The invention relates to the field of gun-launched guidance systems and to a navigation system based on inertial sensors mounted in a spinning projectile using at least one rotation sensing device with input components perpendicular to the spinning body's longitudinal axis, and an appertaining method for upfinding. The phase of the sinusoidal angular rate as detected by a phase-locked loop or correlator is used to determine the local vertical orientation. This invention may be used to align the inertial navigation system in spinning projectiles in ballistic trajectories, which can include artillery shells, satellites or underwater torpedoes.