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Algebraic Geodesy and Geoinformatics

  • Simplifies algebraic notions with examples from the fields of Geodesy and Geoinformatics in a simple and understandable way Updated throughout with latest methods and their extensions to deliver a state-of-the-art toolbook

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xviii
  2. Introduction

    • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
    Pages 1-5
  3. Algebraic symbolic and numeric methods

    1. Front Matter

      Pages 7-7
    2. Basics of ring theory

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 9-16
    3. Basics of polynomial theory

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 17-32
    4. Groebner basis

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 33-47
    5. Polynomial resultants

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 49-62
    6. Linear homotpy

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 63-77
    7. Solutions of Overdetermined Systems

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 79-99
    8. Extended Newton-Raphson method

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 101-110
    9. Procrustes solution

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 111-135
  4. Applications to geodesy and geoinformatics

    1. Front Matter

      Pages 137-137
    2. LPS-GNSS orientations and vertical deflections

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 139-153
    3. Cartesian to ellipsoidal mapping

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 155-171
    4. Positioning by ranging

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 173-216
    5. Positioning by resection methods

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 217-248
    6. Positioning by intersection methods

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 249-263
    7. GNSS environmental monitoring

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 265-287
    8. Algebraic diagnosis of outliers

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 289-301
    9. Datum transformation problems

      • Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik
      Pages 303-338

About this book

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.

Reviews

From the reviews of the second edition:

“I compliment the authors on this book because it brings together mathematical methods for the solution of multi-variable polynomial equations that are hardly covered side by side in any ordinary mathematical book: The book explains both algebraic ("exact") and numerical ("approximate") methods. It also points to the recent combination of algebraic and numerical methods ("hybrid" methods), which is currently one of the most promising directions in the area of computer mathematics. Prof. Dr.phil. Dr.h.c.mult. Bruno Buchberger, Professor of Computer Mathematics, and Head of Softwarepark Hagenberg. … As the person responsible for Mathematica's GroebnerBasis and NSolve implementations, I am delighted to see them put to such practical use. It is, moreover, a pleasure to see methods from an abstract branch of mathematics come into play in attacking problems from a very important branch of technology.” Daniel Lichtblau, Wolfram Research.

“The book consists of the two parts. In the first part, the authors give a review of some known results in linear algebra and numerical methods which are used in the second part. The second part is the basic in the book. … Each theoretical statement given in the book is accompanied with many careful neat examples. A rich bibliography envelopes all basic directions in algebraic geodesy and geoinformatics.”­­­ (I. V. Boikov, Zentralblatt MATH, Vol. 1197, 2010)

Authors and Affiliations

  • Dept. Environmental Earth Sciences, Maseno University, Maseno, Kenya

    Joseph L. Awange

  • Geodätisches Institut, Universität Stuttgart, Stuttgart, Germany

    Erik W. Grafarend

  • Technology & Economics, Dept. Photogrammetry & Geoinformatics, Budapest University of, Budapest, Hungary

    Béla Paláncz

  • Technology & Economics, Dept. Geodesy & Surveying, Budapest University of, Budapest, Hungary

    Piroska Zaletnyik

Bibliographic Information

Buy it now

Buying options

eBook USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access