Skip to main content

Introduction

  • Chapter
  • First Online:
Algebraic Geodesy and Geoinformatics

Abstract

A potential answer to modern challenges faced by geodesists and geoinformatics (see, e.g., Sect. 1-3), lies in the application of algebraic computational techniques. The present book provides an in-depth look at algebraic computational methods and combines them with special local and global numerical methods like the Extended Newton-Raphson and the Homotopy continuation method to provide smooth and efficient solutions to real life-size problems often encountered in geodesy and geoinformatics, but which cannot be adequately solved by algebraic methods alone.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

  1. Awange JL (2002a) Groebner bases, multipolynomial resultants and the Gauss-Jacobi combinatorial algorithms-adjustment of nonlinear GPS/LPS observations. Ph.D. thesis, Department of Geodesy and GeoInformatics, Stuttgart University, Germany. Technical Reports, Report Nr. 2002 (1)

    Google Scholar 

  2. Awange JL, Fukuda Y, Takemoto S, Wickert J, Aoyama Y (2004) Analytic solution of GPS atmospheric sounding refraction angles. Earth, Planets and Space 56: 573–587

    Google Scholar 

  3. Awange JL, Grafarend EW, Fukuda Y, Takemoto S (2005) The application of commutative algebra to Geodesy: two examples. Journal of Geodesy, 79: 93-102

    Article  Google Scholar 

  4. Awange JL, Grafarend EW (2005) Solving Algebraic Computational Problems in Geodesy and Geoinformatics. Springer, Berlin

    Google Scholar 

  5. Bancroft S (1985) An algebraic solution of the GPS equations. IEEE Transaction on Aerospace and Electronic Systems AES- 21: 56–59.

    Article  Google Scholar 

  6. Biagi L, Sanso F (2004) Sistemi di riferimento in geodesia: algebra e geometria dei minimi quadrati per un modello con deficienza di rango (parte seconda). Bollettino di Geodesia e Science Affini 63: 29–52

    Google Scholar 

  7. Cox D, Little J, O’Shea D (1998) Using algebraic geometry. Graduate Text in Mathematics 185. Springer, New York

    Google Scholar 

  8. Grafarend EW, Shan J (1996) Closed-form solution of the nonlinear pseudo-ranging equations (GPS). ARTIFICIAL SATELLITES, Planetary Geodesy 31: 133–147

    Google Scholar 

  9. Hampel FR, Ronchetti EM, Rousseeuw P, Stahel WA (1986) Robust Statistic - the approach based non influence Functions. John Wiley & Sons, New York

    Google Scholar 

  10. Huber PJ (1964) Robust estimation of a location parameter. Annals of Mathematical Statistics 35: 73–101

    Article  Google Scholar 

  11. Huber PJ (1981) Robust Statistics. John Wiley & Sons, New York

    Book  Google Scholar 

  12. Kleusberg A (1994) Die direkte Lösung des räumlichen Hyperbelschnitts. Zeitschrift für Vermessungswesen 119: 188-192

    Google Scholar 

  13. Kleusberg A (2003) Analytical GPS navigation solution. In: Grafarend EW, Krumm FW, Schwarze VS (eds) Geodesy - the Challenge of the 3rd Millennium. Springer, Heidelberg pp.93–96

    Google Scholar 

  14. Lannes A, Durand S (2003) Dual algebraic formulation of differential GPS. Journal of Geodesy 77: 22–29

    Article  Google Scholar 

  15. Lichtenegger H (1995) Eine direkte Lösung des räumlichen Bogenschnitts. Üsterreichische Zeitschrift für Vermessung und Geoinformation 83: 224–226

    Google Scholar 

  16. Merritt EL (1949) Explicit Three-point resection in space. Phot. Eng. 15: 649–665

    Google Scholar 

  17. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in Fortran 77: The art of scientific computing, 2nd edition, Cambridge University Press

    Google Scholar 

  18. (1993) Direkte Lösung des räümlichen Bogenschnitts. Zeitschrift für Vermessungswesen 118: 20–24

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joseph L. Awange .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Awange, J.L., Grafarend, E.W., Paláncz, B., Zaletnyik, P. (2010). Introduction. In: Algebraic Geodesy and Geoinformatics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12124-1_1

Download citation

Publish with us

Policies and ethics