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Sigma Point Kalman Filtering on Matrix Lie Groups Applied to the SLAM Problem

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

This paper considers sigma point Kalman filtering on matrix Lie groups. Sigma points that are elements of a matrix Lie group are generated using the matrix exponential. Computing the mean and covariance using the sigma points via weighted averaging and effective use of the matrix natural logarithm, respectively, is discussed. The specific details of estimating landmark locations, and the position and attitude of a vehicle relative to the estimated landmark locations, is considered.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Montréal, QC, H3A 0C3, Canada

    James Richard Forbes

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    David Evan Zlotnik

Authors
  1. James Richard Forbes
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  2. David Evan Zlotnik
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Correspondence to James Richard Forbes .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Forbes, J.R., Zlotnik, D.E. (2017). Sigma Point Kalman Filtering on Matrix Lie Groups Applied to the SLAM Problem. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_37

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

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