System and method for calculating advance speed of a vehicle

A control system comprising:

• a control circuit including one or more processors, the control circuit configured to receive speed signals indicating an angular speed of wheels of an axle of a vehicle, the control circuit configured to estimate, as a function of said angular speed, a value of adhesion of a contact area of the wheels of said axle to a route, and calculate a value of slip of the wheels of said axle;
• the control circuit configured to generate signals representative of a derivative value of said adhesion as a function of the slip of the wheels of said axle, and to calculate an error signal as a difference between the derivative value and a predetermined reference value;
• the control circuit comprising an adaptive filter that implements a Least Mean Square (LMS) algorithm, the control circuit configured to input the derivative value into the LMS algorithm, the adaptive filter configured to generate a driving signal based on said derivative value that is input, wherein the control circuit is configured to continuously adapt the LMS algorithm based on the error signal to reduce and keep the error signal substantially at zero;
• the control circuit further configured to control a torque exerted on said axle or the wheels of said axle based on said driving signal.