On recursive random prolate hyperspheroids
Share
- 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 (ASRL), University of Toronto
- Number
- TR-2014-JDG002
- arXiv Identifier
- 1403.7664 [math.ST]
- Manuscript
- Open-Access PDF
- https://arxiv.org/pdf/1403.7664
- Google Scholar
- Google Scholar
- 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 ({ASRL}), University of Toronto},
year = {2014},
number = {TR-2014-JDG002},
month = mar,
note = {{arXiv}:1403.7664 {[math.ST]}},
}