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Proceedings Paper

Numerical experiments for nonlinear filters with exact particle flow induced by log-homotopy
Author(s): Fred Daum; Jim Huang
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Paper Abstract

We show numerical experiments on a new theory of exact particle flow for nonlinear filters. This generalizes our theory of particle flow that was already many orders of magnitude faster than standard particle filters and which is several orders of magnitude more accurate than the extended Kalman filter for difficult nonlinear problems. The new theory generalizes our recent log-homotopy particle flow filters in three ways: (1) the particle flow corresponds to the exact flow of the conditional probability density; (2) roughly speaking, the old theory was based on incompressible flow (like subsonic flight in air), whereas the new theory allows compressible flow (like supersonic flight in air); (3) the old theory suffers from obstruction of particle flow as well as singularities in the equations for flow, whereas the new theory has no obstructions and no singularities. Moreover, our basic filter theory is a radical departure from all other particle filters in three ways: (a) we do not use any proposal density; (b) we never resample; and (c) we compute Bayes' rule by particle flow rather than as a point wise multiplication.

Paper Details

Date Published: 15 April 2010
PDF: 15 pages
Proc. SPIE 7698, Signal and Data Processing of Small Targets 2010, 769816 (15 April 2010); doi: 10.1117/12.839299
Show Author Affiliations
Fred Daum, Raytheon (United States)
Jim Huang, Raytheon (United States)


Published in SPIE Proceedings Vol. 7698:
Signal and Data Processing of Small Targets 2010
Oliver E. Drummond, Editor(s)

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