Renormalization group flow in k-space for nonlinear filters, Bayesian decisions and transport

We derive a new algorithm which avoids normalization of the probability density for particle flow. The algorithm was inspired by renormalization group flow in quantum field theory. In contrast with other particle flow algorithms, this one works in k-space rather than state space. We have roughly 30...

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Bibliographic Details
Published in:2015 18th International Conference on Information Fusion (Fusion) pp. 1617 - 1624
Main Authors: Daum, Fred, Jim Huang
Format: Conference Proceeding
Language:English
Published: ISIF 01.07.2015
Subjects:
Accuracy
Approximation methods
extended Kalman filter
Fourier transforms
Mathematical model
Monge-Kantorovich optimal transport
nonlinear filter
Nonlinear filters
particle filter
particle flow
transport problem
Weather forecasting
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Summary:We derive a new algorithm which avoids normalization of the probability density for particle flow. The algorithm was inspired by renormalization group flow in quantum field theory. In contrast with other particle flow algorithms, this one works in k-space rather than state space. We have roughly 30 or 40 algorithms to compute particle flow, and the three best algorithms avoid computing the normalization of the conditional probability density of the state. We explain why explicit normalization often spoils the flow. This phenomenon has been noticed by other researchers for completely different applications (e.g., weather prediction), but apparently the benefits of avoiding normalization are not well known.