A smoother for attitude estimation using inertial and magnetic sensors

A smoother is proposed for an attitude estimation problem, where attitude is estimated using inertial and magnetic sensors. A smoother can provide better results when an offline processing is allowed. A quaternion is used to represent attitude. An indirect Kalman filter is used as a forward and backward filter. In the smoother, the final attitude quaternion is computed using the averaging algorithm of quaternions, which can be computed from a simple optimization problem.