1. Sensitivity of Orbit Predictions to Density Variability
Rodney L. Anderson
George H. Born
Jeffrey M. Forbes
Oct , 2008
MURI Meeting (Boulder, CO)

2. Where should modeling efforts focus to improve orbit prediction?
Horizontal density scales
Type (shape) of density
variations
Magnitude of density
Phase errors (errors in timing)
Significant Prediction Errors
(over 24 hours)
Oct , 2008
Boulder, Colorado

3. Method Integrate two trajectories from same I.C.s in 2-Body Problem
One with “Truth”
density profile
One with alternate
Compare position (RIC) diff. after t
All results are for the CHAMP S/C
Oct , 2008
Boulder, Colorado

4. Prediction Differences using CHAMP & Model Data (2003)
Total Difference
In-track Difference
Oct , 2008
Boulder, Colorado

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?
Oct , 2008
Boulder, Colorado

6. Sine Wave (1 cycle) Position Difference Density over Time
Oct , 2008
Boulder, Colorado

7. Functions Give Similar Results (1 Cycle Cases)
Diff.max  1.3 m
Diff.max  1.4 m
Diff.max  1.55 m
Oct , 2008
Boulder, Colorado

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)
Oct , 2008
Boulder, Colorado

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
Oct , 2008
Boulder, Colorado

10. Smoothed Data (30 min. Interval)
(Day 324 of 2003)
Oct , 2008
Boulder, Colorado

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. = m
Oct , 2008
Boulder, Colorado

12. Comparison over 2003 (24 hour, 30 minute case)
Mean = 6.21 m
Max. = m
Min. = 0.24 m
Oct , 2008
Boulder, Colorado

13. Histogram 30 minute average
2003
2007
Oct , 2008
Boulder, Colorado

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
Oct , 2008
Boulder, Colorado

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
Oct , 2008
Boulder, Colorado