New theory and numerical results for Gromov's method for stochastic particle flow filters

We derive a new exact stochastic particle flow for Bayes' rule using a theorem of Gromov. We also show numerical experiments for high dimensional problems up to d = 100. The accuracy of our new filter is many orders of magnitude better than standard particle filters, and our filter beats the EKF by orders of magnitude for difficult nonlinear problems. The new theoretical result is valid for arbitrary smooth nowhere vanishing densities, whereas our previous theory was derived for the special case of Gaussian densities with linear measurements. It is crucial to mitigate stiffness of the flow in order to achieve good numerical results.