A system for producing an estimation of the overall speed of a vehicle relative to the ground is described which comprises the generation of a measurement of the instantaneous road grip coefficient (μr) of at least one wheel (1) of a vehicle with electric traction wherein a rotary electric machine (2) is coupled to said wheel to drive it individually in traction and in braking. This system comprises an indicator of the torque applied at each instant to that wheel based on the measurement of the current (Ic) in the electric machine, an indicator of the instantaneous dynamic load on said wheel and a stage for calculating the instantaneous road grip coefficient of said wheel (1) relative to the ground based on the torque indicator and the dynamic load indicator in order to determine the ratio of the tangential force applied to the ground by the wheel under the action of said torque to the normal force applied to the ground by the wheel under the action of the dynamic load. One or more tests of the value of the duly calculated road grip coefficient are used to validate the ability of a measurement of the corresponding circumferential wheel speed to supply an adequate approximation of the speed of advance of the vehicle in the position of that wheel.