06 Fakultät Luft- und Raumfahrttechnik und Geodäsie

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/7

Browse

Filters

20081

Settings

Publication Type: search.filters.UBSTyp.Abschlussarbeit (Diplom)Start date: 2003End date: 2009Author: search.filters.author.Guo, Ronggang

Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    Variance-covariance matrix estimation with LSQR in a parallel programming environment
    (2008) Guo, Ronggang
    Knowledge about the gravity field allows an insight into the structure and dynamics of the earth. It provides the geoid as the most important physical reference surface in geodesy and oceanography. Since 2000, the CHAMP (CHAllenging Mini-satellite Payload) mission detects the structure of the global gravity field, followed by the launch of GRACE (Gravity Recovery And Climate Experiment) in 2002. In 2008, finally, the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite is supposed to be set in orbit. These missions demonstrate satellite-based gravity field recovery to be at the center of geo-scientific interest. Interpretation and evaluation of satellite observations are difficult, especially the determination of the unknown gravity field parameters from a huge amount of measurements. Because of the immense demand for memory and computing time, the occurring systems of equations pose a real numerical challenge. Therefore, High-Performance Computing (HPC) is commonly adopted to overcome computational problems. Basically, parallel programming with MPI and OpenMP routines allows to speed up the solution process considerably. In this thesis, firstly global gravity field modelling by means of satellite observations is reviewed. Secondly, the LSQR method (Least-Squares using QR factorization) is introduced in detail in order to solve the resulting least-squares problems. Because the LSQR method is an iterative solver, it basically can not provide the variance-covariance information of the parameter estimate. To investigate the approximate computation of the variance-covariance matrix, two methods are introduced. The first one is based on the generalized inverse of the design matrix. The second approach applies Monte-Carlo integration techniques. Because parallel programming is very helpful to implement such iterative methods, it is necessary to introduce some basic principles and concepts about HPC.