Minimum Divergence Filtering using a Polynomial Chaos Expansion
Bayesian filters for discrete-time systems make use of the Chapman-Kolmogorov equation and Bayes' rule to predict and update the uncertainty of a state. For nonlinear filtering problems, the Bayesian recursion is not guaranteed to close. An assumed density framework can be used to force the recursion to close, where one such realization is the minimum divergence filter, which seeks to minimize the Kullback-Leibler divergence of the assumed density with respect to the reference state density. This results in a moment matching problem, where the moments are traditionally approximated using Gauss-Hermite quadrature. An alternative solution is presented by replacing the Gauss-Hermite quadrature with a polynomial chaos expansion to reduce computational cost and provide a method that is more robust to distributional assumptions. The ability of the polynomial chaos expansion to compute the expected value of a random variable that cannot be assumed Gaussian is tested against a Gauss-Hermite quadrature approximation, unscented transform, and Monte Carlo sampling. Another test is preformed isolating the corrector of the minimum divergence filter with varied prior uncertainties. The two methods are then compared in an orbital state estimation problem.
C. L. Schmid and K. J. DeMars, "Minimum Divergence Filtering using a Polynomial Chaos Expansion," Advances in the Astronautical Sciences, vol. 162, pp. 1909-1928, Univelt Inc., Aug 2018.
AAS/AIAA Astrodynamics Specialist Conference, 2017 (2017: Aug. 20-24, Stevenson, WA)
Mechanical and Aerospace Engineering
Keywords and Phrases
Astrophysics; Digital control systems; Discrete time control systems; Gaussian distribution; Monte Carlo methods, Alternative solutions; Chapman-Kolmogorov equation; Discrete - time systems; Gauss-Hermite quadrature; Kullback Leibler divergence; Monte Carlo sampling; Non-linear filtering problems; Polynomial chaos expansion, Polynomial approximation
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