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 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.