The GNSS integer ambiguities: estimation and validation

Preface
It was in the beginning of the nineties that the first major steps for solving the problem
of GPS integer ambiguity resolution were made. Ten years later part of the problem
could be considered solved, as efficient algorithms were available for the estimation of
the integer ambiguities with the highest possible success rate. However, as a geodesist
one cannot be content with this result, since parameter resolution means estimation and
validation. The latter problem turned out to be very complex due to the non-standard
distributions of the parameters involved.
Prof. Peter Teunissen has made a major contribution to the solution of the integer
estimation problem with the introduction of the LAMBDA method in 1993. He made
me aware of the open problem with respect to integer validation, and - as I started to
work on this problem - has given me indispensable theoretical input.
This thesis starts with a description of the GNSS observation models, and then outlines
the theory on integer estimation and validation as it was available when I started to
work on this topic. This part does contain some relatively new results on the parameter
distributions, and some important comments on the validation procedures as proposed in
the past and used in practice. The remaining chapters are all devoted to ’new’ estimation
and validation algorithms.
In this place I would of course like to thank all of my (former) colleagues at MGP for
their support and contribution to a good research environment. A special thanks goes to
the following people: my promotor Peter Teunissen for the supervision, input, feedback,
comments and discussions; Kees de Jong, my supervisor in the first two years; Dennis
Odijk for proofreading this thesis; Peter Joosten for the computer support; Ria Scholtes
for the administrative support; the members of the examination committee for their
critical reviews and useful comments.
Finally, I would like to thank René for his help with the layout and graphics and of course
his overall support.
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