Geometric-based nonlinear filtering with applications to attitude estimation
Andrle, Michael S.
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The attitude determination problem is one of estimating the orientation of a given body with respect to some reference. This problem is frequently encountered throughout many fields, especially in aerospace engineering where determining or controlling the orientation of aircraft and spacecraft is a prevalent subject. Since this problem was posed by Grace Wahba, it has received an a great amount of attention. A fundamental obstacle in attitude determination is the nature of its parameterizations. Attitude parameters either contain singularities or must satisfy certain constraints. The structure of the problem requires the use of multiple coordinate systems and, in addition, other state quantities involved often depend on the unknown attitude itself. This poses natural difficulties since classical, real-time estimation techniques are constructed upon a single, unconstrained coordinate system. Since the seminal work of Lefferts, Markley and Shuster much research has been conducted in the development of attitude estimation techniques that are both global and effective. This work builds on an existing approach to addressing the attitude parameter constraint problem. It is generalized to account for the representation of state quantities with respect to a random coordinate basis, a structure which is imposed by the unknown orientation of the frame in which the quantities are specified. This objective requires the adaptation of existing filtering algorithms, namely the extended Kalman Filter and the Unscented Kalman Filter, to a modified error metric. Theoretical developments corroborate existing work that addresses the attitude parameter constraint issue while contributing a correct treatment of state quantities represented with respect to the coordinate basis attached to the unknown attitude. The proposed algorithms are validated using both a planar inertial navigation example and a realistic spacecraft attitude determination problem.