A mobile telephony handset has a wireless communications transceiver for exchanging signals with a base station, and a positioning receiver for receiving coded ranging signals from a satellite-based positioning system. The handset is configured such that the positioning receiver is activated only periodically to perform a position fix using the ranging signals and between such active periods is in a power-saving condition. Each position fix includes a respective time measurement in which a precision time indication referenced to the positioning system reference time source is recorded and saved. The handset includes calibration means, which generates a calibrated time reference for performing each of a plurality of new such position fixes. This calibrated reference is derived by summing (a) an elapsed time indication derived from a repeated signal pattern which is received from the base station and is synchronised to the base station reference time source, the elapsed time indication being indicative of the time elapsed since a previous position fix, and (b) the precision time indication obtained with that previous position fix.