Robust Least-Squares Filtering With a Relative Entropy Constraint
نویسندگان
چکیده
We formulate a robust Wiener filtering problem for wide-sense stationary (WSS) Gaussian processes in the presence of modelling errors. It requires solving a minimax problem that consists of finding the best filter for the least-favorable statistical model within a neighborhood of the nominal model. The neighborhood is formed by models whose relative entropy with respect to the nominal model is less than a fixed constant. The standard noncausal Wiener filter is optimal, but the causal Wiener filter is not optimal, and a characterization is provided for the best filter and the corresponding least-favorable model.
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