# Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation

@article{Kelly2019ErgodicityAA, title={Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation}, author={David Kelly and Andrew M. Stuart}, journal={Chinese Annals of Mathematics, Series B}, year={2019} }

For particle filters and ensemble Kalman filters it is of practical importance to understand how and why data assimilation methods can be effective when used with a fixed small number of particles, since for many large-scale applications it is not practical to deploy algorithms close to the large particle limit asymptotic. In this paper we address this question for particle filters and, in particular, study their accuracy (in the small noise limit) and ergodicity (for noisy signal and…

## 4 Citations

Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem

- MathematicsArXiv
- 2017

The issue of non-uniqueness of the filter update formula is discussed, a novel approximation algorithm based on ideas from optimal transport and coupling of measures is formulates and performance of this and other algorithms is illustrated.

Performance Analysis of Local Ensemble Kalman Filter

- Environmental ScienceJ. Nonlinear Sci.
- 2018

This paper rigorously analyzes the local EnKF (LEnKF) for linear systems and shows that the filter error can be dominated by the ensemble covariance, as long as the sample size exceeds the logarithmic of state dimension and a constant depends only on the local radius.

Inverse Problems and Data Assimilation.

- Mathematics
- 2018

These notes are designed with the aim of providing a clear and concise introduction to the subjects of Inverse Problems and Data Assimilation, and their inter-relations, together with citations to…

Data Assimilation and Inverse Problems

- Mathematics
- 2018

It is demonstrated that methods developed in data assimilation may be employed to study generic inverse problems, by introducing an artificial time to generate a sequence of probability measures interpolating from the prior to the posterior.

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