[p2] Parameter optimization


[p2-43]

An Extension of the Ensemble Kalman Filter for Estimating the Observation Error Covariance Matrix Based on the Variational Bayes Method

Akio Nakabayashi(SOKENDAI) and Genta Ueno (The Institute of Statistical Mathematics)

 
Abstract

We will present an extension of the ensemble Kalman filter (EnKF) that can simultaneously estimate the state vector and the observation error covariance matrix by using the variational Bayes (VB) method.
The EnKF is a method for estimating the posterior distribution for the state vector. By using the ensemble-approximated distribution and an update scheme resembling the Kalman filter (KF), the EnKF is remarkably adaptable to applications of high-dimensional systems, such as meteorological phenomena. The EnKF requires that the observation error covariance matrix is set prior to execution. It is known that a poor choice of the observation error covariance matrix can result in under- or overfitting. Therefore, the appropriate estimation of the observation error covariance matrix with the state vector in the filtering is our concern.
In numerical experiments, we examine the capability of our method for a time-variant observation error covariance matrix, and it is noteworthy that our method works well even when the true observation error covariance matrix is nondiagonal.