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

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.

Introduction A simple two body model was used for the

spacecraft integration. Acceleration due to drag:

Velocity relative to the atmosphere:

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

Outline Introduction

Storms in data

Perfect model comparisons

Delays in model data

Delays in real, smoothed data

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.

•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.

Outline Introduction

Storms in data

Perfect model comparisons

Delays in model data

Delays in real, smoothed data

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.

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.

Outline Introduction

Storms in data

Perfect model comparisons

Delays in model data

Delays in real, smoothed data

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.

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.

Two hour delay The simulation was performed using a 2 hour

delay. Same general behavior was observed with

larger magnitudes.

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

during large storms.

Delays in Model Data Very large errors can occur (thousands of

meters).

Time Delays (h) Radial (m) In-track (m) Cross-track (m)

1 0.777 37.94 0.009

2 0.705 32.92 0.007

3 0.998 46.09 0.0104

Mean errors are significant as well (tens of meters).

Mean values of Orbit differences

Outline Introduction

Storms in data

Perfect model comparisons

Delays in model data

Delays in real, smoothed data

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

One hour delay

Two hour delay

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.

Delays in Real, Smoothed Data Maximum errors can reach thousands of

meters. Mean errors are smaller but still significant.

Time Delays (h) Radial (m) In-track (m) Cross-track (m)

1 0.395 20.58 0.0041

2 0.63 40.92 0.0081

3 0.79 61 0.012

Mean values of Orbit differences

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.