11 May 2009 Nonlinear filters with particle flow induced by log-homotopy
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Abstract
We solve the fundamental and well known problem in particle filters, namely "particle collapse" or "particle degeneracy" as a result of Bayes' rule. We do not resample, and we do not use any proposal density; 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. We show numerical results for a new filter that is vastly superior to the classic particle filter and the extended Kalman filter. 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. Moreover, our new filter is two orders of magnitude more accurate than the extended Kalman filter for quadratic and cubic measurement nonlinearities. We also show excellent accuracy for problems with multimodal densities.
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Frederick Daum, Frederick Daum, Jim Huang, Jim Huang, "Nonlinear filters with particle flow induced by log-homotopy", Proc. SPIE 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII, 733603 (11 May 2009); doi: 10.1117/12.814241; https://doi.org/10.1117/12.814241
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