A weighted likelihood criteria for learning importance densities in particle filtering

Selecting an optimal importance density and ensuring optimal particle weights are central challenges in particle-based filtering. In this paper, we provide a two-step procedure to learn importance densities for particle-based filtering. The first stage importance density is constructed based on ensemble Kalman filter kernels. This is followed by learning a second stage importance density via weighted likelihood criteria. The importance density is learned by fitting Gaussian mixture models to a set of particles and weights. The weighted likelihood learning criteria ensure that the second stage importance density is closer to the true filtered density, thereby improving the particle filtering procedure. Particle weights recalculated based on the latter density are shown to mitigate particle weight degeneracy as the filtering procedure propagates in time. We illustrate the proposed methodology on 2D and 3D nonlinear dynamical systems.