An invariant upperbound for the GNSS bootstrappend ambiguity success-rate

Carrier phase ambiguity resolution is the key to fast and high precision GPS 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. The success or failure of carrier phase ambiguity resolution can be predicted by means of the probability of correct integer estimation, also referred to as the ambiguity success-rate. Upperbounds of the success-rate can be used to decide that ambiguity resolution has become unreliable. In this contribution we prove an upperbound for the bootstrapped success-rate. The upperbound is easy to compute and it is invariant for the class of admissible ambiguity transformations.