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Abstract:
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The ensemble Kalman filter (EnKF) is a popular and highly successful technique for data assimilation in high-dimensional state-space models. The EnKF represents distributions of interest by an ensemble, which is a form of dimension reduction that enables straightforward forecasting even for complicated and expensive evolution models. However, the EnKF update step involves estimation of the large forecast covariance matrix based on an often small ensemble. Many existing regularization techniques rely on spatial localization, which may ignore long-range dependence. Instead, we propose regularization based on sparse inverse Cholesky factors, which shrinks the forecast covariance matrix toward a known class of covariance functions. Our approach is highly flexible and computationally scalable. In our numerical experiments, our approach was more accurate and less sensitive to misspecification of tuning parameters than tapering-based regularization
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