A Gauss-Markov-like theorem for integer GNSS ambiguities.

Abstract

Carrier phase integer 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. In Teunissen (1999) we introduced the class of admissible integer estimators and showed that the integer lest-squares estimator is the optimal estimator within this class. In Teunissen (2002) we introduced an alternative class of ambiguity estimators. This class of integer equivariant (IE) estimators still obeys the integer remove-restore principle. In the present contribution we will determine the "best" estimator within the IE-class. The minimum mean squared error is taken as the criterion for "best". As our main result we have a Gauss-Markow-like theorem which introduces a new minimum variance unbiased ambiguity estimator which is always superior to the well-known best linear unbiased ambiguity estimator (BLU) of the Gauss-Markov theorem.