Estimation of variance-covariance components for geodetic observations and implications on deformation trend analysis
The statistical methods for the estimation of the variance-covariance components for unbalanced data are reviewed in this thesis. Computational aspects of the presented methods are compared and their applicability to geodetic data is discussed. Prior information about the unknown variance components is introduced within the framework of the Generalized Maximum Likelihood (GML) methodology. The inverted gamma prior is used to introduce prior information about the variance components, and the noninformative prior is used when no prior information is available. The Fisher scoring method is applied to the resulting posterior probability density functions and the estimating equations are derived. Prior information is also introduced by means of the weighted constraints on the unknown variance-covariance components in the dispersion-mean model. The estimating equations of the dispersion-mean model with weighted constraints are derived, and conditions for equivalence between the dispersion-means model with weighted constraints and the GML estimation are formulated. The effect of neglecting the errors of the estimated variance-covariance components. In the least squares adjustment, on the covariance matrix of the estimated location parameters is discussed. The influence of different aspects of the estimation of variance components on the results pf spatial deformation trend analysis is investigated, based on practical examples. These include the amount of prior information, the choice of the method of estimation, and the choice of the error model. An efficient numerical algorithm for detecting influential observations, in terms of their influence on the results of variance components estimation, is developed and tested on geodetic survey data. All numerical procedures and algorithms developed in the thesis are demonstrated on practical examples.