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Improved Ssa Through Orbit Determination of Two- Line Element Sets

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Improved Ssa Through Orbit Determination of Two- Line Element Sets 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) 250.00 SURSDJDWLRQRIDVLQJOH7/(DUHVKRZQ6FDOHVEHWZHHQ 33331 WKHJUDSKVDUHQRWWKHVDPH6DWHOOLWHVDUHIURPWKHWRS 200.00 *HRH\H'HOWD5%-DVRQDQG $MDVDL7KH2'HSKHPHULVLVQRWDOZD\VWKHEHVW ) m 150.00 RIWHQ FORVH RU DO LWWOH EHWWHU DQG WKH QXPEHU RI 7/(V k e ( c Predicted vs TLE splice VHHPHGWRDIIHFWWKHILW UHVXOWLQJLQVPDOOHUXQFHUWDLQW\ ren e ff i 100.00 GXULQJ WKH 2' SURFHVVLQJ ,I WKH 2' SURFHVVLQJ D \LHOGHGEHWWHUUHVXOWVLQDOOFDVHVWKHEOXHOLQHVKRXOG 50.00 OD vs TLE splice EHORZHUWKDQWKHUHGOLQHIRUDOOWKHSUHGLFWHGFDVHV 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. D 3.00 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 m 1.50 k 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.
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