On the integer normal distribution of the GPS ambiguities.

Abstract

Carrier phase ambiguity resolution is the key to fast and high precision GPS kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. In order to describe the quality of the integer ambiguities, their distributional properties need to be known. This contribution introduces the probability mass function of the integer least-squares ambiguities. This integer normal distribution is needed in order to infer objectively whether or not ambiguity resolution can eexpected to be successful. Some of its properties are discussed. Attention is given in particular to the probability of correct integer estimation. Various diagnostic measures are presented for evaluating this probability.