Method for calibrating a local positioning system based on time-difference-of-arrival measurements

A method for calibrating a time difference of arrival-based local positioning system for kD localization, k=2 or 3, comprising:

• estimating initial beacon positions:
• 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;
• calculating N residual error vectors through calculation of N positions of the mobile node, by the N sets of time difference of arrival measurements and beacon positions, a calculation of the nth position of the mobile node enabling a calculation of an nth initial residual error vector, the calculation of each nth position of the mobile node using the beacon positions and the nth set of measurement;
• determining optimal beacon positions that minimize an objective function depending on the N residual error vectors;
• and
• calibrating the local positioning system based on the optical beacon positions,
• wherein the step of determining optimal beacon positions comprises varying assumed beacon positions from the initial positions until the objective function meets a termination criterion, and
• wherein the method comprises a step of re-estimating initial beacon positions when the norm of the residual error vectors corresponding to the initial beacon positions are higher than a threshold.