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16 April 2008 Particle flow for nonlinear filters with log-homotopy
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Abstract
We describe a new nonlinear filter that is vastly superior to the classic particle 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 2 or 3. We consider nonlinear estimation problems with dimensions varying from 1 to 20 that are smooth and fully coupled (i.e. dense not sparse). 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 collapse" as a result of Bayes' rule. We use a log-homotopy to derive the ODE that describes particle flow. This paper was written for normal engineers, who do not have homotopy for breakfast.
© (2008) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Fred Daum and Jim Huang "Particle flow for nonlinear filters with log-homotopy", Proc. SPIE 6969, Signal and Data Processing of Small Targets 2008, 696918 (16 April 2008); https://doi.org/10.1117/12.764909
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