11. Principles of Least Squares

  1. Charles D. Ghilani Ph.D. Professor

Published Online: 9 MAR 2010

DOI: 10.1002/9780470586266.ch11

Adjustment Computations: Spatial Data Analysis, Fifth Edition

Adjustment Computations: Spatial Data Analysis, Fifth Edition

How to Cite

Ghilani, C. D. (2010) Principles of Least Squares, in Adjustment Computations: Spatial Data Analysis, Fifth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470586266.ch11

Author Information

  1. The Pennsylvania State University, USA

Publication History

  1. Published Online: 9 MAR 2010
  2. Published Print: 3 MAR 2010

ISBN Information

Print ISBN: 9780470464915

Online ISBN: 9780470586266

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Keywords:

  • principles of least squares;
  • closed polygon traverse;
  • horizontal angle and distance observations;
  • errors in observations - conforming to laws of probability;
  • fundamental principle of least squares;
  • using matrices for forming normal equations

Summary

This chapter contains sections titled:

  • Introduction

  • Fundamental Principle of Least Squares

  • Fundamental Principle of Weighted Least Squares

  • Stochastic Model

  • Functional Model

  • Observation Equations

  • Systematic Formulation of the Normal Equations

  • Tabular Formation of the Normal Equations

  • Using Matrices to Form Normal Equations

  • Least Squares Solution of Nonlinear Systems

  • Least Squares Fit of Points to a Line or Curve

  • Calibration of an EDM Instrument

  • Least Squares Adjustment Using Conditional Equations

  • The Previous Example Using Observation Equations

  • Software

  • Problems