23 May 2013 Particle flow with non-zero diffusion for nonlinear filters
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Abstract
We derive several new algorithms for particle flow with non-zero diffusion corresponding to Bayes’ rule. This is unlike all of our previous particle flows, which assumed zero diffusion for the flow corresponding to Bayes’ rule. We emphasize, however, that all of our particle flows have always assumed non-zero diffusion for the dynamical model of the evolution of the state vector in time. Our new algorithm is simple and fast, and it has an especially nice intuitive formula, which is the same as Newton’s method to solve the maximum likelihood estimation (MLE) problem (but for each particle rather than only the MLE), and it is also the same as the extended Kalman filter for the special case of Gaussian densities (but for each particle rather than just the point estimate). All of these new flows apply to arbitrary multimodal densities with smooth nowhere vanishing non-Gaussian densities.
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Fred Daum, Fred Daum, Jim Huang, Jim Huang, } "Particle flow with non-zero diffusion for nonlinear filters", Proc. SPIE 8745, Signal Processing, Sensor Fusion, and Target Recognition XXII, 87450P (23 May 2013); doi: 10.1117/12.2009363; https://doi.org/10.1117/12.2009363
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