An inertial measurement system for a spinning projectile includes: a first, roll gyro to be oriented substantially parallel to the spin axis of the projectile; a second gyro and a third gyro with axes arranged with respect to the roll gyro; a controller, arranged to: compute a current projectile attitude from the outputs of the first, second and third gyros, the computed attitude comprising a roll angle, a pitch angle and a yaw angle; calculate a roll angle error; provide the roll angle error as an input to a Kalman filter that outputs a roll angle correction and a roll rate scale factor correction; and apply the calculated roll angle correction and roll rate scale factor correction to the output of the roll gyro.