Adjustment theory. An introduction for students and practitioners of surveying and geoinformation (Q2761410)

This book on adjustment theory is presented with 12 chapters. \S 1 (40 pages) reviews descriptive statistics, in particular the multivariate Gauss-Laplace normal distribution. The statistics of directional data (von Mises - Fisher distribution) are missing. With respect to the ``nonlinear random effects model'' variance - covariance transformation (``error propagation'') is given in \S 2 (15 pages). Confidence regions and statistical tests (errors of the first and second kind) are treated in \S 3 (28 pages). Fundamentals of adjustment theory, here understood as ``least squares'', are the subject of \S 4 (57 pages). Constraints and restrictions ``of fixed type'' are introduced into adjustment theory of linearized models, in particular the Gauss - Helmert model of ``condition equations with unknowns'', in \S 5 (30 pages). An elegant \S 6 (20 pages) on robust parameter estimation (\(M\)-, \(L\)-, \(Ls\)-norm estimators and their generalizations) is added. Due to its importance in practice, the datum problem is reviewed in \S 7 (50 pages). NEWLINENEWLINENEWLINEQuality measures as well as reliability measures are discussed in \S 8 (32 pages). There is a special problem in \S 9 (25 pages) on ``special aspects'', namely the linearization of a nonlinear fixed effects model: Since by introducing approximate parameters within the linearization problem, the datum problem is already solved, in contrast to the treatment in \S 9.3. The datum transformation problems (conformal group: parameters of type translation, rotation and scale) are discussed in great detail in \S 10 (30 pages). In contrast, \S 11 (22 pages) deals with ``regression and collocation'', namely the ``mixed model''. A special highlight is \S 12, entitled ``congruence tests and Kalman filtering'' (25 pages), which is applied to deforming networks. NEWLINENEWLINENEWLINEThe book has been written for the practitioner, namely experimentalists who have to analyze their data with respect to a model which is linear or nonlinear with respect to unknown parameters, here always fixed effects. Estimators or predictors of type BLUUE, BLUUP for first moments and of type BIQUUE, BIQE for second moments, namely variance - covariance components estimation, are badly missing. In toto, the text can be warmly recommended to any analyst as a beginner of learning adjustment theory. More advanced and further reaching texts are listed.