Erik W. Grafarend Livres

This work provides a comprehensive examination of the Grand Universe of linear and weakly nonlinear regression models across the first eight chapters, combining both algebraic and stochastic perspectives. An important lemma connects best linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model with a least squares solution (LESS) in linear systems, highlighting the interplay between stochastic models and algebraic solutions. The initial six chapters focus on underdetermined and overdetermined linear systems, including those with data defects, and explore various estimators such as MINOLESS, BLIMBE, BLUMBE, and others. A key feature is the simultaneous determination of the first and second central moments of a probability distribution through the E-D correspondence and its Bayesian design. Additional topics include continuous versus discrete networks, Grassmann-Pluecker coordinates, and Taylor-Karman criterion matrices, along with FUZZY sets. Chapter seven delves into overdetermined nonlinear systems on curved manifolds, emphasizing the von Mises-Fisher distribution for circular data. The final chapter addresses probabilistic regression within the Gauss-Markov model with random effects, leading to BLIP and VIP estimators, including Bayesian methods. Four appendices supplement the text, covering tensor algebra, sampling distributions, basic statistical concepts, and Groebner basis algebra, including the Buchberger Al

In the context of Geographical Information Systems (GIS), this book provides a comprehensive review of Map Projections. The initial chapters lay a foundational understanding of mapping from a left Riemann manifold to a right one, focusing on conformal, equiaerial, equidistant, perspective, and geodetic projections. It explores the transition from a Riemann manifold to a Euclidean manifold and discusses the design of various coordinate systems, with particular attention to surfaces of Gaussian curvature zero. A significant portion is dedicated to mapping the sphere and ellipsoid-of-revolution to tangential planes, cylinders, and cones using different aspects. The text also examines Geodetic Mappings and the Datum Problem. Subsequent sections introduce optimal map projections through variational calculus for the sphere and ellipsoid, generating harmonic maps. Alternative maps for various structures, such as torus, hyperboloid, paraboloid, onion shape, and clothoid, are presented, highlighting their applications in Project Surveying. Finally, the book discusses Datum Transformation using the Conformal Group C10 (3) in three-dimensional Euclidean space, a ten-parameter conformal transformation that preserves infinitesimal angles and distance ratios. Numerical examples from both classical and contemporary map projections, along with twelve appendices, further illustrate the diverse and intricate world of Map Projections.

Diese Monografie stellt Methoden zur Lösung von unter- bzw. überbestimmten Gleichungssystemen vor, darunter Minimumnormmethoden bezüglich gewichteter Normen. Es werden sowohl lineare als auch nichtlineare Gleichungssysteme betrachtet, wobei auch zufällige Effekte berücksichtigt werden. In einem ausführlichen Anhang werden die nötigen Grundlagen aus der Linearen Algebra und der Analysis vermittelt.

Geodesy as the science which determines the figure of the earth, its orientation in space and its gravity field as well as its temporal changes, produces key elements in describing the kinematics and the dynamics of the deformable body "earth". It contributes in particular to geodynamics and opens the door to decode the complex interactions between components of "the system earth". In the breathtaking development recently a whole arsenal of new terrestrial, airborne as well as satelliteborne measurement techniques for earth sciences have been made available and have broadened the spectrum of measurable earth parameters with an unforeseen accuracy and precision, in particular to resolve the factor time. The book focusses on these topics and gives a state of the art of modern geodesy.