Rigid Body Attitude Estimation- An Overview and Comparative Stud.pdf

During the last decades ekf has been successfully

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During the last decades, EKF has been successfully applied to many Aeronautics appli- cations [Toda et al., 1969b], [Farrell, 1967], [Garcfa-Velo and Walker, 1997]. The existing EKF approaches for the attitude determination di ff er in the parametrization of attitude. The earliest applications used the Euler angles parameterization [Farrell, 1970]. How- ever, since three-dimensional parameterizations of the attitude face topological obstruc- tions, Euler angles and other similar parameterizations cannot be both global and non- singular [Stuelpnagel, 1964b]. However, the four-dimensional quaternion parametrization represents the attitude with only one redundant parameter. This representation is global and can be easily transformed into a rotation matrix. Another advantage of the quaternion is that system kinematics equation can be expressed in a bilinear form of the attitude and the an- gular velocity vector. These advantages have all contributed to the popularity of quaternion- based Kalman filters among researchers [Markley, 2003], [Bar-Itzhack and Oshman, 1985]. In order to maintain orthogonality in the estimated attitude and avoid singularity of the
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C hapter 4. D ynamic A ttitude F iltering and E stimation 43 covariance matrix, the quaternion norm constraint should be taken into account by nor- malizing the quaternion estimate vector. It is known that in case of a slowly time-varying attitude, normalization can result in faster convergence and when attitude changes fast, it is necessary to do this in order to avoid divergence [Deutschmann et al., 1992]. The most simple quaternion normalization consists in dividing the estimated quaternion after each update stage by its Euclidean norm [Bar-Itzhack, 1971]. Although this act, known as the “brute force” normalization, is outside the filter’s algorithm and its estimation process, it is shown that normalizing the estimated quaternion does not a ff ect the propagation of the co- variance matrix. In [Bar-Itzhack et al., 1991], several quaternion normalization algorithms are compared and new methods are introduced. The authors in [Le ff erts et al., 1982] dis- cussed the problem with three di ff erent approaches. The author in [Shuster, 2003a], [Shuster, 2003b] examined both cases of constrained and unconstrained quaternion estimations. It was shown, with examples, that the uncon- strained quaternion estimates may lead to di ff erent estimation results that can depend on the choice of measurement sensitivity matrix. Therefore, it is advised to use constrained techniques to avoid problems such as obtaining singular inverse covariance matrices. The authors in [Zanetti et al., 2009] have recently showed that constrained estimation is math- ematically equivalent to the unconstrained estimation when a brute force normalization is applied. In general, the Kalman filtering approach has shown better performance than many other attitude estimation approaches. In [Marques et al., 2000], a comparison between the dynamic EKF and the deterministic method of SVD can be found . The experiment, which
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