In a positioning system, a plurality of transmitter units (2, 3, 4, 5) transmit respective transmitter-specific identification signals at intervals, which are received at a mobile receiver unit (7). A processing system (7; 9) identifies the transmitter unit that transmitted each received identification signal, and, for each signal, determines range data from time of arrival data and determines distance data from Doppler shift information. The range data and distance data are compared to determine range error data. A position estimate for the mobile receiver unit (7) is determined by solving an optimisation problem using range estimates determined for the plurality of transmitter units, weighted in dependence on the range error data.