Title: Nonlinear Kalman Filtering with Divergence Minimization,
Abstract: We consider the nonlinear Kalman filtering problem using Kullback-Leibler
(KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear
Kalman filters, nonlinear Kalman filters do not have closed form Gaussian
posteriors because of a lack of conjugacy due to the nonlinearity in the
likelihood. In this paper we propose novel algorithms to optimize the forward
and reverse forms of the KL divergence, as well as the alpha-divergence which
contains these two as limiting cases. Unlike previous approaches, our
algorithms do not make approximations to the divergences being optimized, but
use Monte Carlo integration techniques to derive unbiased algorithms for direct
optimization. We assess performance on radar and sensor tracking, and options
pricing problems, showing general improvement over the UKF and EKF, as well as
competitive performance with particle filtering.