IMPROVED SSA THROUGH ORBIT DETERMINATION OF TWO- LINE ELEMENT SETS

David A. Vallado(1), Benjamin Bastida Virgili (2), Tim Flohrer(2)

 &HQWHUIRU6SDFH6WDQGDUGVDQG,QQRYDWLRQ$QDO\WLFDO*UDSKLFV,QF&DPSXV'U6XLWH&RORUDGR 6SULQJV&RORUDGR(PDLOGYDOODGR#DJLFRP  (6$(62&6SDFH'HEULV2IILFH5REHUW%RVFK6WU'DUPVWDGW*HUPDQ\(PDLO ^EEDVWLGDWIORKUHU`#HVDLQW  ABSTRACT known and we gather information from several sources for this discussion. Essentially, the observations are Orbit determination processing of two-line element collected several times a day at the Joint Space (TLE) sets to extract additional orbital accuracy has Operations Center (JSPOC) operated by the US Air been studied for several years. Various approaches have Force Space Command (AFSPC). Once the claimed success, and full catalog processing is observations pass through an initial association and conducted at ESA. We extend the existing analyses and verification pass, they are passed to the Orbit conduct detailed evaluations of alternatives for the OD determination operation. OD is conducted on the processing. This includes examination of the number of observations, once using SGP4, and once using TLEs used, method of splicing ephemerides, force numerical techniques. Periodically, about every 8 hours, models, fit spans, satellite category, and if the satellite is a new snapshot of the system is extracted and the classified as maneuverable. element sets begin the process to arrive at www.space- track.org for dissemination to the public. This operation 1 INTRODUCTION inserts a time delay for use of the TLEs even if a user is able to immediately download and use each new TLE. The Two-Line Elements (TLEs) that result from The Celestrak site mirrors these timing updates with a Simplified General Perturbation 4 (SGP4) orbit short additional (minutes) delay. determination allow rapid, modestly accurate propagation of space object motion. As the only openly Public release of the TLE catalog has occurred for many available, comprehensive catalog of space objects, the years, first through NASA, and more recently through U.S. TLE database supports many technical analyses. the www.space-track.org web site. In addition, However, it is generally well known that the TLEs are Celestrak (http://www.celestrak.com/) has maintained a of limited accuracy, and often contain mis-tagged and website for obtaining the TLE catalog for several missed maneuver information. decades. The catalogs provided by these sources contain only objects deemed unclassified by AFSPC. Other The Simplified General Perturbations (SGP) model catalogs exist, but are not as comprehensive for all series began development in the 1960s, and became orbital regimes and types. All data for this paper comes operational in the early 1970s. The development from the publically available http://www.celestrak.com/ culminated in Simplified General Perturbations-4 website. (SGP4), and although the name is similar, the mathematical technique is very different from the 1.1 Problem Statement original SGP technique. Several papers trace the history of SGP4 including [13] in 2006 with a comprehensive The fundamental limitations of TLEs are the facts that update to the SGP4 computer code, with test cases, and they are of limited accuracy, and that they do not come analysis. with a covariance, making it very difficult to use in practical operations such as conjunction analyses. There Over time, there have been numerous studies of TLE are only two general solutions: processing the TLEs to limitations, methods for accuracy improvement, for try and extract additional information, and fusing TLEs generating a covariance matrix, and various other with independent data. Both approaches can use Orbit operational applications. Ref. [12] summarized much of Determination (OD), but the first solution has more the literature that has accumulated over the years with numerous approaches. The latter approach is the best respect to TLEs, their use and accuracy. Attention was opportunity to determine accuracy and covariance paid to the OD processing of TLE information, and information, but it’s also the most difficult as additional initial runs were made to assess the viability of this observational data must be available. approach. This paper extends that analysis and performs additional tests against a variety of orbital classes. We extend existing analyses and conduct detailed evaluations of alternatives for the OD processing. This The exact process for updating the TLEs is not well

