An Analysis of the Quaternion Attitude Determination Filter

Abstract

The full-quaternion attitude determination filter is analyzed to address questions of co-variance singularity and quaternion normalization. It is shown how nonsingularity of the covariance in the extended Kaiman filter depends on the initial covariance, the process noise matrix, and implementation details of the filter. The covariance of a normalized quaternion estimate and the various means to achieve normalization are examined. The effect of a quaternion measurement update on the covariance and on the norm of the estimated quaternion is analyzed. It is also shown that the multiplicative and additive quaternion updates are equivalent. These are distinguished from an update called “rotational,” which was proven elsewhere to be the constrained maximum-likelihood optimal update. It is demonstrated that the reduced-order body-referenced attitude determination filter is embedded in the full-quaternion filter.