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Estimation, Search, and Planning (ESP) Research Group

The probability density function of a transformation-based hyperellipsoid sampling technique

Authors
  1. Jonathan D. Gammell
  2. Timothy D. Barfoot
Publication Date
Abstract

Sun and Farooq [2] showed that random samples can be efficiently drawn from an arbitrary n-dimensional hyperellipsoid by transforming samples drawn randomly from the unit n-ball. They stated that it was a straightforward to show that, given a uniform distribution over the n-ball, the transformation results in a uniform distribution over the hyperellipsoid, but did not present a full proof. This technical note presents such a proof.

Publication Details
Type
Technical Report
Institution
Autonomous Space Robotics Lab, University of Toronto
Number
TR-2014-JDG004
arXiv Identifier arXiv
1404.1347 [math.ST]
Manuscript
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BibTeX Entry
@techreport{gammell_arxiv14b,
author = {Jonathan D Gammell and Timothy D Barfoot},
title = {The probability density function of a transformation-based hyperellipsoid sampling technique},
institution = {Autonomous Space Robotics Lab, University of Toronto},
year = {2014},
number = {TR-2014-JDG004},
month = apr,
note = {{arXiv}:1404.1347 {[math.ST]}},
}