Angular Correlation Using Rogers-Szeg?-Chaos

Christine Schmid and Kyle J. DeMars
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Christine Schmid: Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA
Kyle J. DeMars: Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA

Mathematics, 2020, vol. 8, issue 2, 1-24

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.

Keywords: polynomial chaos; Szeg? polynomials; directional statistics; Rogers-Szeg?; state estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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