Drift homotopy methods for a non-Gaussian filter

We present a novel approach for improving particle filters suited for a nonlinear and non-Gaussian environment. First, the non-Gaussian densities are approximated by a Gaussian mixture model. Next, we employ an approach based on drift homotopy for stochastic differential equations. Drift homotopy constructs a Markov Chain Monte Carlo step which is appended to the particle filter algorithm. This extra step moves the weighted samples closer to the associated observations while at the same time respecting the stochastic dynamics. The algorithm has been implemented in a non-Gaussian problem of diffusion in a double well potential.