"Angular Correlation using Rogers-Szego-chaos" by Christine Schmid and Kyle J. DeMars
 

Abstract

Polynomial chaos expresses a probability density function (pdf) as a linear combination of basis polynomials. If the density and basis polynomials are over the same field, any set of basis polynomials can describe the pdf; however, the most logical choice of polynomials is the family that is orthogonal with respect to the pdf. This problem is well-studied over the field of real numbers and has been shown to be valid for the complex unit circle in one dimension. The current framework for circular polynomial chaos is extended to multiple angular dimensions with the inclusion of correlation terms. Uncertainty propagation of heading angle and angular velocity is investigated using polynomial chaos and compared against Monte Carlo simulation.

Department(s)

Mechanical and Aerospace Engineering

Publication Status

Open Access

Keywords and Phrases

Directional statistics; Polynomial chaos; Rogers-Szego; State estimation; Szego polynomials

International Standard Serial Number (ISSN)

2227-7390

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Feb 2020

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