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Estimation, Search, and Planning (ESP) Research Group

On recursive random prolate hyperspheroids

Authors
  1. Jonathan D. Gammell
  2. Siddhartha S. Srinivasa
  3. Timothy D. Barfoot
Publication Date
Abstract

This technical note analyzes the properties of a random sequence of prolate hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is defined by a sample drawn randomly from the previous volume such that the sample lies on the new surface (Fig. 1). Section 1 defines the prolate hyperspheroid coordinate system and the resulting differential volume, Section 2 calculates the expected value of the new transverse diameter given a uniform distribution over the existing prolate hyperspheroid, and Section 3 calculates the convergence rate of this sequence. For clarity, the differential volume and some of the identities used in the integration are verified in Appendix A through a calculation of the volume of a general prolate hyperspheroid.

Publication Details
Type
Technical Report
Institution
Autonomous Space Robotics Lab, University of Toronto
Number
TR-2014-JDG002
arXiv Identifier arXiv
1403.7664 [math.ST]
Manuscript
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BibTeX Entry
@techreport{gammell_arxiv14,
author = {Jonathan D Gammell and Siddhartha S Srinivasa and Timothy D Barfoot},
title = {On recursive random prolate hyperspheroids},
institution = {Autonomous Space Robotics Lab, University of Toronto},
year = {2014},
number = {TR-2014-JDG002},
month = mar,
note = {{arXiv}:1403.7664 {[math.ST]}},
}