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On recursive random prolate hyperspheroids

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

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