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

Sahani Pathiraja; Wilhelm Stannat

doi:10.3934/fods.2021023

Article Contents

2021, Volume 3, Issue 3: 615-645. Doi: 10.3934/fods.2021023 open access

This issue Previous Article A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation Next Article Stability of non-linear filter for deterministic dynamics

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

Sahani Pathiraja^1, , and
Wilhelm Stannat^2,3,

1.
University of Potsdam, Institute of Mathematics, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany
2.
TU Berlin, Institute of Mathematics, Str. des 17. Juni 136, D-10623 Berlin, Germany
3.
Bernstein Center for Computational Neuroscience, Philippstr. 13, 10115 Berlin, Germany

^* Corresponding author: Sahani Pathiraja
^* Corresponding author: Sahani Pathiraja

Received: March 2021

Revised: July 2021

Early access: September 2021

Published: September 2021

This research has been partially funded by the Deutsche Forschungsgemeinschaft (DFG)-Project-ID 318763901 - SFB1294.

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Abstract

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 are of interest in their own right. These are then used to establish a roadmap to obtaining well-posedness and convergence of the finite $ N $ system to its mean field limit. A number of possible future research directions are also discussed.

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Mathematics Subject Classification: 60H10, 35Q93, 35J05, 60J60, 60J27, 62M05.

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