The GNSS integer ambiguities: Estimation and validation

The GNSS integer ambiguities: Estimation and validation

Verhagen, S.

Teunissen, P.J.G. (promotor)

Aerospace Engineering

2005-01-31

The principle of positioning with the Global Positioning System (GPS) is based on determining the distance of at least four GPS satellites to a receiver. For that purpose the so-called code measurements can be used, so that the position of the receiver can be determined up to several meters. In order to allow for navigation with centimeter accuracy, it is however required to use the very precise carrier phase measurements, since the phase of the carrier wave of the GPS signal can be measured up to several millimeters. Unfortunately, a receiver can only measure the phase of the carrier ââ¬â that is the fraction of the wavelength at the time of arrival. The wavelength is approximately 20 centimeters, and it is not known how many complete waves have preceded the one at the time of arrival. Therefore the phase measurements are called ambiguous. And that brings the problem of 'integer ambiguity resolution'. The goal of this research has been to set up a procedure for ambiguity resolution, such that there is a sound theoretical foundation for the estimation as well as the validation procedure. Until now that was not the case. Different approaches have been considered, and it was shown that an optimal method can be set up, based on the new principle of Integer Aperture estimation. But there are also alternative methods, which are computationally more attractive, and for which it has been shown that their solution is close to optimal. Furthermore, it has been shown that the principle of Integer Aperture estimation gives a theoretical foundation for the traditional validation procedures, as used until now. The result of this research is, that there is now a complete theory available, which gives a solution to the problem of integer ambiguity resolution. This allows for the first time to make inferences on the statistical reliability of the estimated ambiguities. This is an important step, since for many applications not only precision but also reliability is a very important measure in order to decide whether or not one can safely use the navigation system.

global navigation satellite systems
integer ambiguity resolution
estimation and validation

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doctoral thesis

(c) 2005 S. Verhagen