Nonlinear Kalman Filtering with Divergence Minimization
This provides improved filtering methods for nonlinear state estimation problems in domains like tracking and finance, though it appears incremental relative to existing divergence-based approaches.
The authors tackled the nonlinear Kalman filtering problem by proposing novel algorithms that optimize KL and α-divergence measures without approximations, using Monte Carlo integration. They demonstrated general improvement over UKF and EKF, and competitive performance with particle filtering in radar/sensor tracking and options pricing applications.
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $α$-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.