A mobile device supports positioning with positioning reference signals (PRS) on multiple beam by dividing the PRS processing into two separate modes, an acquisition mode and a tracking mode. In acquisition mode, the mobile device performs a fast scan of all of the beams from a base station transmitting PRS using less than the full set of resources for the PRS, i.e., less than the full bandwidth and/or less than the full number of repetitions of the PRS. The mobile device may select the best beams to use for positioning, e.g., based on signal strength metric. In tracking mode, the mobile device tracks the PRS from only the selected beams using the full set of resources for the PRS. The mobile device may return to acquisition mode after a predetermined number of positioning occasions or if the selected beams are no longer valid due to movement or change in conditions.