Online Estimation of Colored Observation Noise Parameters within an Ensemble Kalman Filtering Framework

This work addresses the problem of data assimilation into large-dimensional systems with colored observation noise of unknown statistics, a scenario that will become more common in the near future with the deployment of denser observational networks of high spatio-temporal coverage. Here, we are interested in the ensemble Kalman filtering (EnKF) framework which has been derived around a white observation noise assumption. recently introduced colored observation noise-aware EnKFs in which the noise was modeled as a first-order autoregressive (AR) model. This work generalizes the above mentioned filters to further learn online the statistics of the AR model. We follow the state augmentation approach to first simultaneously estimate the state and the AR model transfer matrix, then the variational Bayesian approach to further estimate the AR model noise covariance parameters. We accordingly derive two filtering EnKF-like algorithms, which estimate those statistics together with the system state. We demonstrate the effectiveness of the proposed colored observation noise-aware filtering schemes, and compare their performances based on several numerical experiments conducted with the Lorenz-96 model.