A method for managing longitudinal speed of an autonomous vehicle travelling on a traffic lane including stop signage located in front of the autonomous vehicle. The autonomous vehicle is equipped with a first detector to detect a first range and a second detector to detect a second range. The first range is greater than the second range. The method includes detecting the stop signage by the first detector and implementing a first deceleration logic and detecting the stop signage by the second detector and implementing a second deceleration logic. The first and second deceleration logic implement jerks, the absolute value of which is less than a first threshold. The second deceleration logic controls the stopping of the autonomous vehicle with an accuracy of around one centimeter relative to the stop signage.