A processing system (7; 9) for use in a positioning system, the positioning system comprising a mobile receiver unit and a plurality of transmitter units (2, 3, 4, 5), each configured to transmit respective transmitter-specific identification signals at intervals, wherein the processing system (7; 9) is configured to identify the respective transmitter unit (2, 3, 4, 5) that transmitted each received identification signal, wherein the processing system (7; 9) is further configured, for each of the plurality of transmitter units (2, 3, 4, 5), to: - determine a time of arrival of each of a plurality of the identification signals received by the mobile receiver unit from the transmitter unit (2, 3, 4, 5) during a time window; - process the times of arrival to determine range data representative of a plurality of distances between the transmitter unit (2, 3, 4, 5) and the mobile receiver unit at intervals during the time window; - determine Doppler-shift information from the plurality of received identification signals; - use the Doppler-shift information to determine velocity data representative of one or more values of a component of velocity of the mobile receiver unit during the time window; - perform an integration operation on the velocity data to determine distance data representative of one or more values of a component of distance travelled by the mobile receiver unit over one or more intervals during the time window; characterised in that the processing system (7; 9) is further configured, for each of the plurality of transmitter units (2, 3, 4, 5) to: - perform a comparison operation on the range data and the distance data to determine range error data for the transmitter unit (2, 3, 4, 5); and - use the range data to determine a range estimate representative of a distance between the transmitter unit (2, 3, 4, 5) and the mobile receiver unit; and further characterised in that: the processing system (7; 9) is further configured to determine a position estimate for the mobile receiver unit by solving an optimisation problem using the range estimates determined for the plurality of transmitter units (2, 3, 4, 5), wherein the range estimate for each transmitter unit (2, 3, 4, 5) is weighted in the optimisation problem in dependence on the range error data determined for the respective transmitter unit (2, 3, 4, 5). wherein the processing system (7; 9) is configured to identify the respective transmitter unit (2, 3, 4, 5) that transmitted each received identification signal, wherein the processing system (7; 9) is further configured, for each of the plurality of transmitter units (2, 3, 4, 5), to: - determine a time of arrival of each of a plurality of the identification signals received by the mobile receiver unit from the transmitter unit (2, 3, 4, 5) during a time window; - process the times of arrival to determine range data representative of a plurality of distances between the transmitter unit (2, 3, 4, 5) and the mobile receiver unit at intervals during the time window; - determine Doppler-shift information from the plurality of received identification signals; - use the Doppler-shift information to determine velocity data representative of one or more values of a component of velocity of the mobile receiver unit during the time window; - perform an integration operation on the velocity data to determine distance data representative of one or more values of a component of distance travelled by the mobile receiver unit over one or more intervals during the time window; - determine a time of arrival of each of a plurality of the identification signals received by the mobile receiver unit from the transmitter unit (2, 3, 4, 5) during a time window; - process the times of arrival to determine range data representative of a plurality of distances between the transmitter unit (2, 3, 4, 5) and the mobile receiver unit at intervals during the time window; - determine Doppler-shift information from the plurality of received identification signals; - use the Doppler-shift information to determine velocity data representative of one or more values of a component of velocity of the mobile receiver unit during the time window; - perform an integration operation on the velocity data to determine distance data representative of one or more values of a component of distance travelled by the mobile receiver unit over one or more intervals during the time window; characterised in that the processing system (7; 9) is further configured, for each of the plurality of transmitter units (2, 3, 4, 5) to: - perform a comparison operation on the range data and the distance data to determine range error data for the transmitter unit (2, 3, 4, 5); and - use the range data to determine a range estimate representative of a distance between the transmitter unit (2, 3, 4, 5) and the mobile receiver unit; and - perform a comparison operation on the range data and the distance data to determine range error data for the transmitter unit (2, 3, 4, 5); and - use the range data to determine a range estimate representative of a distance between the transmitter unit (2, 3, 4, 5) and the mobile receiver unit; and further characterised in that: the processing system (7; 9) is further configured to determine a position estimate for the mobile receiver unit by solving an optimisation problem using the range estimates determined for the plurality of transmitter units (2, 3, 4, 5), wherein the range estimate for each transmitter unit (2, 3, 4, 5) is weighted in the optimisation problem in dependence on the range error data determined for the respective transmitter unit (2, 3, 4, 5).