A positioning system has an initiator device configured for emitting a high-speed wireless signal, at least one reference device configured for receiving the high-speed wireless signal and emitting a low-speed wireless signal after receiving the high-speed wireless signal, at least one target device each having one or more components for receiving the low-speed wireless signals, and at least one engine configured for determining the position of each of the at-least-one target device by calculating the distance between the target device and each of the at-least-one reference device based on at least the times-of-arrival of the low-speed wireless signals, each time-of-arrival being the time that the corresponding low-speed wireless signal being received by the target device, and determining the position of the target device based on the calculated distances.