A method of calculating a speed of an aircraft, a method for calculating a protection radius, a positioning system and an associated aircraft are disclosed. In one aspect, the method includes obtaining a measured speed of the aircraft and obtaining a measured position of the aircraft, associated with a reliability protection radius related to position. The method also includes calculating, by a correction loop, a corrected speed, wherein the calculation of the corrected speed includes calculating a calculated position by integration of the corrected speed, and correcting the measured speed as a function of a difference between the calculated position and the measured position. The method further comprising calculating a reliability protection radius related to the corrected speed.