In this study, we present an attempt to use low earth orbit (LEO) satellites as an alternative method of positioning in situations where the global navigation satellite system (GNSS) is rendered unusable by spoofing or jamming attacks. Specifically, we used the received Doppler frequency from the satellite with a receiver externally connected to a precision clock oscillator, such as a rubidium oscillator. If a precise clock oscillator is used, the frequency offset can be removed at the receiver side. As a result, we could obtain the absolute Doppler frequency of each LEO satellite. Based on this information, the approximate position within a few hundred meters could be determined. This strategy was inspired by WiFi fingerprinting, an indoor location estimation method. A map of the Doppler frequencies to be received can be created by measuring the Doppler frequency of each satellite at each measurement point. The position can be estimated by matching the Doppler frequency measured by the receiver to the map. A simulation was conducted using an almanac of the Iridium satellite constellation. The receiver position was assumed to be in Tokyo, Japan. The accuracy of the orbits for these Iridium satellites was assumed to be the same as the accuracy of the orbits for the current GPS/GNSS. The total number of constellations was set to 66. Once the time and location were determined, the Doppler frequency to be measured could be predicted. The observation accuracy applied was verified to be the same as in the case of GPS. Furthermore, the accuracy of the measured Doppler frequency on the receiver side was set to 0.1 Hz. Using a precise clock oscillator, the Doppler frequency could indeed be measured with an accuracy of 0.1 Hz (as the signal strength was stronger, we thought that it was achievable).