The invention relates to an alignment method based on a simplified mode allowing processing using an invariant Kalman filter, in which each speed involved in the navigation equations is expressed in a work reference frame (Rt) translated with respect to an inertial reference frame (Ri) and for which the origin moves along a reference inertial trajectory, the carrier of which is assumed to be close (geographic origin for alignment with the sun at known position, GPS trajectory for alignment in-motion, etc.). This simplified mode comprises the repetition of the following steps to estimate a mobile carrier state (P): —propagation (PROP) determining an estimated current state from a preceding estimated state, inertial sensor measurements and theoretical information on the carrier trajectory (P) —updating (MAJ) the estimated state using theoretical information on the carrier trajectory (P). The deterministic uncertainties of the sensors (bias/drift/scale factors, etc.) are only estimated during the propagation and update steps. A perturbation step (PERT) then allows inclusion of the values ignored in the simplified mode and estimation of these values by an optimisation method.