1. Validation of SGP4 and IS-GPS-200D Against GPS Precise Ephemerides T.S. Kelso 2007 January 29

2. Overview • Introduction • Objectives • Test & Truth Data • Methodology & Results • Conclusions • Future Research

3. 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

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

5. 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 CelesTrak

6. Test Data

7. 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/GandG/sathtml/PEexe.html

8. Methodology: Almanac Comparison • Compare SEM almanacs to precise ephemerides • Propagate IAW IS-GPS-200D 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)

9. Results: Almanac Comparison

10. Results: Almanac Comparison

11. Results: Almanac Comparison

12. Results: Almanac Comparison

13. 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

14. Methodology: TLE Comparison • Compare TLEs to precise ephemerides • Propagate IAW SGP4 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

15. Results: TLE Comparison

16. Results: TLE Comparison

17. Results: TLE Comparison

18. Results: TLE Comparison

19. 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

20. 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

21. 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

22. Results: TLE Consistency

23. Results: TLE Consistency

24. Results: TLE Consistency

25. Results: TLE Consistency

26. 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

27. 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

28. 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

29. Questions?