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.