The use of the pseudorange information contained within the GPS carrier phase observables enables to achieve a high level of positioning accuracy, but requires the resolution of the intrinsic cycle ambiguities of the phase measurements. Several methods have been proposed that can solve the ambiguities without static initialization by performing a search of the most coherent values of the double difference ambiguities of four particular satellites. They belong to the class of the multiple hypotheses sequential tests, that check each envisaged hypothesis against a decision criterion. A new method of ambiguity resolution on-the-fly, designed to make an optimal use of all the available measurements, is proposed in this paper. The decision criterion used by this method is the a posteriori probability of each potential solution. The mathematical developments involved in the design of the method are exposed, and the first simulation results obtained are presented, showing the validity of the concept proposed in this paper.