Implications of Errors in Density Response Time Delay on Satellite Prediction Error

1. Implications of Errors in Density Response Time Delay on Satellite Prediction Error Rodney L. Anderson and Christian P. Guignet October 28, 2010, NADIR MURI meeting

2. Introduction • Orbit prediction relies on the prediction of density from atmospheric models. • Model predictions can sometimes be inaccurate, especially during magnetic storms. • A previous study by Forbes showed a premature increase in density predicted by a model caused a as large an error as predicting no variation. • J. M. Forbes, “Low-Altitude Satellite Ephemeris Prediction” • Delays of 1-4 hours are not uncommon. • This study seeks to quantify these errors by examining time delays in the density model.

3. Introduction • A simple two body model was used for the spacecraft integration. • Acceleration due to drag: • Velocity relative to the atmosphere:

4. Introduction • Atmospheric model used: NRLMSISE-00 • Model densities were computed using values provided from the CHAMP spacecraft. • Densities obtained from observations by the CHAMP satellite were used as truth. • Density data used spans 2003 through 2008. • CHAMP was in a low Earth orbit with inclination of approximately 87° and initial altitude of 457 km. http://science.nasa.gov/media/medialibrary/2010/03/31/champ.jpeg

5. Outline • Introduction • Storms in data • Perfect model comparisons • Delays in model data • Delays in real, smoothed data

6. Storms in Data • Multiple storms are examined to determine possible delays between model prediction and truth density. • The model densities are computed using the CHAMP altitude and position. • A 701 point smoothing is then used to observe the peaks in the densities.

7. October, 2003 – 1.5 hours • November, 2003 – 1.68 hours • July, 2004 – 3.15 hours • November, 2004 – 3.18 hours • Used in delayed orbit study.

8. Outline • Introduction • Storms in data • Perfect model comparisons • Delays in model data • Delays in real, smoothed data

9. Perfect Model Comparison • A spacecraft is integrated twice: • First orbit uses model densities. • Second uses CHAMP densities. • Initial 400 km, polar orbit. • 24 hour integrations are performed over years 2003-2008. • Results are given in the Radial, In-track, and Cross-track directions.

11. Perfect Model Comparison • Largest differences occur in the in-track direction. • Errors are in agreement with previous study by Anderson et al. • R. L. Anderson, G. H. Born, and J. M. Forbes, “Sensitivity of Orbit Predictions to Density Variability” • Differences are largest during more active times.

12. Outline • Introduction • Storms in data • Perfect model comparisons • Delays in model data • Delays in real, smoothed data

13. Delays in Model Data • How can delays in predicting the density effect a satellite’s orbit? • Delays were introduced into the model by altering the inputs by a number of hours. • 1, 2, and 3 hour delays are examined. • A spacecraft was again integrated as before: • Once using perfect model inputs. • A second time using the delayed inputs. • Simulation performed for the year 2003.

14. One hour delay • A delay of one hour is added to the model inputs. • Largest difference again occurs in the in-track direction • Cross-track difference is significantly less than a meter.

15. Two hour delay • The simulation was performed using a 2 hour delay. • Same general behavior was observed with larger magnitudes.

16. Three hour delay • Behavior similar to 1 and 2 hour delays. • The large spikes in the orbit differences occur during large storms.

17. Delays in Model Data • Very large errors can occur (thousands of meters). Mean values of Orbit differences • Mean errors are significant as well (tens of meters).

18. Outline • Introduction • Storms in data • Perfect model comparisons • Delays in model data • Delays in real, smoothed data

19. Delays in Real, Smoothed Data • Quantify the effect of the time delay on orbit prediction using real-world density fluctuations. • Perform the same simulation before using different densities: • First orbit integrated using smoothed CHAMP density. • 701 point smoothing used to remove short term variations. • Second orbit integrated using same density delayed by a specified amount of time. • Simulation performed over 2003-2008

20. One hour delay

21. Two hour delay

22. Three hour delay • Orbit differences in this simulation are similar to those seen in the model simulation. • Maximum differences occur during times of high geomagnetic activity.

23. Delays in Real, Smoothed Data • Maximum errors can reach thousands of meters. • Mean errors are smaller but still significant. Mean values of Orbit differences

24. Conclusions • Model predictions of density can lag behind actual density values, especially during times of high geomagnetic activity. • Delays of several hours are possible. • Density predictions can have a significant effect on satellite orbit predictions. • Orbit errors due to density delays can reach thousands of meters. • Mean values of the orbit errors are still significant.