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A Multiplicative Residual Approach To Attitude Kalman Filtering With Unit-Vector Measurements

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Abstract

Using direction vectors of unit length as measurements for attitude estimation in an extended Kalman filter inevitably results in a singular measurement covariance matrix. Singularity of the measurement covariance means no noise is present in one component of the measurement. Unit-vector measurements have no noise in the radial component. Singular measurement covariances can be dealt with by the classic Kalman filter formulation as long as the estimated measurement covariance is non-singular in the same direction. Unit-vector measurements violate this condition because both the true measurement and the estimated measurement have perfectly known lengths. Minimum variance estimation for the unit-vector attitude Kalman filter is studied in this work. An optimal multiplicative residual approach is presented. The proposed approach is compared with the classic additive residual attitude Kalman filter.

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  1. The Charles Stark Draper Laboratory, GN&C Manned Space Systems, 17629 El Camino Real, Suite 470, Houston, Texas, 77058

    Renato Zanetti

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  1. Renato Zanetti
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Correspondence to Renato Zanetti.

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Zanetti, R. A Multiplicative Residual Approach To Attitude Kalman Filtering With Unit-Vector Measurements. J of Astronaut Sci 57, 793–801 (2009). https://doi.org/10.1007/BF03321530

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  • DOI: https://doi.org/10.1007/BF03321530

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