Erik Grafarend's Books

Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik Grafarend,Joseph L. Awange

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Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik Grafarend,Joseph L. Awange

Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.

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1026

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Springer Science & Business Media

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ISBN 10

3642222412

ISBN 13

9783642222412

Map Projections

Cartographic Information Systems

By: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

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Map Projections

Cartographic Information Systems

By: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

In the context of Geographical Information Systems (GIS) the book offers a timely review of Map Projections. The first chapters are of foundational type. We introduce the mapping from a left Riemann manifold to a right one specified as conformal, equiaerial and equidistant, perspective and geodetic. In particular, the mapping from a Riemann manifold to a Euclidean manifold ("plane") and the design of various coordinate systems are reviewed . A speciality is the treatment of surfaces of Gaussian curvature zero. The largest part is devoted to the mapping the sphere and the ellipsoid-of-revolution to tangential plane, cylinder and cone (pseudo-cone) using the polar aspect, transverse as well as oblique aspect. Various Geodetic Mappings as well as the Datum Problem are reviewed. In the first extension we introduce optimal map projections by variational calculus for the sphere, respectively the ellipsoid generating harmonic maps. The second extension reviews alternative maps for structures , namely torus (pneu), hyperboloid (cooling tower), paraboloid (parabolic mirror), onion shape (church tower) as well as clothoid (Hight Speed Railways) used in Project Surveying. Third, we present the Datum Transformation described by the Conformal Group C10 (3) in a threedimensional Euclidean space , a ten parameter conformal transformation. It leaves infinitesimal angles and distance ratios equivariant. Numerical examples from classical and new map projections as well as twelve appendices document the Wonderful World of Map Projections.

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941

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Springer

Published Date

ISBN 10

3642364942

ISBN 13

9783642364945

Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik W. Grafarend,Silvelyn Zwanzig,Joseph L. Awange

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Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik W. Grafarend,Silvelyn Zwanzig,Joseph L. Awange

This book provides numerous examples of linear and nonlinear model applications. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view and a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss–Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so-called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann–Plucker coordinates, criterion matrices of type Taylor–Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overjet. This second edition adds three new chapters: (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (2) Bayes methods that covers (i) general principle of Bayesian modeling. Explain the notion of prior distribution and posterior distribution. Choose the pragmatic approach for exploring the advantages of iterative Bayesian calculations and hierarchical modeling. (ii) Present the Bayes methods for linear models with normal distributed errors, including noninformative priors, conjugate priors, normal gamma distributions and (iii) short outview to modern application of Bayesian modeling. Useful in case of nonlinear models or linear models with no normal distribution: Monte Carlo (MC), Markov chain Monte Carlo (MCMC), approximative Bayesian computation (ABC) methods. (3) Error-in-variables models, which cover: (i) Introduce the error-in-variables (EIV) model, discuss the difference to least squares estimators (LSE), (ii) calculate the total least squares (TLS) estimator. Summarize the properties of TLS, (iii) explain the idea of simulation extrapolation (SIMEX) estimators, (iv) introduce the symmetrized SIMEX (SYMEX) estimator and its relation to TLS, and (v) short outview to nonlinear EIV models. The chapter on algebraic solution of nonlinear system of equations has also been updated in line with the new emerging field of hybrid numeric-symbolic solutions to systems of nonlinear equations, ermined system of nonlinear equations on curved manifolds. The von Mises–Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special Gauss–Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra, and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger algorithm, especially the C. F. Gauss combinatorial algorithm.

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1127

Publisher

Springer Nature

Published Date

ISBN 10

3030945987

ISBN 13

9783030945985

Algebraic Geodesy and Geoinformatics

By: Joseph L. Awange,Erik W. Grafarend,Béla Paláncz,Piroska Zaletnyik

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Algebraic Geodesy and Geoinformatics

By: Joseph L. Awange,Erik W. Grafarend,Béla Paláncz,Piroska Zaletnyik

While preparing and teaching ‘Introduction to Geodesy I and II’ to undergraduate students at Stuttgart University, we noticed a gap which motivated the writing of the present book: Almost every topic that we taught required some skills in algebra, and in particular, computer algebra! From positioning to transformation problems inherent in geodesy and geoinformatics, knowledge of algebra and application of computer algebra software were required. In preparing this book therefore, we have attempted to put together basic concepts of abstract algebra which underpin the techniques for solving algebraic problems. Algebraic computational algorithms useful for solving problems which require exact solutions to nonlinear systems of equations are presented and tested on various problems. Though the present book focuses mainly on the two ?elds, the concepts and techniques presented herein are nonetheless applicable to other ?elds where algebraic computational problems might be encountered. In Engineering for example, network densi?cation and robotics apply resection and intersection techniques which require algebraic solutions. Solution of nonlinear systems of equations is an indispensable task in almost all geosciences such as geodesy, geoinformatics, geophysics (just to mention but a few) as well as robotics. These equations which require exact solutions underpin the operations of ranging, resection, intersection and other techniques that are normally used. Examples of problems that require exact solutions include; • three-dimensional resection problem for determining positions and orientation of sensors, e. g. , camera, theodolites, robots, scanners etc.

