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}
}
  • D. Kelly, A. Stuart
  • Published 26 November 2016
  • Environmental Science
  • Chinese Annals of Mathematics, Series B
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… 
Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem
TLDR
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
TLDR
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.
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
TLDR
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.

References

SHOWING 1-10 OF 82 REFERENCES
Can local particle filters beat the curse of dimensionality
TLDR
It is argued that it is often possible, at least in principle, to develop local particle filtering algorithms whose approximation error is dimension-free and the key to such developments is the decay of correlations property, which is a spatial counterpart of the much better understood stability property of nonlinear filters.
Nonlinear stability and ergodicity of ensemble based Kalman filters
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their
Performance Bounds for Particle Filters Using the Optimal Proposal
AbstractParticle filters may suffer from degeneracy of the particle weights. For the simplest “bootstrap” filter, it is known that avoiding degeneracy in large systems requires that the ensemble size
Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical
Robustness and Accuracy of finite Ensemble Kalman filters in large dimensions
Contemporary data assimilation often involves more than a million prediction vari- ables. Finite ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable
Particle approximations of the score and observed information matrix in state space models with application to parameter estimation
TLDR
This work presents two particle algorithms to compute the score vector and observed information matrix recursively in nonlinear non-Gaussian state space models and shows how both methods can be used to perform batch and recursive parameter estimation.
Nonlinear data assimilation in geosciences: an extremely efficient particle filter
Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical
Deterministic Mean-Field Ensemble Kalman Filtering
TLDR
A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule, which is therefore asymptotically superior to standard EnkF when the dimension $d<2\kappa$.
Optimality of the auxiliary particle filter
In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by Pitt and Shephard [17]. Besides establishing a central limit theorem
...
...