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    Volumetric Uncertainty Bounds and optimal configurations for Converging Beam Triple LIDAR

    Brooms, Anthony and Holtom, Theodore C. (2020) Volumetric Uncertainty Bounds and optimal configurations for Converging Beam Triple LIDAR. Technical Report. Birkbeck, University of London, London, UK.

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    Abstract

    We consider the problem of quantifying uncertainty for converging beam triple LIDAR when the input uncertainty follows a uniform distribution. We determine expressions for the range (i.e. set of reachable points) for the reconstructed velocity vector as a function of any particular setting of the nominal input parameters and determine an explicit lower (and upper) bound on the (averaged) volume (with respect to Lebesgue measure), in R 3 , of that range. We show that the size of any such bound is inversely proportional to the absolute value of the triple scalar product of the unit vectors characterizing the Doppler measurement directions (optimized over the uncertainty region) in R 6 associated with the nominal angle settings under consideration. This leads to the conclusion that the nominal LIDAR configurations that minimize output uncertainty ought to be those in which the value of the triple scalar product of the Doppler unit vectors is at its largest.

    Metadata

    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #56
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Maura Paterson
    Date Deposited: 17 Jun 2020 10:01
    Last Modified: 22 Jul 2020 03:31
    URI: http://eprints.bbk.ac.uk/id/eprint/32257

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