A method of despreading GPS spread spectrum signals containing pseudorandom noise (PRN) code sequences and received by a GPS receiver (24) is disclosed together with a GPS receiver (24) and a mobile communications device (MS1) (especially a mobile cellular telephone) for the same. The method comprises the steps of providing Doppler information relating to an estimate of the variation in Doppler shift as observed on the target signal by the GPS receiver and which is attributable to the motion of the GPS satellite; and correlating the target signal with a reference signal containing corresponding PRN code sequences, wherein, in the course of a single dwell, the correlation is modified as a function of the Doppler information.