1. Validation of SGP4 and IS-GPS-200D Against GPS Precise Ephemerides
AGI User's Conference
October 2005
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 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

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?