Abstract
The estimation of the orientation of a rigid body is important in the aerospace and robotics fields. The attitude of a rigid body is naturally described by a rotation matrix, which belongs to the special orthogonal group of rigid-body rotations, denoted by . Because of the orthonormality and determinant constraints, parameterizations of are often used. However, parameterizations may suffer from singularities or nonuniqueness of representation. Recently, there has been significant interest in working directly with and more generally with . This paper presents a discrete-time Kalman-like filter that performs estimation directly on . The filter presented honors the orthonormality and determinant constraints associated with . The developed filter is applied to a spacecraft attitude estimation problem that involves estimation on . Its effectiveness is demonstrated in a numerical example, comparing its performance with the well-established multiplicative extended Kalman filter and the recently developed norm-constrained extended Kalman filter.
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