The paper presents a numerical algorithm used to establish the position of a vehicle reported to the Earth 's geographical frame. The method we suggest based on the direct integration of the equation of inertial navigation, considering the vehicle's attitude as a result of the integration of the differential matriceal attitude equation. This integration is performed using a quick method, the induced commutation error being avoided with a numerical logistics which implies the usage of the data acquisition card from strap-down gyrometers in the navigation processor