Integer aperture GNSS ambiguity resolution

Abstract

GNSS carrier phase ambiguity resolution is the key to fast and high-precision satellite positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. In (Teunissen, 1998, 1999) we introduced the class of admissible integer (I) estimators and showed that the integer least-squares estimator is the optimal ambiguity estimator within this class. In (Teunissen, 2002a, b) we introduced the class of integer equivariant (IE) estimators and determined the best ambiguity estimator within this class. This best integer equivariant estimator is unbiased and of minimum variance. In the present contribution we will introduce a third class of ambiguity estimators. This class of integer aperture (IA) estimators is larger than the I-class, but smaller than the IE-class. The IA-estimator is of a hybrid nature since its outcome may be integer-valued or real-valued. We also give a probabilistic description of IA-estimators. This is needed in order to be able to propagate the inherent uncertainty in the data rigorously and to give a proper probabilistic evaluation of the final result. The framework of IA-estimation also incorporates the important problem of ambiguity discernibility. By setting the size and shape of the integer aperture pull-in region of an IA-estimator, the user has control over the fail-rate of the estimator and thus also over the amount of discernibility.