A carrier phase ambiguity estimator with easy-to-evaluate fail-rate

Abstract

In (Teunissen, 2003) we introduced the class of integer aperture (IA) estimators. This class is larger than the class of integer (I) estimators, but smaller than the class of integer equivariant (IE) estimators. The IA-estimator is of a hybrid nature since its outcome may be integer-valued or real-valued. For its probabilistic evaluation one needs to take both the success-rate and fail-rate into account, since these two probabilities do not sum up to one as it is the case with integer estimators. The IA-estimators also take care of the so-called discernibility problem of GNSS ambiguity resolution. In the present contribution we will introduce one particular integer aperture estimator, the ellipsoidal IA-estimator. This estimator has the advantage that a rigorous and easy-to-evaluate probabilistic description of its performance can be given. It will also be shown that some well-known discernibility tests which are used in practice are in fact examples of IA-estimators.