Covariance Analysis of Maximum Likelihood Attitude Estimation

Abstract

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 Fisher information matrix is derived for attitude determination based on such direct sensor measurements, and the wide field-of-view measurement model is shown to have the same Fisher information matrix. 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.