A MULTIPLICATIVE RESIDUAL APPROACH TO ATTITUDE KALMAN FILTERING WITH UNIT-VECTOR MEASUREMENTS

摘要

Using direction vectors of unit length as measurements for attitude estimationin an extended Kalman filter inevitably results in a singular measurementcovariance matrix. Singularity of the measurement covariance means no noiseis present in one component of the measurement. Singular measurementcovariances can be dealt with by the classic Kalman filter formulation as longas the estimated measurement covariance is non singular in the same direction.Unit vector measurements violate this condition since both the true measurementand the estimated measurement have perfectly known lengths. Minimumvariance estimation for the unit vector attitude Kalman filter is studied in thiswork. An optimal multiplicative residual approach is presented. The proposedapproach is compared with the classic additive residual attitude Kalman filter.