The use of the pseudorange information contained within the GPS carrier phase measurements enables to achieve a high level of positioning accuracy. But full access to this accuracy in real time for dynamic applications, like aircraft landing, requires the resolution "on the- fly" of the intrinsic ambiguity of the phase measurements. This can be done using one of the numerous ambiguity searching procedures, among which ones are LSAST and MAPAS. These two methods can be seen as sequential tests of the same multiple hypotheses. They use distinct decision criteria, and this results in different implementation constraints, run-time capabilities and performances. Both of them show a similar behaviour when applied to clean data, but MAPAS appears to be more robust when using data affected by multipath. The comparison starts with a parallel presentation of the mathematical developments involved in the design of the two methods, then their practical advantages are reviewed and some results are shown of their application to clean and corrupted data.