The invention relates to the field of inertial navigation systems and in particular to a method for determining the attitude, position, and velocity of a mobile device from knowledge of the direction of the earth's magnetic field in an absolute reference frame and signals supplied to processing means (4) of these signals by gyroscopic measuring means (1) in three axes, accelerometric measuring means (2) in three axes, and magnetic measuring means (3) in three axes, said measuring means being located on-board the device and according to three three-dimensional reference frames connected to the device reference frame OdXdYdZd, and characterized by comprising: a first step in which the attitude of the device is calculated at time K−1 from: signals coming from the gyroscopic measuring means (1) at time k signals coming from the accelerometric measuring means (2) at time k+1 the position and velocity of the device in the absolute reference frame at time k signals supplied by the magnetic measuring means (3) representing the projection of the earth's magnetic field in the three-dimensional magnetic reference frame linked to the device, a second step in which the position of the device and its velocity in the absolute reference frame at time k+1 are calculated from: the attitude calculated in the first step signals coming from the accelerometric measuring means (2) at time k+1 signals coming from the gyroscopic measuring means (1) at time k the position and velocity of the device in the absolute reference frame at time k signals supplied by the magnetic measuring means (3) representing the projection of the earth's magnetic field in the reference frame.