ , Lee KW , Lee JC Operation results of STSAT-2C satellite KSAS Proceedings of 2014 KSAS Spring Conference Wonju, Korea 17-18 April 2014
Kim JH , Park SY , Kim YR , Park ES , Jo JH 2011 Analysis of scaling parameters of the batch unscented transformation for precision orbit determination using satellite laser ranging data J. Astron. Space Sci 28 183 - 192    DOI : 10.5140/JASS.2011.28.3.183
Kim YR , Park SY , Park ES , Lim HC 2012 Preliminary products of precise orbital determination using satellite laser ranging observations for ILRS AAC J. Astron.Space Sci. 29 275 - 285    DOI : 10.5140/JASS.2012.29.3.275
Kim YR , Park E , Lim HC 2013 Orbit determination and analysis for STSAT-2C ILRS Proceedings of the 18th International Workshop on Laser Ranging Fujiyoshida, Japan 11-15 November 2013
Kim YR , Park E , Oh HJ , Park SY , Lim HC 2013 Precise orbital and geodetic parameter estimation using SLR observations for ILRS AAC J. Astron. Space Sci. 30 269 - 277    DOI : 10.5140/JASS.2013.30.4.269
Kim YR , Park E , Lim HC 2014 Precise orbit determination for STSAT-2C and KOMPSAT-5 with satellite laser ranging KSAS Wonju, Korea Proceedings of 2014 KSAS Spring Conference 16-18 April 2014
Kim YR , Park E , Choi EJ , Park SY , Park C 2014 Precise orbit determination using the batch filter based on particle filtering with genetic resampling approach Adv. Space Res 54 998 - 1007    DOI : 10.1016/j.asr.2014.06.001
Lee DJ , Alfriend KT 2007 Sigma Point Filtering for Sequential Orbit Estimation and Prediction J. Spacecraft Rockets 44 388 - 398    DOI : 10.2514/1.20702
Lejba P , Schillak S , Wnuk E 2007 Determination of orbits and SLR stations' coordinates on the basis of laser observations of the satellites Starlette and Stella Adv. Space Res 40 143 - 149    DOI : 10.1016/j.asr.2007.01.067
Lejba P , Schillak S 2011 Determination of station positions and velocities from laser ranging observations to Ajisai, Starlette and Stella satellites Adv. Space Res. 47 654 - 662    DOI : 10.1016/j.asr.2010.10.013
Lim HC , Seo YK , Na JK , Bang SC , Lee JY 2010 Tracking capability analysis of ARGO-M satellite laser ranging system for STSAT-2 and KOMPSAT-5 J. Astron. Space Sci. 27 245 - 252    DOI : 10.5140/JASS.2010.27.3.2457.3.245
Lim HC , Bang SC , Yu SY , Seo YK , Park ES 2011 Study on the optoelectronic design for Korean mobile satellite laser ranging system J. Astron. Space Sci. 28 155 - 162    DOI : 10.5140/JASS.2011.28.2.155
Mathews PM , Herring TA , Buffett BA 2002 Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior J. Geophys. Res. 107 2068 -    DOI : 10.1029/2001JB000390
McCarthy DD , Petit G 2004 IERS conventions (2003)
Mendes VB , Prates G , Pavlis EC , Pavlis DE , Langley RB 2002 Improved mapping functions for atmospheric refraction correction in SLR Geophys. Res. Lett 29 1414 -    DOI : 10.1029/2001GL014394
Mendes VB , Pavlis EC 2004 High-accuracy zenith delay prediction at optical wavelengths Geophys. Res. Lett. 31 L14602 -    DOI : 10.1029/2004GL020308
Nah JK , Jang JG , Jang BH , Han IW , Han JY 2013 Development of optical system for ARGO-M J. Astron. Space Sci. 30 49 - 58    DOI : 10.5140/JASS.2013.30.1.049
Park E , Yu SY , Lim HC , Bang SC , Seo YK 2012 Status and progress of ARGO-M system development Publ. Korean Astron. Soc 27 49 - 59    DOI : 10.5303/PKAS.2012.27.3.049
Park ES , Park SY , Roh KM , Choi KH 2010 Satellite orbit determination using a batch filter based on the unscented transformation Aerosp. Sci. Technol 14 387 - 396    DOI : 10.1016/j.ast.2010.03.007
Pavlis DE , Luo S , Dahiroc P 1998 GEODYN II system description, Hughes STX Contractor Report Greenbelt, Maryland
Pearlman MR , Degnan JJ , Bosworth JM 2002 The international laser ranging service Adv. Space Res. 30 135 - 143    DOI : 10.1016/S0273-1177(02)00277-6
Ray RD 1999 A global ocean tide model from TOPEX/POSEIDON altimetry: GOT99.2, NASA Goddard Space Flight Center technical memorandum
Sang J , Bennett JC 2014 Achievable debris orbit prediction accuracy using laser ranging data from a single station Adv. Space Res. 54 119 - 124    DOI : 10.1016/j.asr.2014.03.012
Seo YK , Lim HC , Rew DY , Jo JH , Park JU 2010 Study on the preliminary design of ARGO-M operation system J. Astron. Space Sci 27 393 - 400    DOI : 10.5140/JASS.2010.27.4.393
Standish EM , Newhall XX , Williams JG , Folkner WM 1995 JPL planetary and Lunar ephemerides
Tapley BD , Ries JC , Bettadpur S , Chambers D , Cheng M 2005 GGM02 - An improved Earth gravity field model from GRACE J. Geodesy 79 467 - 478    DOI : 10.1007/s00190-005-0480-z