Robust Filtering for Linear Discrete-Time Systems with Parametric Uncertainties: A Krein Space Estimation Approach

A new unified robust filtering algorithm is proposed for discrete-time linear systems with uncertainties described by sum quadratic constraints. The proposed method extends the existing Krein space estimation theory to robust filtering problem. It is shown that the robust filtering problem can be cast into the minimization problem of an indefinite quadratic form. By interpreting the uncertainties as another noise sources, the Krein space approach converts the minimization problem into the generalization of the Krein space Kalman filtering problem with an additional condition. This approach can be applied to H₂ (Kalman) filtering problem and to H_∞ filtering problem as well. Moreover, the resulting robust filters have the similar recursive structures to various forms of the conventional Kalman filter, which makes the filters easy to design. Numerical examples verify the performances and the robustness of the proposed filters.