In a positioning system, a plurality of transmitter units (2, 3, 4, 5) transmit respective locating signals which are received at a mobile receiver unit (7). A processing system (7; 9) identifies the transmitter unit that transmitted each locating signal, and determines, for each transmitter unit, range data representative of a respective distance between the transmitter unit and the mobile receiver unit. The processing system determines a position estimate for the mobile receiver unit (7) by solving an optimisation problem that depends on i) the range data determined for the plurality of transmitter units, ii) data representative of the positions of the plurality of transmitter units in an environment (1), and iii) data representative of a position of a surface (1a, 1b, 1c, 1d, 1e; 601, 602) in the environment, by optimising for an objective function comprising a cost term that depends on a distance between the surface and the position estimate.