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380

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Springer Science & Business Media

Published Date

ISBN 10

3642121241

ISBN 13

9783642121241

Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik Grafarend,Joseph L. Awange

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Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik Grafarend,Joseph L. Awange

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Page Count

1026

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Springer Science & Business Media

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ISBN 10

3642222412

ISBN 13

9783642222412

Map Projections

Cartographic Information Systems

By: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

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Map Projections

Cartographic Information Systems

By: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

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941

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ISBN 10

3642364942

ISBN 13

9783642364945

Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik W. Grafarend,Silvelyn Zwanzig,Joseph L. Awange

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Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

By: Erik W. Grafarend,Silvelyn Zwanzig,Joseph L. Awange

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1127

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Springer Nature

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ISBN 10

3030945987

ISBN 13

9783030945985

Solving Algebraic Computational Problems in Geodesy and Geoinformatics

The Answers To Modern Challenges

By: Joseph L. Awange,Erik W. Grafarend

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Solving Algebraic Computational Problems in Geodesy and Geoinformatics

The Answers To Modern Challenges

By: Joseph L. Awange,Erik W. Grafarend

Charity Mupanga, the resilient and maternal proprietor of Harrods International Bar (and Nightspot) faces her toughest challenge in Dizzy Worms, the final novel in Michael Holman's acclaimed trilogy set in the African slum of Kireba. Faced with a Health and Safety closure, Charity has a week to appeal and the chances of success seem negligible: elections are imminent, and Kireba is due to become a showcase of President Josiah Nduka's 'slum rehabilitation program', backed by gullible foreign donors. But before taking on Nduka and the council, she has a promise to keep – to provide a supply of her famous sweet doughballs to a small army of street children, as voracious as they are malodorous . . . Michael Holman uses his witty satirical pen to brilliant effect in this affectionate portrait of a troubled region, targeting local politicians, western diplomats, foreign donors and journalists, puncturing pretensions and questioning the philosophy of aid.

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352

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Springer Science & Business Media

Published Date

ISBN 10

354023425X

ISBN 13

9783540234258

Map Projections

Cartographic Information Systems

By: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

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Map Projections

Cartographic Information Systems

By: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

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935

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Springer

Published Date

ISBN 10

3642364934

ISBN 13

9783642364938

Algebraic Applications of Photogrammetry, Remote Sensing and Computer Vision

By: Joseph Awange,Erik Grafarend,Fabio Crosilla,Bela Palancz,John Kiema

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Algebraic Applications of Photogrammetry, Remote Sensing and Computer Vision

By: Joseph Awange,Erik Grafarend,Fabio Crosilla,Bela Palancz,John Kiema

With the ever increasing modernization of computers, image processing and analysis is becoming more and more necessary in various sectors. In computer vision and model-based vision for example, algebraic methods are gaining momentum in performing adjustments that play essential roles in obtaining accurate structure and motion estimates, while in photogrammetry they are used to perform bundle adjustment to obtain dense 3-dimensional (3D) surface models from images taken from photographs. Most recently, there is a close link between CV and photogrammetry, as unordered image blocks from close range and UAVs have to be processed. Indeed, in recent years, the demand for realistic reconstruction and modeling of objects and human bodies is increasing both for animation and medical applications. In radiostereometric analysis (RSA), for example, algebraic methods play the significant role of constructing the projection geometries and reconstructing the 3D-coordinates of the patient markers. Radiostereometric analysis has been widely used in orthopaedics for studying, e.g., prosthetic implant migration and wear, joint stability and kinematics, bone growth, and fracture healing. These applications of algebraic methods, just to list but a few, underscores the need for further improvements and refinements of the existing techniques, and also testing others that could offer more flexibility and optimum results. This book presents modern and efficient algebraic methods that are capable of meeting the challenges posed by the need for efficient algorithms to process and analyze images. The book will be useful to computer scientists, geographers, Earth scientists, mathematicians and environmentalists to list a few.

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Page Count

400

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Springer

Published Date

ISBN 10

3319053671

ISBN 13

9783319053677

Book's by Erik Grafarend

Applications of Linear and Nonlinear Models

Applications of Linear and Nonlinear Models

Map Projections

Map Projections

Applications of Linear and Nonlinear Models

Applications of Linear and Nonlinear Models

Algebraic Geodesy and Geoinformatics

Algebraic Geodesy and Geoinformatics

Applications of Linear and Nonlinear Models

Applications of Linear and Nonlinear Models

Map Projections

Map Projections

Applications of Linear and Nonlinear Models

Applications of Linear and Nonlinear Models

Solving Algebraic Computational Problems in Geodesy and Geoinformatics

Solving Algebraic Computational Problems in Geodesy and Geoinformatics

Map Projections

Map Projections

Algebraic Applications of Photogrammetry, Remote Sensing and Computer Vision

Algebraic Applications of Photogrammetry, Remote Sensing and Computer Vision

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