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International Conference on Geometric Science of Information

GSI 2017: Geometric Science of Information pp 336–344Cite as

Uniform Observability of Linear Time-Varying Systems and Application to Robotics Problems

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

Abstract

Many methods have been proposed to estimate the state of a nonlinear dynamical system from uncomplete measurements. This paper concerns an approach that consists in lifting the estimation problem into a higher-dimensional state-space so as to transform an original nonlinear problem into a linear problem. Although the associated linear system is usually time-varying, one can then rely on Kalman’s linear filtering theory to achieve strong convergence and optimality properties. In this paper, we first present a technical result on the uniform observability of linear time-varying systems. Then, we illustrate through a problem arising in robotics how this result and the lifting method evoked above lead to explicit observability conditions and linear observers.

These results were obtained while all authors were with ISIR. This work was supported by the “Chaire d’excellence en Robotique RTE-UPMC”.

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Notes

  1. 1.

    For simplicity we assume that the camera frame and IMU frame coincide.

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Author information

Authors and Affiliations

  1. ISIR, Sorbonne Universités, UPMC Univ. Paris 06, CNRS UMR 7222, Paris, France

    Pascal Morin & Glauco Scandaroli

  2. ONERA - The French Aerospace Lab, Palaiseau, France

    Alexandre Eudes

Authors
  1. Pascal Morin
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  2. Alexandre Eudes
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  3. Glauco Scandaroli
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Corresponding author

Correspondence to Pascal Morin .

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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Morin, P., Eudes, A., Scandaroli, G. (2017). Uniform Observability of Linear Time-Varying Systems and Application to Robotics Problems. 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_39

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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