19 May 2006 Non-particle filters
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Abstract
We have developed a new nonlinear filter that is superior to particle filters in five ways: (1) it exploits smoothness; (2) it uses an exact solution of the Fokker-Planck equation in continuous time; (3) it uses an FFT to compute the effect of process noise at discrete times; (4) it uses the adjoint method to compute the optimal density of points in state space to represent the smooth conditional probability density, and (5) it uses Bayes' rule exactly by exploiting the exponential family of probability densities. In contrast to particle filters, which do not exploit smoothness, the new filter does not use importance sampling or Monte Carlo methods. The new non-particle filter should be superior to particle filters for a broad class of practical problems. In particular, the new filter should dramatically reduce the curse of dimensionality for many (but not all) important real world nonlinear filter problems.
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Fred Daum, Fred Daum, } "Non-particle filters", Proc. SPIE 6236, Signal and Data Processing of Small Targets 2006, 623614 (19 May 2006); doi: 10.1117/12.659732; https://doi.org/10.1117/12.659732
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