## On recursive random prolate hyperspheroids

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- 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]

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- Open-Access PDF
- https://arxiv.org/pdf/1403.7664
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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 ({ASRL}), University of Toronto},

year = {2014},

number = {TR-2014-JDG002},

month = mar,

note = {{arXiv}:1403.7664 {[math.ST]}},

}