Unmanned aircraft systems (UASs) have been developed and studied as temporal communication systems for emergency and rescue services during disasters, such as earthquakes and serious accidents. In a typical UAS model, several unmanned aerial vehicles (UAVs) are used to provide services over a large area. The UAV is comprised of a transmitter and receiver to transmit/receive the signals to/from terrestrial stations and terminals. Therefore, the carrier frequencies of the transmitted and received signals experience Doppler shifts due to the variations in the line-of-sight velocity between the UAV and the terrestrial terminal. Thus, by observing multiple Doppler shifts from different UAVs, it is possible to detect the position of a user that possesses a communication terminal for the UAS. This study aims to present a methodology for position detection based on the least-squares method to the Doppler shift frequencies. Further, a positioning accuracy index is newly proposed, which can be used as an index for measuring the position accurately, instead of the dilution-of-precision (DOP) method, which is used for global positioning systems (GPSs). A computer simulation was conducted for two different flight route models to confirm the applicability of the proposed positioning method and the positioning accuracy index. The simulation results confirm that the parameters, such as the flight route, the initial position, and velocity of the UAVs, can be optimized by using the proposed positioning accuracy index.