25 September 2007 Nonlinear filters with log-homotopy
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Abstract
We derive and test a new nonlinear filter that implements Bayes' rule using an ODE 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 construct this ODE. Our new algorithm is vastly superior to the classic particle filter, and we do not use any proposal density supplied by an EKF or UKF or other outside source. This paper was written for normal engineers, who do not have homotopy for breakfast.
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Fred Daum, Jim Huang, "Nonlinear filters with log-homotopy", Proc. SPIE 6699, Signal and Data Processing of Small Targets 2007, 669918 (25 September 2007); doi: 10.1117/12.725684; https://doi.org/10.1117/12.725684
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