Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter

Xiaodong Luo, Ibrahim Hoteit
2011 Monthly Weather Review  
We propose a robust ensemble filtering scheme based on the H_∞ filtering theory. The optimal H_∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H_∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H_∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case
more » ... corresponds to the Kalman filter. The original form of the H_∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore we introduce a variant that solves some time-local constraints instead, and hence we call it the time-local H_∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), we also propose the concept of ensemble time-local H_∞ filter (EnTLHF). We outline the general form of the EnTLHF, and discuss some of its special cases. In particular, we show that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. We use some numerical examples to assess the relative robustness of the TLHF/EnTLHF in comparison with the corresponding KF/EnKF method.
doi:10.1175/mwr-d-10-05068.1 fatcat:dasrhxft2zggvgn2rh7amouvje