Small curvature particle flow for nonlinear filters

We derive seven new particle flow algorithms for nonlinear filters based on the small curvature condition inspired by fluid dynamics. We find it extremely interesting that this physically motivated condition generalizes two of our previous exact flow algorithms, namely incompressible flow and Gaussian flow. We derive a new algorithm to compute the inverse of the sum of two linear differential operators using a second homotopy, similar to Feynman's perturbation theory for quantum electrodynamics as well as Gromov's h-principle.