Angular Correlation using Rogers-SzegÖ-Chaos
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.
C. L. Schmid and K. J. Demars, "Angular Correlation using Rogers-SzegÖ-Chaos," Advances in the Astronautical Sciences, vol. 168, pp. 1583-1601, Univelt Inc., Jan 2019.
29th AAS/AIAA Space Flight Mechanics Meeting, 2019 (2019: Jan. 13-17, Maui, HI)
Mechanical and Aerospace Engineering
Keywords and Phrases
Intelligent systems; Monte Carlo methods; Probability density function; Space flight, Angular correlations; Complex units; Heading angles; Linear combinations; One dimension; Polynomial chaos; Probability density function (pdf); Uncertainty propagation, Polynomials
International Standard Book Number (ISBN)
International Standard Serial Number (ISSN)
Article - Conference proceedings
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01 Jan 2019