Covariance analysis of maximum likelihood attitude estimation

An attitude determination covariance measurement model for unit vector sensors with a wide field-of-view is analyzed and compared to the classic QUEST covariance model. The wide field-of-view model has been previously proposed as a more realistic alternative for sensors where measurement accuracy depends on angular distance from the boresight axis. Both QUEST and the wide field-of-view models are evaluated relative to a measurement model that uses the two-dimensional sensor focal plane measurements directly, rather than first converting them to unit vectors. The Cramér-Rao lower bound is derived for attitude determination based on such direct sensor measurements, and the wide field-of-view measurement model is shown to achieve this Cramér-Rao lower bound. Numerical simulations confirm that an extended Kalman filter based on the wide field-of-view model outperforms a filter based on the QUEST measurement model, and also that the wide field-of-view 3σ bounds are effectively identical to those of a filter based on the direct two-dimensional sensor measurements.