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Nonsingular Attitude Filtering Using Modified Rodrigues Parameters

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Abstract

A method to estimate the general rigid body attitude using a minimal modified Rodrigues parameters (MRP) coordinate set is presented. The singularity avoidance technique is based on the stereographic projection properties of the MRP set, and makes use of a simple mapping relationship between MRP representations. Previous work has used the MRP duality to avoid singular attitude descriptions but has ignored the associated covariance transformation. This article presents a mapping to transform the state covariance matrix between these two representations as the attitude description is mapped between the two possible MRP sets. Second-order covariance transformations suitable for divided difference filtering are also provided. The MRP filter formulation based on extended Kalman filtering and divided difference filtering is compared with a standard multiplicative quaternion Kalman filter in an example problem.

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Authors and Affiliations

  1. Analytical Mechanics Associates, Inc., 303 Butler Farm Road, Suite 104A, Hampton, VA, 23666

    Christopher D. Karlgaard (Senior Project Engineer, Member AAS)

  2. Aerospace Engineering Sciences Department, University of Colorado, Boulder, CO, 80309-0431

    Hanspeter Schaub (Associate Professor, Member AAS)

Authors
  1. Christopher D. Karlgaard
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  2. Hanspeter Schaub
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Correspondence to Christopher D. Karlgaard.

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Karlgaard, C.D., Schaub, H. Nonsingular Attitude Filtering Using Modified Rodrigues Parameters. J of Astronaut Sci 57, 777–791 (2009). https://doi.org/10.1007/BF03321529

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