______Proc. ‘6th European Conference on Space Debris’ Darmstadt, Germany, 22–25 April 2013 (ESA SP-723, August 2013)

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Ref. [12] conducted some preliminary tests to determine 0.00 11/7/11 11/9/11 11/11/11 11/13/11 11/15/11 11/17/11 11/19/11 11/21/11 11/23/11 11/25/11 the effect of numerically processing the TLE spliced Date orbits. The spliced orbits “should” most closely 8.00 7616 approximate the truth, so both the numerically 7.00 generated OD ephemeris and a simple TLE predicted ephemeris near the end OD time were compared to the 6.00 longer TLE spliced ephemeris. Figure 3 shows their

) 5.00

m results. Notice that while there is sometimes an k e (

c Predicted vs TLE splice 4.00 improvement, not all cases were better. The initial ren e ff i uncertainty was set to 1 km.

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2.00 We mentioned the backwards SGP4 propagation here, OD vs TLE splice but it could be forward from each TLE epoch, or 1.00 midpoint as well. The idea is that we are comparing to

0.00 11/7/11 11/9/11 11/11/11 11/13/11 11/15/11 11/17/11 11/19/11 11/21/11 11/23/11 11/25/11 future TLE’s that may or may not all have the same Date amount of error in them.

2.50 Because a Kalman filter OD process was used for some 33105 initial tests, the only parameter that seemed to make a

2.00 difference in the processing (other than the results shown later in this paper for Batch Least Squares

) techniques), was the initial assumed uncertainty. Using

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e ( a 5 km as the initial uncertainty, we found the c Predicted vs TLE splice ren e OD vs TLE splice comparisons in Figure 3. ff

i 1.00 D These results seemed to indicate that calibration

0.50 satellites (Jason 2 and Ajasai) might perform better with the OD processing. This was an initial impetus to

0.00 exploring various OD processing alternatives in the 11/7/11 11/9/11 11/11/11 11/13/11 11/15/11 11/17/11 11/19/11 11/21/11 11/23/11 11/25/11 Date remainder of the paper.

3.00 16908 2 PROCESS OUTLINE

2.50 2.1 Develop orbital classes from which to pick 2.00 candidate satellites ) m k e (

c Predicted vs TLE splice 1.50 Selecting orbital classes let us examine if there is an ren e OD vs TLE splice ff

i effect of certain orbital classes on the accuracies of the D 1.00 TLEs, and therefore, of the ability to improve the OD through processing the TLE information. The ESA 0.50 Database and Information System Characterizing Objects in Space (DISCOS) system categorizes 0.00 11/7/11 11/9/11 11/11/11 11/13/11 11/15/11 11/17/11 11/19/11 11/21/11 11/23/11 11/25/11 satellites and we choose the following categories. Data Date is as of 2013-02-27 and the total catalog is about 17000 )LJXUH  'LIIHUHQFH 3ORWV IRU 6SOLFHG 7/( (SKHPHULV objects. Our selections represent about 74% of the DQG2'DQG3UHGLFWLRQ  NP LQLWLDO XQFHUWDLQW\  7KH catalog, but could have been conducted for the whole WHVWVIRUFRPSDULQJDVSOLFHG7/(WRDQ2'RIDSRUWLRQ catalog with slight adjustments to the setup and RI WKH VSOLFHG HSKHPHULV DQGW KH FRPSDULVRQ ZLWK D additional time. Orbital Categories Eccentiricity / Mean Altitude km Number in % of Category Name Inclination (perigee/apogee) Catalog catalog Low Near Earth LEO Circular 0.00 < e < 0.05 0 < alt < 575 400 2.35 Medium Near Earth LEO Circular 0.00 < e < 0.05 575 < alt < 1000 6564 38.61 High Near Earth LEO Circulr 0.00 < e < 0.05 1000 < alt < 2500 2147 12.63 Near Earth LEO Eccentric 0.05 < e < 1.00 0 < alt < 2500 623 3.66 Navigation NSO Satellites 50 < i < 70 18100-24300 / 18100-24300 253 1.49 GTO GEO Transfer 0 < i < 55 100-2000 / 34786-36786 232 1.36 MEO Mid Earth 0 < i < 180 2000-34786 / 2000-34786 200 1.18 HEO Highly Elliptical 0 < i < 180 100-34586 / 38586-90000000 895 5.26 GEO Geosynchronous 0 < i < 70 32986-38586 / 32986-38586 1176 6.92 High Altitude HAO Above GEO 0.0 < i < 180 38586-90000000 / 38586-90000000 54 0.32

