A Bayesian adaptive ensemble Kalman filter for sequential state and parameter estimation

TL;DR

This paper introduces a fully Bayesian adaptive ensemble Kalman filter that explicitly accounts for parameter uncertainty and combines information over time for improved sequential state and parameter estimation.

Contribution

It presents a novel Bayesian methodology with grid-based and Gaussian approximations for joint state and parameter estimation in ensemble Kalman filters.

Findings

Outperforms existing methods in simulated data scenarios

Effectively incorporates parameter uncertainty over time

Demonstrates applicability with real data

Abstract

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to implement the method we consider two representations of the marginal posterior distribution of the parameters: a grid-based approach and a Gaussian approximation. Contrary to existing algorithms, the new method explicitly accounts for parameter uncertainty and provides a formal way to combine information about the parameters from data at different time periods. The method is illustrated and compared to existing approaches using simulated and real data.