The Bingham-Gauss Mixture Filter for Pose Estimation


The Bingham-Gauss density quantifies the uncertainty of a state vector comprised of an attitude quaternion and other Euclidean states on its natural manifold, the unit hypercylinder, without the need to assume that the attitude error is small. The Bingham-Gauss density is developed, which facilitates a tractable implementation of an approximate Bayesian filter in which the true state densities, as quantified by the Chapman-Kolmogorov equation and Bayes' rule, are approximated by a Bingham-Gauss density through moment matching, which is the Kullback-Leibler optimal approximation. The Bingham-Gauss density is then used to develop the Bingham-Gauss mixture (BGM) density. Methods to approximate a Bingham-Gauss density by a BGM density are presented. The BGM filter is then developed, which is an approximate Bayesian filter quantifying the approximate temporal and measurement evolution of a BGM density. The BGM filter is then applied to estimate the relative dynamic pose of an inspector spacecraft with respect to a target spacecraft given nonlinear measurements in order to show its efficacy.

Meeting Name

AIAA/AAS Astrodynamics Specialist Conference (2016: Sep. 13-16, Long Beach, CA)


Mechanical and Aerospace Engineering

Keywords and Phrases

Astrophysics; Bandpass filters; Gaussian distribution; Mixtures; Spacecraft; Approximate Bayesian; Chapman-Kolmogorov equation; Kullback-Leibler; Nonlinear measurement; Optimal approximation; Relative dynamics; State densities; Target spacecraft; Bins

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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© 2016 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.

Publication Date

01 Sep 2016

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