2.3.2 OD Force Models 2.2 Consider the following sub-categories – active (maneuvering), calibration, debris We selected various force models to use with each orbital class. Atmospheric drag presented some options. JSPOC tracks calibration satellites differently from DISCOS assumes a standard mass and area. The BStar other objects because additional observations are needed term could approximate a BC, but there is a large to produce the higher accuracy orbits. Likewise, actively variability because the BStar term soaks up the error maneuvering satellites receive significantly more from reduced force models, limited tracking, etc. We tracking than debris objects because if the time between opted to use area and mass from DISCOS and the observations encompasses one or more maneuvers, the available atmospheric drag models (MSIS-90, and satellite may become lost and present challenges to NRLMSIS-00). Although we performed analyses in the recover and re-establish the orbit. (NB: Some efforts past, the goal of doing this operation at the current time exist to determining maneuvers [9]. Detecting would necessitate using predicted satellite indices, maneuvers lets us classify active/non-active objects either from NOAA/NGDC, or ESA. This prohibits (within certain limits, of course) for LEO. For GEO we using the Jacchia-Bowman atmospheric models because used the list of controlled objects as per the ESA there is about a 1 month lag in the delivery of the Classification of Geosynchronous Objects covering appropriate indices. The force models did not seem to 2012 (Issue 15, T.Flohrer, 2013). Ref. [6] presented make any difference in the initial runs. We used a 30 × results from a Matlab evaluation of looking at TLEs to 30 JGM3 gravity model in all cases except GEO and try and understand maneuvers. His results were HAO where we used an 8 × 8 field. NRLMSIS-00 was reasonable, although they highlighted the wide used for all orbits affected by atmospheric drag, and variability of the TLEs.) For the remaining categories, third body and solar radiation pressure were used for there is an associated decrease in accuracy as the higher altitude orbits. number of observations decreases. 2.3.3 OD Processing fit span 2.3 Study the effect of – The observations here are the TLEs, and the associated 2.3.1 How to form the Reference Orbit ephemerides derived from them. Existing studies have generally used 1 day ephemerides for all orbital classes. Forming the reference ephemeris (forward splicing, However, common practice uses several fit spans for mid-point, backwards) can assume many forms. A small different orbital classes. This implies processing a day study was conducted to determine the differences in the or so for LEO orbits, and a week or more for GEOs. We approaches, and which method could produce better used one day for LEOs, and one week for all others. results. We concluded that the backwards ephemeris produced slightly better results.

