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Coulomb's law particle flow for nonlinear filters

We have invented a new theory of exact particle flow for nonlinear filters. The flow of particles corresponding to Bayes' rule is computed from the gradient of the solution of Poisson's equation, and it is analogous to Coulomb's law. Our theory is a radical departure from other particle filters in several ways: (1) we compute Bayes' rule using a flow of particles rather than as a pointwise multiplication; (2) we never resample particles; (3) we do not use a proposal density; (4) we do not use importance sampling or any other MCMC algorithm; and (5) our filter is roughly 6 to 8 orders of magnitude faster than standard particle filters for the same accuracy.