Method for the geolocation of a device transmitting a signal containing at least one message to a plurality of relay satellites (102a, 102b, 102c, 102d, 102e) in a medium earth orbit, visible from the said device, receiving the said message and transmitting it to processing means, said method comprising at least the following steps: ∘ determination of the times of reception T Ri of the said message by the said relay satellites, ∘ determination of the pseudo-distances D i between the said device and the said relay satellites by solving the system of equations T Ri = D i /c + T e, where c is the speed of propagation of the transmitted signal, T e is the time of transmission of the message by the device and i varying from 1 to the number N vis of visible relay satellites, wherein T e, or alternatively the timely uncertainty between T e and times of reception T Ri, is unknown, o a step of searching for and acquiring, by reception means contained in the said device, a number N of satellite radio navigation signals, N being at least equal to 2+m-N vis where m is the number of space coordinates of the said device and N vis is the number of relay satellites visible from the device, ∘ determination of the time lags between the transmission of the radio navigation signals and their reception by the said device, ∘ transmission by the said device of these time lags in the said message, ∘ determination of the position of the said device from at least the said pseudo-distances D i, from the positioning coordinates of the said relay satellites and by the additional solving of the following equations: T Rj (GNSS) = D j (GNSS)/c + T ej (GNSS), where T Rj (GNSS) is the time of reception, by the beacon, of the radio navigation signal transmitted by the GNSS satellite j, T ej (GNSS) is its time of transmission and D j (GNSS) is the pseudo-distance between the beacon and the GNSS satellite j. ∘ determination of the times of reception T Ri of the said message by the said relay satellites, ∘ determination of the pseudo-distances D i between the said device and the said relay satellites by solving the system of equations T Ri = D i /c + T e, where c is the speed of propagation of the transmitted signal, T e is the time of transmission of the message by the device and i varying from 1 to the number N vis of visible relay satellites, wherein T e, or alternatively the timely uncertainty between T e and times of reception T Ri, is unknown, o a step of searching for and acquiring, by reception means contained in the said device, a number N of satellite radio navigation signals, N being at least equal to 2+m-N vis where m is the number of space coordinates of the said device and N vis is the number of relay satellites visible from the device, ∘ determination of the time lags between the transmission of the radio navigation signals and their reception by the said device, ∘ transmission by the said device of these time lags in the said message, ∘ determination of the position of the said device from at least the said pseudo-distances D i, from the positioning coordinates of the said relay satellites and by the additional solving of the following equations: T Rj (GNSS) = D j (GNSS)/c + T ej (GNSS), where T Rj (GNSS) is the time of reception, by the beacon, of the radio navigation signal transmitted by the GNSS satellite j, T ej (GNSS) is its time of transmission and D j (GNSS) is the pseudo-distance between the beacon and the GNSS satellite j.