Ph.D. Thesis, Institut f¨ur Geod¨asie und Geoinformation der Universit¨at Bonn, Bonn, June, 2007.

Paper abstract bibtex

Paper abstract bibtex

Large-scaled least squares problems require tailored numerical techniques to overcome the computational burden. For these types of problems iterative strategies are suitable because of their flexibility and effectiveness. The first shortcoming of iterative strategies in least squares estimation is the fact that the inverse of the normal equation matrix as the carrier of the covariance information is not available or very expensive to compute. Another shortcoming within iterative strategies arises when different types of observation groups with different stochastic properties are to be combined. In this case the choice of optimum weight factors, and eventually regularization parameters, by means of variance component estimation is essential for obtaining reliable estimates of the unknown parameters. Unfortunately, the conventional method of variance component estimation requires the repeated inversion of large products of matrices. This thesis presents algorithms based on Monte Carlo methods, which can be integrated very efficiently into iterative solvers, and which are demonstrated to close the aforementioned gaps. Tailored strategies for different types of solution techniques with respect to normal equations, observation equations and combined models are treated. In addition, the thesis presents new criteria to define confidence regions of the estimated variance information of the parameters, as well as for all additional derived quantities. The developed algorithms for computing variance/covariance matrices and for obtaining variance components are tailored to be integrated into the Preconditioned Conjugate Gradients Multiple Adjustment (PCGMA) algorithm of Schuh 1996 and Boxhammer 2006. These algorithms are applied in a case study to simulated GOCE data, where Satellite Gravity Gradiometry (SGG) data in form of observation equations and Satellite-to-Satellite tracking (SST) data in form of normal equations are combined for recovering the Earth's gravity field.

@phdthesis{alkathib_monte_2007, address = {Bonn}, type = {{PhD} {Thesis}}, title = {On {Monte} {Carlo} methods with applications to the current satellite gravity missions}, url = {http://hss.ulb.uni-bonn.de:90/2007/1078/1078.htm}, abstract = {Large-scaled least squares problems require tailored numerical techniques to overcome the computational burden. For these types of problems iterative strategies are suitable because of their flexibility and effectiveness. The first shortcoming of iterative strategies in least squares estimation is the fact that the inverse of the normal equation matrix as the carrier of the covariance information is not available or very expensive to compute. Another shortcoming within iterative strategies arises when different types of observation groups with different stochastic properties are to be combined. In this case the choice of optimum weight factors, and eventually regularization parameters, by means of variance component estimation is essential for obtaining reliable estimates of the unknown parameters. Unfortunately, the conventional method of variance component estimation requires the repeated inversion of large products of matrices. This thesis presents algorithms based on Monte Carlo methods, which can be integrated very efficiently into iterative solvers, and which are demonstrated to close the aforementioned gaps. Tailored strategies for different types of solution techniques with respect to normal equations, observation equations and combined models are treated. In addition, the thesis presents new criteria to define confidence regions of the estimated variance information of the parameters, as well as for all additional derived quantities. The developed algorithms for computing variance/covariance matrices and for obtaining variance components are tailored to be integrated into the Preconditioned Conjugate Gradients Multiple Adjustment (PCGMA) algorithm of Schuh 1996 and Boxhammer 2006. These algorithms are applied in a case study to simulated GOCE data, where Satellite Gravity Gradiometry (SGG) data in form of observation equations and Satellite-to-Satellite tracking (SST) data in form of normal equations are combined for recovering the Earth's gravity field.}, language = {English}, school = {Institut f¨ur Geod¨asie und Geoinformation der Universit¨at Bonn}, author = {Alkathib, Hamza}, month = jun, year = {2007}, }

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