A method for determining the position and orientation of a vehicle includes constructing, for several instants tk ranging between instants toj−1 and toj, an estimate of the instantaneous value of the physical quantity on the basis of the measurements of an inertial navigation unit; constructing an estimate of the physical quantity for the instant toj by computing the arithmetic mean of the constructed instantaneous values; computing a deviation between a measurement of the physical quantity obtained on the basis of the measurement of an odometer and an estimate of the physical quantity at the instant toj; and correcting, as a function of the deviation computed for the instant toj, estimated positions and orientations of the vehicle, in order to obtain a corrected position and a corrected orientation.