Attitude Quaternion Estimation Using a Spectral Perturbation Approach

All quaternion methods for static attitude determination currently rely on either the spectral decomposition of a 4 x 4 matrix (q-Method) or finding the maximum eigenvalue of a 4th-order characteristic equation (QUEST). Using a spectral perturbation approach, we show it is possible to analytically estimate the attitude quaternion to high accuracy and recursively calculate the maximum-likelihood attitude quaternion to arbitrary numerical precision. Analytic or recursive estimation removes several numerical difficulties which are inherent to state-of-the-art algorithms, suggesting our results may substantially benefit high-frequency and limited memory embedded software implementations, such as those commonly used on spacecraft computers.