Transcript Validation of SGP4 and IS-GPS-200D Against GPS Precise

Validation of SGP4 and IS-GPS-200D
Against GPS Precise Ephemerides
T.S. Kelso
2007 January 29
Overview
• Introduction
• Objectives
• Test & Truth Data
• Methodology & Results
• Conclusions
• Future Research
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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
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Objectives
• Examine COVGEN approach
– Test original assumptions
– Use high-precision ephemerides (GPS)
– Ensure all test data is publicly available
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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
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Test Data
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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
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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)
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Results: Almanac Comparison
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Results: Almanac Comparison
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Results: Almanac Comparison
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Results: Almanac Comparison
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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
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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
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Results: TLE Comparison
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Results: TLE Comparison
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Results: TLE Comparison
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Results: TLE Comparison
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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
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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
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Methodology: TLE Consistency
• Compare each pair of TLEs
–
–
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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
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Results: TLE Consistency
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Results: TLE Consistency
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Results: TLE Consistency
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Results: TLE Consistency
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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
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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
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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
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Questions?