Nowadays, one of the main research topic on GNSS positioning is PPP ambiguity resolution (PPP- AR) as well as the ambiguity convergence (PPP-AC) time required to reach some level of accuracy. Several papers have been published concerning PPP-AR. In this contribution the aim is to answer the following questions in the context of PPP: a) Once you know the position of one station how long should take to reach accuracy of the ambiguities in the level of at least 1/3 of a cycle; b) Once you know the ambiguity with this level of precision, how long should take to obtain a position with 3D- precision better than 10 cm. In a first case, we will use the ion-free observable, so without a priori knowing about the ionosphere and estimating the troposphere residuals after applying an appropriated model. In the second case, we will assess the original observables and include the ionosphere delay for each satellite to be estimated in the model, assuming or not some knowledge about the a priori ionosphere delay. In both cases, the receiver clock errors are treated as white noise. All other effects such as Earth tides, ocean tide loading, antenna phase center corrections, phase wind up, phase bias (PB) and code bias (CB) should have been taken into account. Mathematical fundamental and results from data under different atmosphere conditions will be presented.