eng
Kubáček, Lubomír
Statistical theory of geodetic networks
Creating geodetic networks presents many problems from viewpoint of measurement techniques, physics, mathematics, and, primarily, mathematical statistics. The aim of this book is to deal with statistical problems. Geodesists themselves are experienced in handling the huge amount of data obtained from measurement, which must be analyzed from several aspects; in mathematical statistics relatively advanced theory of processing data has been developed and theory can throw fresh light upon of the some problems in geodetic networks. There are many fine works on these issues in geodesy, nevertheless the class of statistical problems in geodetic networks is so vast that many problems has not been described and solved yet. For reading this book only elementary statistical knowledge is necessary, which corresponds to the second and third year at technical universities. In the following text statistical solutions of problems are given in pure mathematical form. Therefore a form of „definition“, “lemma“, “theorem“, “corollary“ and „remark“ is frequently used. Numerical examples are rare. The size of the book would become unbearably enlarged. An example is given in such situation only when it is simple and helps to understand the practical effect of presented theory. The book consists of five chapters. The first one „Preliminaries“, consists of notation used in the following chapters, basic facts from the linear theory of statistical models and a motivation example. The second one „Basic problems in geodetic networks“, concentrates on stochastic relationships between two or among several points, transformation of coordinates, free geodetic networks, minimum norm quadratic unbiased estimators of variance components (MINQUE), basic facts from the optimum design of experiment, theory of sensitivity, threshold ellipses and problems of accuracy of entries of design and covariance matrix. The third chapter „Special structure of geodetic networks“, deals with a multistage network, multiepoch network, connecting networks and additional measurement. In the fourth chapter, „Miscellaneous problems“, the H-optimum estimator for network parameters is introduced along with the problem of accurate points in the second stage measurement, Helmet transformation with errors in both coordinate systems and the optimum elimination of parameters. The last chapter „Weakly nonlinear models“, undertakes to study influence of model nonlinearity on the bias of estimators, confidence ellipses, risk of statistical tests and on a power function of statistical tests.
2014-01-11T14:36:20Z
http://knihovna.vugtk.cz/record/30802