Description

After a satellite has been launched, it is often unclear whether the satellite is following the expected trajectory. In order to determine on which trajectory the satellite actually is, a parameter estimation problem using measurement data from observing ground stations is formulated.

The unknowns of this parameter estimation problem may either be a six-dimensional state vector (three coordinates for both position and velocity) or the Kepler elements of the ellipsoidal orbit. It is already known that at least in some cases the latter formulation can be of some advantage. In particular, for the PROBA scenario provided to the IWR by the ESA it turns out that the convergence region of the Gauß-Newton method is significantly larger if the Kepler formulation is used.

However, since the trajectory of the satellite is almost circular, some of the Kepler elements are almost undefined. It is the purpose of this software practical to investigate whether a reformulation to non-singular Kepler elements can further improve the convergence behaviour.

Aim

The focus of the software practical is on the application. The following tasks have to be carried out:

• Software installation
• Understanding the relevant parts of the source code
• Understanding the transformation of standard Kepler elements to nonsingular elements and implementation in software
• Formulation of satellite dynamics in non-singular elements and implementation
• Systematic tests of the convergence behaviour of the Gauß-Newton method and comparison to standard Kepler elements and state vector formulation

Size of the project

This project is suited for one or two students as an advanced practical.

Requirements

• Some knowledge of either FORTRAN or C. (The code is in FORTRAN, but easy to understand if you have some knowledge of C)
• Some knowledge of parameter estimation in dynamic systems

Further reading

• A book and other helpful sources will be given to you at the beginning of the project.

Contact

Dipl.-Phys. Simon Lenz
Interdisciplinary Center for Scientific Computing (IWR)
Im Neuenheimer Feld 368
Universität Heidelberg

e-mail: simon.lenz@iwr.uni-heidelberg.de
Room : INF 368 (IWR), R 412