Validation of SGP 4 and ISGPS200 D Against

Validation of SGP 4 and IS-GPS-200 D Against GPS Precise Ephemerides T. S. Kelso 2007 January 29

Overview • Introduction • Objectives • Test & Truth Data • Methodology & Results • Conclusions • Future Research Pg 2 of 29

Introduction • TLEs are the only source of full-catalog elements • TLEs do not come with covariance data • Several past attempts to estimate covariance – MAESTRO • Used limited-access observations • Same observations used to create TLEs – COVGEN • Performed TLE consistency check with publicly available data • Incorrectly assumed errors were unbiased and independent of propagation direction Pg 3 of 29

Objectives • Examine COVGEN approach – Test original assumptions – Use high-precision ephemerides (GPS) – Ensure all test data is publicly available Pg 4 of 29

Test Data • Used only operational GPS satellites • Eliminated satellites with extended outages • Selected period where remaining satellites were outage free • Days 150 -210 of 2006 selected – Obtained all SEM almanacs for this period – Obtained all TLEs for selected satellites for this period – All data publicly available from Celes. Trak Pg 5 of 29

Test Data Pg 6 of 29

Truth Data • Used GPS Precise Ephemerides from NGA – ECEF position and velocity at 15 -min intervals – Accurate to better than 25 cm • Agreement with IGS data was 16. 8 cm ± 1. 1 cm (1σ) • IGS data advertised as accurate to < 5 cm – Data publicly available • http: //earth-info. nga. mil/Gand. G/sathtml/PEexe. html Pg 7 of 29

Methodology: Almanac Comparison • Compare SEM almanacs to precise ephemerides – Propagate IAW IS-GPS-200 D to same time points as precise ephemerides – Precise ephemerides used as reference – RIC coordinates of almanac position error calculated – Collected RIC error as a function of propagation interval • Interval limited to ± 15 days from epoch (TOA) Pg 8 of 29

Results: Almanac Comparison Pg 9 of 29

Results: Almanac Comparison Pg 10 of 29

Results: Almanac Comparison Pg 11 of 29

Results: Almanac Comparison Pg 12 of 29

Results: Almanac Comparison • In-track error dominant • Radial and cross-track errors not significantly biased • In-track error showed a range of biases • Errors symmetric to propagation direction • Errors grow as a function of propagation interval Pg 13 of 29

Methodology: TLE Comparison • Compare TLEs to precise ephemerides – Propagate IAW SGP 4 to same time points as precise ephemerides – Precise ephemerides used as reference – RIC coordinates of TLE position error calculated – Collected RIC error as a function of propagation interval • Interval limited to ± 15 days from TLE epoch Pg 14 of 29

Results: TLE Comparison Pg 15 of 29

Results: TLE Comparison Pg 16 of 29

Results: TLE Comparison Pg 17 of 29

Results: TLE Comparison Pg 18 of 29

Results: TLE Comparison • In-track error dominant • Significant biases in in-track error • Errors clearly not symmetric with respect to propagation direction • Biases increase with propagation direction • Variances often nearly static Pg 19 of 29

Results: Almanac & TLE Comparison • Error profiles significantly different – Maximum errors comparable over ± 15 day interval – Minimum 1σ almanac error smaller than minimum 1σ TLE error – Minimum almanac error occurred at 0 propagation time – Minimum TLE error occurred prior to TLE epoch – Almanac errors only moderately biased – TLE errors significantly biased – Almanac errors symmetric – TLE errors asymmetric Pg 20 of 29

Methodology: TLE Consistency • Compare each pair of TLEs – – TLEi propagated tj-ti and compared to TLEj at tj TLEj propagated ti-tj and compared to TLEi at ti RIC position difference calculated relative to reference Collected RIC difference as a function of propagation interval • Interval limited to ± 15 days from reference TLE epoch Pg 21 of 29

Results: TLE Consistency Pg 22 of 29

Results: TLE Consistency Pg 23 of 29

Results: TLE Consistency Pg 24 of 29

Results: TLE Consistency Pg 25 of 29

Results: TLE Consistency • Good overall match to TLE comparison errors • Artificial pinching at 0 propagation time • Slight skewing due to minimum error not being at 0 propagation time Pg 26 of 29

Conclusions • Almanac and TLE prediction errors comparable – Error profiles differ significantly • TLE consistency analysis does reasonably approximate true error characteristics • Significant biases in TLE errors can lead to an overestimation in total error • Removing bias could improve prediction • Error characteristics differ significantly within orbit class Pg 27 of 29

Future Research • Use Kalman filter to: – Estimate and eliminate bias while calculating covariance – Regenerate improved TLE • Allows use of improved data in existing software • Provides covariance for uncertainty estimation • Additionally, perform analysis for LEO and GEO satellites to confirm results of this study Pg 28 of 29

Questions?