Nonlinear Filters with Particle Flow

We have invented a new particle filter, which improves accuracy by several orders of magnitude compared with the extended Kalman filter for difficult nonlinear problems. Our filter runs many orders of magnitude faster than standard particle filters for problems with dimension higher than four. We do not resample particles, and we do not use any proposal density, which is a radical departure from other particle filters. We show very interesting movies of particle flow and many numerical results. The key idea is to compute Bayes’ rule using a flow of particles rather than as a point wise multiplication; this solves the well known problem of “particle degeneracy”. Our derivation is based on freshman calculus and physics. This talk is for normal engineers who do not have log-homotopy for breakfast.