Angular Correlation Using Rogers-Szegő-Chaos Academic Article

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.

authors

• DeMars, Kyle

published proceedings

• MATHEMATICS

altmetric score

• 0.5

author list (cited authors)

• Schmid, C., & DeMars, K. J.

citation count

• 0

complete list of authors

• Schmid, Christine||DeMars, Kyle J

publication date

• February 2020

publisher

• MDPI  Publisher

published in

• MATHEMATICS  Journal

keywords

• Directional Statistics
• Polynomial Chaos
• Rogers-szeg
• State Estimation
• Szeg Polynomials

Digital Object Identifier (DOI)

• 10.3390/math8020171

start page

• 171

end page

• 171

volume

• 8

issue

• 2

URL

• http://dx.doi.org/10.3390/math8020171