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 www.agi.com

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

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

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

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

Test Data

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

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)

Results: Almanac Comparison

Results: Almanac Comparison

Results: Almanac Comparison

Results: Almanac Comparison

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

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

Results: TLE Comparison

Results: TLE Comparison

Results: TLE Comparison

Results: TLE Comparison

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

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

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

Results: TLE Consistency

Results: TLE Consistency

Results: TLE Consistency

Results: TLE Consistency

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

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

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

Questions?