A positioning system accurately estimates transmission times of signals from a signal transmitter and measures a position of a receiver on the basis of the transmission times. The receiver 10 comprises a velocity-vector calculating unit 12 calculating velocity vectors of GPS satellites 20 on the basis of signals from the GPS satellite; a satellite selecting unit 13 generating a combination of velocity vectors from the calculated velocity vectors and selecting a combination of GPS satellites from the GPS satellites on the basis of the combination of velocity vectors; a position calculating unit 15 calculating positions of the receiver 10 at a plurality of times, the times being signal transmission times, on the basis of signals from the selected GPS satellites; and a position-accuracy evaluating unit 17 evaluating the accuracy of the calculated positions of the receiver 10, setting one time selected from the plurality of times corresponding to the plurality of positions as a transmission time, and setting the position of the receiver 10 corresponding to the transmission time as an estimated position.