Analysis of the feedback particle filter with diffusion map based approximation of the gain

@article{Pathiraja2021AnalysisOT,
  title={Analysis of the feedback particle filter with diffusion map based approximation of the gain},
  author={Sahani Pathiraja and Wilhelm Stannat},
  journal={Foundations of Data Science},
  year={2021}
}
<p style='text-indent:20px;'>Control-type particle filters have been receiving increasing attention over the last decade as a means of obtaining sample based approximations to the sequential Bayesian filtering problem in the nonlinear setting. Here we analyse one such type, namely the feedback particle filter and a recently proposed approximation of the associated gain function based on diffusion maps. The key purpose is to provide analytic insights on the form of the approximate gain, which… 
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A McKean-Vlasov equation that contains the data stream as a common driving rough path is studied, establishing propagation of chaos for the associated interacting particle system, which is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework.

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