A system for establishing the speed, in a safe manner, of an object (1) which is travelling along a known trajectory, including a device (3, 7) for locating the object and direction of its movement, a receiver (6) for receiving a signal from a plurality of satellites (4, 5) and processing units. For each satellite, a processing unit (8) includes a frequency meter for measuring the frequency shift of the signal received relative to the frequency of the signal transmitted, a device for establishing the vectorial difference of the speeds of the object and the satellite by calculating the Doppler effect and, a calculator of the speed in the movement direction of the object. The measurements of the frequency shift are repeated independently on signals from a plurality of satellites, and the results obtained are combined in order to obtain a speed with the desired level of safety.