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15 April 2010Generalized 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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Fred Daum, Jim Huang, "Generalized particle flow for nonlinear filters," Proc. SPIE 7698, Signal and Data Processing of Small Targets 2010, 76980I (15 April 2010); https://doi.org/10.1117/12.839421