Browsing by Author "Guo, Ronggang"

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    Systematical analysis of the transformation procedures in Baden-Württemberg with least squares and total least squares methods
    (2007) Guo, Ronggang
    For the concrete "Introduction of ETRS89 into Baden-Württemberg" the transformation with the two models of the 7-Parameter Helmert transformation and the 6-Parameter Helmert transformation using the 131 collocated points (131 BWREF points in Baden-Württemberg) are firstly tested and discussed. Because of the special characteristic of the main triangle net of Baden-Württemberg (countrywide variable net scales, inhomogeneous point accuracies and transformation residual in the decimeter level) an alternative transformation procedure with the Total Least-Squares method is also applied in the estimation of the 7-Parameter Helmert transformation and 6-Parameter Affine transformation based on the 131 collocated points. After the review of basis mathematic background of the TLS method, these methods are complemented with MATLAB. Furthermore, 10 selected points are as test points to study the influence on those points after using TLS transformation parameters. The results are analyzed and compared with these results from the conventional LS method, and the advantages and shortcomings of this TLS method are discussed.
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    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.