x Force models for various orbital classes added only a Revelin. (2007). Improvement of the Two-Line small effect. Element Accuracy Assessment Based on a Mixture of Gaussian Laws. 3DSHU$$6SUHVHQWHGDW We also determined some new results. WKH$$6$,$$$VWURG\QDPLFV6SHFLDOLVW&RQIHUHQFH 0DFNLQDF0,. x The largest uncertainty in virtually all cases was in 4. Flohrer, T., et al. (2009). Improving ESA’S the along-track direction. The notable exception was Collision Risk Estimates by an Assessment of the for GEO orbits where the radial component was very TLE Orbit Errors of the US SSN Catalogue. 3DSHU large. 6 SUHVHQWHG DW WKH WK (XURSHDQ 6SDFH 'HEULV x HEO and GTO orbits consistently experienced the &RQIHUHQFH 'DUPVWDGW *HUPDQ\ 0 DUFK ±  largest uncertainty. Next in decreasing uncertainty $SULO. were GEO and MEO, and then the NSO and all the LEO orbits. 5. Flohrer, T., H. Krag, and H. Klinkrad. (2008). x LEO orbits seemed to have about a 1 km epoch Assessment and Categorization of TLE Orbit Errors uncertainty for all configurations. for the US SSN Catalogue. 3DSHUSUHVHQWHGDWWKH x HEO and GTO orbits showed about a 6-8 km epoch $0267HFKQLFDO&RQIHUHQFH0DXL+,. uncertainty, GEO orbits were about 2-4 km, MEO 6. Kelecy, T., et al. (2007). Satellite Maneuver were about 1-2 km and NSO were about 1 km. Detection Using Two-line Element (TLE) Data. x Forming the reference orbit backwards does appear 3DSHU SUHVHQWHG DW WKH $026 7HFKQLFDO to improve results. The method of forming the TLE &RQIHUHQFH0DXL+, ephemeris is important for OD tests because the greatest accuracy for a TLE is generally best before  Legendre, P., B. Deguine, R. Garmier, and B. the TLE epoch. Revelin. (2006). Two-Line Element Accuracy x Force models, specifically the atmospheric model, Assessment Based on a Mixture of Gaussian Laws. do not seem to make much difference. At the level of 3DSHU $,$$  SUHVHQWHG DW WKH accuracy of the TLE, it is probably not observable. $VWURG\QDPLFV6SHFLDOLVW&RQIHUHQFH$XJXVW .H\VWRQH&2 x Fit spans likely did make a difference, since we were only using 1 TLE for the whole time. Time did not 8. Legendre, P., R. Garmier, G. Prat, B. Revelin, and S. permit tests of splicing TLEs when forming the Delavault. (2008). Improvement of the Two-Line reference OD ephemeris. The 7 day fit span was Element Accuracy Assessment Based on a Mixture probably also responsible for the larger uncertainty of Gaussian Laws $GY $VWURQDXW 6FL, 129(3), in non-LEO categories compared to results in [4]. 2189-2207. x Object type (category, maneuverable, calibration, 9. Lemmens, S. (2012). Non-natural event detection etc.) seemed to be a factor in some cases and should method for satellites in Low Earth Orbit. 3DSHU probably be kept as a part of the standard treatment )SUHVHQWHGDWWKHWK&263$56FLHQWLILF in processing the catalog data. $VVHPEO\-XO\0\VRUH,QGLD x Object size seemed to be a factor, but it’s also possible that this observation is also affected by the 10. Levit, C., and W. Marshall. (2011). Improved orbit orbital regimes within the various object size predictions using two-line elements. $GY 6S 5HV. categories. 47, 1107-. 11. Muldoon, A. R., et al. (2009). Improved orbital 5 REFERENCES debris trajectory estimation based on sequential TLE 1. Cappellucci, D. A. (2005). Special Perturbations to Processing. 3DSHU ,$&$ SUHVHQWHG DW WKH General Perturbations Extrapolation Differential WK,QWHUQDWLRQDO$VWURQDXWLFDO&RQJUHVV'DHMHRQ Correction in Satellite Catalog Maintenance. 3DSHU 6RXWK.RUHD. $$6SUHVHQWHGDWWKH$$6$,$$6SDFHIOLJKW 12. Vallado, D. A., and P. Cefola. (2012). Two-Line 0HFKDQLFV &RQIHUHQFH -DQXDU\   Element Sets – Practice and Use. 3DSHU ,$& &RSSHU0RXQWDLQ&2. & SUHVHQWHG DW WKH UG ,QWHUQDWLRQDO 2. Delavault, S. (2008). Improvement of the TLE $VWURQDXWLFDO&RQJUHVV2FWREHU1DSOHV Accuracy Model Based on a Gaussian Mixture ,WDO\ Depending on the Propagation Duration. 3DSHU 13. Vallado, D. A., et al. (2006). Revisiting Spacetrack $,$$ SUHVHQWHG DW WKH $,$$$$6 Report #3. 3DSHU$,$$SUHVHQWHGDWWKH $VWURG\QDPLFV6SHFLDOLVW&RQIHUHQFH$XJXVW $,$$$$6 $VWURG\QDPLFV 6SHFLDOLVW &RQIHUHQFH +RQROXOX+,. $XJXVW.H\VWRQH&2 3. Delavault, S., P. Legendre, R. Garmier, and B.