Gaussian sum particle flow filter

Particle flow filters provide an approach for state estimation in nonlinear systems. They can outperform many particle filter implementations when the state dimension is high or when the measurements are highly informative. Instead of employing importance sampling, the particles are migrated by numerically solving differential equations that describe a flow from the prior to the posterior at each time step. An analytical solution for the flow equation requires a Gaussian assumption for both the prior and the posterior. Recently Khan et al. [1] devised an approximate flow that could address the case when the prior is represented by a Gaussian Mixture Model (GMM) and the likelihood function is Gaussian. The solution involved inversion of a large matrix which made the computational requirements scale poorly with the state dimension. In this paper, we devise an approximate particle flow filter for the case when both the prior and the likelihood are modeled using Gaussian mixtures. We perform numerical experiments to explore when the proposed method offers advantages compared to existing techniques.