Integer Least-Squares

  • P. J. G. Teunissen
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


Carrier phase ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. A proper handling of carrier phase ambiguity resolution requires a proper understanding of the underlying theory of integer inference. In this contribution a brief review is given of the probabilistic theory of integer ambiguity estimation with special emphasis on the integer least-squares principle. We describe the concept of ambiguity pull-in regions, introduce the class of admissible integer estimators, determine their probability mass functions and show how their variability affect the uncertainty in the so-called ‘fixed’ baseline solution. The theory is worked out in more detail for integer least-squares and integer bootstrapping. It is shown that the integer least-squares principle maximizes the probability of correct integer estimation. Sharp and easy-tocompute bounds are given for both the ambiguity success rate and the baseline’s probability of concentration.


GNSS ambiguity resolution integer least-squares 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • P. J. G. Teunissen
    • 1
  1. 1.Department of Mathematical Geodesy and PositioningDelft University of TechnologyDelftThe Netherlands

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