Particle Filtering for Attitude Estimation Using a Minimal Local-Error Representation: A Revisit

For spacecraft attitude representation, the quaternion is preferred over other representations due to its bilinear nature of the kinematics and the singularity-free property. However, when applied in the attitude estimation filters, its unity norm constraint can be easily destroyed by the quaternions averaging operation. Although the brute-force quaternion normalization can be implemented, this strategy is crude and may be not sufficient for some filters which necessitate the state covariance calculations [2-4]. In [1] a quaternion-based particle filtering (QPF) for spacecraft attitude estimation has been proposed based on the local/global attitude representation. For the local/global representation, the unconstrained three-dimensional representation, say modified Rodrigues parameter (MRP), is used for the local-error space while the quaternion is used for the global representation and propagation. With this ingenious structure, the unconstrained local-error representation is used directly as the state in the developed QPF, which can maintain the unity norm of the quaternion in a nature way. Therefore, there is no need to perform the brute-force quaternion normalization any more. Since the MRP and quaternion based particles are used simultaneously in the filtering cycle of the QPF, they should be transformed to each other, which necessitates a fiducial attitude quaternion (see Eq. (18) in [1]). In the QPF, the estimated quaternion that is given by