Alleviating ambiguous pseudorange reconstruction in connection with satellite-based positioning of mobile terminals with assistance data such as Assisted GPS (AGPS). An initial pseudorange selection cycle includes: determining a first admissible pseudorange associated with a first satellite; determining all pseudoranges associated with at least two additional satellites which combined with the first pseudorange form admissible relative pseudoranges; forming a set of pseudorange vectors representing all possible combinations of the determined pseudoranges associated with the first and at least two additional satellites; and forming a set of selected pseudorange vectors by selecting at least one vector from the set of pseudorange vectors.