A log homotopy based particle flow solution for mixture of Gaussian prior densities

Particle flow filters, also known as Daum-Huang filters (DHF), provide an alternative method for the state estimation of non-linear / non-Gaussian systems, in a Bayesian context. These filters incorporate the measurements in several steps, which is manifested in the form of the gradual update of particles states. Updates are performed by solving an ordinary differential equation, also called the flow equation. Several such equations have been derived, each based on distinct assumptions. Amongst others, the so called Exact flow has been more commonly used. It relies on approximating the prior density by a single multivariate Gaussian. In this paper we generalize this, and consider prior represented as a sum of Gaussian densities. We then derive particle flow equations and provide an implementation framework. We numerically show that the DHF based on our new flow outperforms the Exact flow based DHF, and achieves performance comparable to the bootstrap particle filter.