Minimization of the Kullback-Leibler Divergence for Nonlinear Estimation
A nonlinear approximate Bayesian filter, named the minimum divergence filter (MDF), is proposed in which the true state density is approximated by an assumed density. The parameters of the assumed density are found by minimizing the Kullback-Leibler divergence of the assumed density with respect to the true density that is defined by either the Chapman-Kolmogorov equation or Bayes-Rule for the predictor and corrector steps, respectively. When an assumed Gaussian density is used and the system dynamics and measurement model possess additive Gaussian-distributed noise, the predictor of the MDF is identical to the predictor used under the Kalman framework, and the corrector defines the mean and covariance of the posterior Gaussian density as the first and second central moments of the posterior defined by Bayes-Rule. Because the MDF works for arbitrary densities, it can also quantify the temporal and measurement evolution of the parameters of an assumed directional state density. Simulations are shown to compare the MDF to standard Kalman-type filters, as well as the ability of the MDF to correct the parameters of an assumed Gauss-Bingham density given a von Mises-distributed line-of-sight measurement.
J. E. Darling and K. J. DeMars, "Minimization of the Kullback-Leibler Divergence for Nonlinear Estimation," Proceedings of the AAS/AIAA Astrodynamics Specialist Conference (2015, Vail, CO), vol. 156, pp. 213-232, Univelt Inc., Aug 2016.
AAS/AIAA Astrodynamics Specialist Conference (2015: Aug. 9-13, Vail, CO)
Mechanical and Aerospace Engineering
Keywords and Phrases
Astrophysics; Gaussian distribution; Approximate Bayesian; Chapman-Kolmogorov equation; Gaussian distributed noise; Kullback Leibler divergence; Line-of-sight measurements; Measurement model; Non-linear estimation; Second central moments; Parameter estimation
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International Standard Serial Number (ISSN)
Article - Conference proceedings
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