Brooms, Anthony C. 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 Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Maura Paterson |
| Date Deposited: | 17 Jun 2020 10:01 |
| Last Modified: | 09 Aug 2023 12:48 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/32257 |
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