Sensitivity of Orbit Predictions to Density Variability

1
Sensitivity of Orbit Predictions to Density
Variability

• Rodney L. Anderson
• George H. Born
• Jeffrey M. Forbes

2
Where should modeling efforts focus to improve
orbit prediction?

• Horizontal density scales
• Type (shape) of density
• variations
• Magnitude of density
• variations
• Phase errors (errors in timing)

Significant Prediction Errors (over 24 hours)
3
Method

• Integrate two trajectories from
• same I.C.s in 2-Body Problem
• One with Truth
• density profile
• One with alternate
• density profile
• Compare position (RIC) diff. after ?t
• All results are for the CHAMP S/C

4
Prediction Differences using CHAMP Model Data
(2003)
Total Difference
In-track Difference
5
Isolate Effect of Different Horizontal Density
Scales

• Determine component of orbit prediction model
  error caused by different horizontal density
  scales
• Determine error introduced by missing a single
  wavelength (scale)
• Integrate one trajectory with nominal density
• Integrate one trajectory with density
  perturbation function (25 amplitude)
• Does the type of function matter?
• Which scales are most important?

6
Sine Wave (1 cycle)
Position Difference
Density over Time
7
Functions Give Similar Results
(1 Cycle Cases)
Diff.max ? 1.3 m
Diff.max ? 1.4 m
Diff.max ? 1.55 m
8
One, Two Three Day Integration Times
Diff.max ? 3 m
Diff.max ? 6 m
Diff.max ? 9 m
In-track Differences
24 hours
48 hours
72 hours

• Orbit differences with 10,000 km wavelength
  increase by about 3 m per day (CHAMP S/C)

9
Predictions with Measured vs. Smoothed CHAMP Data

• What happens if multiple wavelengths are ignored?
• Use smoothing or averaging over different time
  intervals
• Raw data
• 6 minute averaging
• 30 minute averaging
• Reduces power of shorter wavelengths

10
Smoothed Data (30 min. Interval)
(Day 324 of 2003)
11
Comparison over 2003(24 hour, 6 minute case)

• Differences are primarily in the in-track
  direction
• Mean 0.63 m
• Max. 10.7 m
• Min. 0.019 m

12
Comparison over 2003(24 hour, 30 minute case)

• Mean 6.21 m
• Max. 56.21 m
• Min. 0.24 m

13
Histogram 30 minute average
2003
2007
14
Conclusions

• Single wavelength perturbations can give meter
  level errors
• Neglecting density scales below
• 1000 km gives meter level errors (for CHAMP)
• 8000 km gives errors on the order of 10s of
  meters (for CHAMP)
• Errors small but significant enough to take into
  account in models

15
Current Status

• Examining contribution of different components to
  error
• Additional altitudes
• Eccentric orbits
• Perturbations that die off
• Different density altitudes
• In-phase and out-of-phase perturbations
• Time delay (phase) issues
• Implementing density models in GIPSY-OASIS
• Including additional satellites