Generalized particle flow for nonlinear filters

We generalize the theory of particle flow to stabilize the nonlinear filter. We have invented a new nonlinear filter that is vastly superior to the classic particle filter and the extended Kalman filter (EKF). In particular, the computational complexity of the new filter is many orders of magnitude less than the classic particle filter with optimal estimation accuracy for problems with dimension greater than 4. Our accuracy is typically several orders of magnitude better than the EKF for nonlinear problems. We do not resample, and we do not use any proposal density from an EKF or UKF or other filter. Moreover, our new algorithm is deterministic, and we do not use any MCMC methods; this is a radical departure from other particle filters. The new filter implements Bayes' rule using particle flow rather than with a pointwise multiplication of two functions; this avoids one of the fundamental and well known problems in particle filters, namely "particle degeneracy." In addition, we explicitly stabilize our particle filter using negative feedback, unlike standard particle filters, which are generally very inaccurate for plants with slow mixing or unstable dynamics. This stabilization improves performance by several orders of magnitude for difficult problems.

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