Abstract
A robust ensemble filtering scheme based on the H. filtering theory is proposed. The optimal H-infinity 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-infinity filter is more robust than the Kalman filter, in the sense that the estimation error in the H-infinity filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter.
The original form of the H-infinity filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H-infinity filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H-infinity filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are discussed. In particular, it is shown 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. Some numerical examples are used to assess the relative robustness of the TLHF EnTLHF in comparison with the corresponding KF-EnKF method.