Inertial navigation system

An inertial measurement system for a spinning projectile comprising:

• 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 such that they define a three dimensional coordinate system;
• at least a first linear accelerometer
• 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;
• compute a current projectile velocity vector from the outputs of at least the first linear accelerometer;
• combine a magnitude of said velocity vector with an expected direction for said vector to form a current projectile pseudo-velocity vector;
• provide the velocity vector and the pseudo-velocity vector to a Kalman filter that outputs a roll gyro scale factor error calculated as a function of the difference between the velocity vector and the pseudo-velocity vector;
• and
• apply the roll gyro scale factor error from the Kalman filter as a correction to the output of the roll gyro.