On the computation of the best integer equivariant estimator

Abstract

Carrier phase integer ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. In this contribution we study some of the computational aspects of best integer equivariant estimation. The best integer equivariant (BIE) estimator is the optimal estimator of the class of integer equivariant estimators, which is one of the three classes of estimators for carrier phase ambiguity resolution. The two other classes are the class of integer estimators and the class of integer aperture estimators. Since the BIE-estimator can not be computed exactly, it is shown how to approximate this estimator while retaining the property of integer equivariance. It is also shown how the decorrelating Z-transformation and the integer search of the LAMBDA method can be used to speed up the computation of the BIE-estimator.