An inertial measurement system comprising: a first, roll gyro with an axis 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; operate a Kalman filter that receives a plurality of measurement inputs including at least roll angle, pitch angle and yaw angle and that outputs at least a roll angle error; initialise the Kalman filter with a roll angle error uncertainty representative of a substantially unknown roll angle; generate at least one pseudo-measurement from stored expected flight data; provide said pseudo-measurement(s) to the corresponding measurement input of the Kalman filter; and apply the roll angle error from the Kalman filter as a correction to the roll angle.