A fresh perspective on research for nonlinear filters

We give a fresh perspective on research for nonlinear filters with particle flow. Such research is an interesting mixture of theory and numerical experiments, as well as tradeoffs in filter implementation using GPUs and fast approximate k-NN algorithms, and fast approximate Poisson solvers. Our fundamental idea is to compute Bayes' rule using an ordinary differential equation ( ODE) rather than a pointwise multiplication; this solves the problem of particle degeneracy. Our filter is many orders of magnitude faster than standard particle filters for high dimensional problems, and it is several orders of magnitude more accurate than the EKF for difficult nonlinear problems, including problems with multimodal densities.