A method for calibrating a time difference of arrival-based local positioning system for k−D localization, k=2 or 3, includes collecting N sets of time difference of arrival measurements related to a mobile node, N≥2, each nth set of measurements being performed by Bn beacon nodes among B beacon nodes of the positioning system while the mobile node is located is a nth position within a region covered by the positioning system, Bn≥k+2, and determining optimal beacon positions that minimize an objective function depending on N residual error vectors, the calculation of each nth position of the mobile node using beacon positions and the nth set of measurements, the calculation allowing the calculation of the nth residual error vector.