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.
Recommended Citation
C. Schmid and K. J. DeMars, "Angular Correlation using Rogers-Szego-chaos," Mathematics, vol. 8, no. 2, article no. 171, MDPI, Feb 2020.
The definitive version is available at https://doi.org/10.3390/math8020171
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
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Feb 2020
